# <1 178 817 -274 16 1> <20> <-q> <-a>
(0, 1, -17, 289)
(0, 1, -2, 4)
(0, 1, -6, 36)
(0, 1, -9, 81)
(0, 1, 0, 0)
(0, 1, 4, 16)
(1, -11, 18, 3466)
(1, -17, 0, -2)
(1, -2, 0, -125)
(1, -2, 0, -52)
(1, -6, 0, -12)
(1, -8, 12, 104)
(1, -9, 0, -6)
(1, 0, 0, 7104)
(1, 11, 13, -351)
(1, 2, -4, -348)
(1, 2, -8, -321)
(1, 4, -6, -40)
(1, 4, 0, 40)
(1, 5, 2, 138)
(1, 6, -2, 32)
(1, 8, 10, -72)
(1, 8, 2, -24)
(1369, 10952, 21904, 236784)
(289, -4913, 0, -5470)
(4, -32, 48, 23557)
(4, -56, 36, 341)
(4, 16, 0, 197)
(49, -539, 882, 7190)
(5329, -21316, 21316, 291216)
(81, -729, 0, -2714)
(9, -54, 0, -425)
(9, 13, 10, 370)
(9, 144, -72, 1744)
(9, 18, -72, -188)
(9, 63, 9, 313)
# <21 116 171 128 55 12 1> <20> <-q> <-a>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -12, 17, -300)
(1, -2, -5, 64)
(1, -2, 3, -112)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -4, 5, -116)
(1, -6, -1, -24)
(1, -6, 7, -136)
(3, -14, 3, -117)
(3, -6, 1, -160)
(5, -14, 3, -232)
# <3 -1 2 5 -4 1 4> <20> <-q> <-a>
(0, 0, 16, 65)
(0, 1, -1, -7)
# <0 1 2 -1 3 1 1> <20> <-q> <-a>
(0, 0, 4, -11)
(0, 1, 0, 0)
# <1 2 -1 3 1 2> <20> <-q> <-a>
(0, 1, 0, 0)
(0, 2, 1, 1)
(1, -1, 2, 2)
(1, 0, 0, 2)
(1, 3, 10, 14)
(2, 0, 5, 4)
(2, 1, 0, 0)
(2, 1, 0, 48)
(2, 2, 1, -6)
(576, 576, 144, -1367)
# <1 178 817 -274 16 1> <60> <-q> <-a>
(0, 1, -17, 289)
(0, 1, -2, 4)
(0, 1, -6, 36)
(0, 1, -9, 81)
(0, 1, 0, 0)
(0, 1, 4, 16)
(0, 16, 100, 625)
(0, 81, 252, 784)
(1, -10, -28, -852)
(1, -11, 18, 3466)
(1, -13, -35, -831)
(1, -15, 54, 438)
(1, -17, 0, -2)
(1, -2, -24, -589)
(1, -2, 0, -125)
(1, -2, 0, -52)
(1, -27, 10, 110)
(1, -5, -36, -682)
(1, -6, -56, -460)
(1, -6, 0, -12)
(1, -8, 12, 104)
(1, -9, 0, -6)
(1, 0, 0, 7104)
(1, 11, 13, -351)
(1, 15, 24, -618)
(1, 2, -4, -348)
(1, 2, -8, -321)
(1, 22, -42, 1024)
(1, 30, -6, 48)
(1, 4, -6, -40)
(1, 4, 0, 40)
(1, 40, -12, 152)
(1, 5, -38, -162)
(1, 5, 2, 138)
(1, 6, -2, 32)
(1, 60, 54, 288)
(1, 8, 10, -72)
(1, 8, 2, -24)
(100, 1025, -850, -816)
(100489, -1205868, 3617604, 28204704)
(1369, 10952, 21904, 236784)
(16, 25, 6, 24364)
(169, -845, -6084, -32822)
(1764, 5488, 0, 84981)
(196, -192, 112, 9989)
(2304, 3328, 64, 166273)
(25, -475, 850, 46974)
(25, -50, -600, -2996)
(25, 41, 22, 1014)
(2500, 15625, 0, 70156)
(289, -4913, 0, -5470)
(36, 153, -450, 1000)
(4, -27, 15, 2985)
(4, -32, 48, 23557)
(4, -55, -44, -1812)
(4, -56, 36, 341)
(4, -7, -52, -3084)
(4, 16, 0, 197)
(4, 21, 7, 185)
(4, 232, -60, 37)
(4, 25, -6, 128)
(4, 25, 0, 116)
(4, 40, 132, 1013)
(4761, 5290, -29624, -2428268)
(484, 2057, -6050, -5568)
(49, -539, 882, 7190)
(5329, -21316, 21316, 291216)
(81, -729, 0, -2714)
(9, -135, 486, 710218)
(9, -171, 306, 2626)
(9, -54, 0, -425)
(9, 10, -56, -89)
(9, 13, 10, 370)
(9, 144, -72, 1744)
(9, 18, -72, -188)
(9, 28, 0, 600)
(9, 34, 10, 2176)
(9, 43, -12, 186)
(9, 63, 9, 313)
# <1 178 817 -274 16 1> <20> <-q>
(0, 1, -2, 4)
(0, 1, 0, 0)
(0, 1, 4, 16)
(1, -17, 0, -2)
(1, -6, 0, -12)
(1, -9, 0, -6)
# <21 116 171 128 55 12 1> <20> <-q>
(0, 0, 1, -19)
# <3 -1 2 5 -4 1 4> <20> <-q>
(0, 1, -1, -7)
# <0 1 2 -1 3 1 1> <20> <-q>
(0, 0, 4, -11)
(0, 1, 0, 0)
# <1 2 -1 3 1 2> <20> <-q>
(0, 1, 0, 0)
(0, 2, 1, 1)
(1, -1, 2, 2)
(1, 0, 0, 2)
(1, 3, 10, 14)
(2, 0, 5, 4)
(2, 1, 0, 0)
(2, 2, 1, -6)
# <1 178 817 -274 16 1> <200> <-q> <-1>
(0, 1, -9, 81)
# <2 0 0 0 0 0 3> <300> <-q> <-1>
(1, -1, -1, 4)
# <1 6 5 22 22 8 1> <200> <-q> <-f> <[%ld:%ld:%ld:%ld]> | cat; echo
[0:0:1:-6][1:-6:9:46][1:0:0:4][0:1:-3:20][0:1:-3:16][0:1:0:2][0:1:0:-2][9:-27:0:-14][1:-3:0:-2][3:-12:1:-6][3:-3:8:-30]
# <1 178 817 -274 16 1> <60> <-q> <-a> <-f> <<%ld|%ld|%ld|%ld>> | cat; echo
<100489|-1205868|3617604|28204704><5329|-21316|21316|291216><1|0|0|7104><1369|10952|21904|236784><0|1|-17|289><0|1|-9|81><0|1|-6|36><0|1|-2|4><0|1|0|0><0|1|4|16><0|16|100|625><0|81|252|784><1|-27|10|110><25|-475|850|46974><9|-171|306|2626><1|-17|0|-2><289|-4913|0|-5470><9|-135|486|710218><1|-15|54|438><4|-56|36|341><1|-13|-35|-831><1|-11|18|3466><49|-539|882|7190><1|-10|-28|-852><1|-9|0|-6><81|-729|0|-2714><4|-32|48|23557><1|-8|12|104><1|-6|-56|-460><1|-6|0|-12><9|-54|0|-425><169|-845|-6084|-32822><1|-5|-36|-682><25|-50|-600|-2996><1|-2|-24|-589><1|-2|0|-52><1|-2|0|-125><9|18|-72|-188><1|2|-8|-321><1|2|-4|-348><1|4|-6|-40><4|16|0|197><1|4|0|40><1|5|-38|-162><1|5|2|138><1|6|-2|32><9|63|9|313><1|8|2|-24><1|8|10|-72><4|40|132|1013><1|11|13|-351><1|15|24|-618><9|144|-72|1744><1|22|-42|1024><1|30|-6|48><1|40|-12|152><4|232|-60|37><1|60|54|288><4|-55|-44|-1812><4|-27|15|2985><4|-7|-52|-3084><36|153|-450|1000><484|2057|-6050|-5568><4|21|7|185><4|25|-6|128><4|25|0|116><2500|15625|0|70156><100|1025|-850|-816><9|10|-56|-89><4761|5290|-29624|-2428268><9|13|10|370><9|28|0|600><1764|5488|0|84981><9|34|10|2176><9|43|-12|186><16|25|6|24364><25|41|22|1014><2304|3328|64|166273><196|-192|112|9989>
# <1 178 817 -274 16 1> <100> <-q> <-f> <%ld,%ld,%ld,%ld;> | cat; echo
0,1,-9,81;0,1,-6,36;0,1,-2,4;0,1,0,0;0,1,4,16;1,-17,0,-2;1,-9,0,-6;1,-6,0,-12;1,-2,0,-52;1,4,-6,-40;1,4,0,40;1,6,-2,32;1,8,2,-24;1,8,10,-72;1,30,-6,48;9,10,-56,-89;9,70,4,76;
# <21 116 171 128 55 12 1> <100> <-q> <-n> <0> <-N> <0>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -2, -5, 64)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -6, -1, -24)
# <21 116 171 128 55 12 1> <100> <-q> <-N> <0>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -2, -5, 64)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -6, -1, -24)
# <21 116 171 128 55 12 1> <300> <-q> <-n> <0>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -12, 17, -300)
(1, -2, -5, 64)
(1, -2, 3, -112)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -4, 5, -116)
(1, -6, -1, -24)
(1, -6, 7, -136)
(3, -14, 3, -117)
(3, -6, 1, -160)
(5, -14, 3, -232)
(5, -58, 15, -176)
(7, -4, -41, 268)
(8, -19, -30, 190)
# <21 116 171 128 55 12 1> <300> <-q> <-n> <2>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -12, 17, -300)
(1, -2, -5, 64)
(1, -2, 3, -112)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -4, 5, -116)
(1, -6, -1, -24)
(1, -6, 7, -136)
(3, -14, 3, -117)
(3, -6, 1, -160)
(5, -14, 3, -232)
(5, -58, 15, -176)
(7, -4, -41, 268)
(8, -19, -30, 190)
# <21 116 171 128 55 12 1> <300> <-q> <-n> <8> <-N> <5>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -12, 17, -300)
(1, -2, -5, 64)
(1, -2, 3, -112)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -4, 5, -116)
(1, -6, -1, -24)
(1, -6, 7, -136)
(3, -14, 3, -117)
(3, -6, 1, -160)
(5, -14, 3, -232)
(5, -58, 15, -176)
(7, -4, -41, 268)
(8, -19, -30, 190)
# <21 116 171 128 55 12 1> <300> <-q> <-n> <3> <-N> <30> <-p> <30>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -12, 17, -300)
(1, -2, -5, 64)
(1, -2, 3, -112)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -4, 5, -116)
(1, -6, -1, -24)
(1, -6, 7, -136)
(3, -14, 3, -117)
(3, -6, 1, -160)
(5, -14, 3, -232)
(5, -58, 15, -176)
(7, -4, -41, 268)
(8, -19, -30, 190)
# <21 116 171 128 55 12 1> <100> <-q> <-p> <3>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -2, -5, 64)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -6, -1, -24)
# <21 116 171 128 55 12 1> <300> <-q> <-n> <25> <-p> <10>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -12, 17, -300)
(1, -2, -5, 64)
(1, -2, 3, -112)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -4, 5, -116)
(1, -6, -1, -24)
(1, -6, 7, -136)
(3, -14, 3, -117)
(3, -6, 1, -160)
(5, -14, 3, -232)
(5, -58, 15, -176)
(7, -4, -41, 268)
(8, -19, -30, 190)
# <21 116 171 128 55 12 1> <300> <-q> <-M> <6>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -12, 17, -300)
(1, -2, -5, 64)
(1, -2, 3, -112)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -4, 5, -116)
(1, -6, -1, -24)
(1, -6, 7, -136)
(3, -14, 3, -117)
(3, -6, 1, -160)
(5, -14, 3, -232)
(5, -58, 15, -176)
(7, -4, -41, 268)
(8, -19, -30, 190)
# <21 116 171 128 55 12 1> <300> <-q> <-n> <2> <-M> <4> <-N> <4>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -12, 17, -300)
(1, -2, -5, 64)
(1, -2, 3, -112)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -4, 5, -116)
(1, -6, -1, -24)
(1, -6, 7, -136)
(3, -14, 3, -117)
(3, -6, 1, -160)
(5, -14, 3, -232)
(5, -58, 15, -176)
(7, -4, -41, 268)
(8, -19, -30, 190)
# <1 178 817 -274 16 1> <4500> <-q> <-s> <1>
(0, 1, -17, 289)
(0, 1, -2, 4)
(0, 1, -6, 36)
(0, 1, -9, 81)
(0, 1, 0, 0)
(0, 1, 4, 16)
(0, 16, 100, 625)
(0, 81, 252, 784)
(1, -10, -28, -852)
(1, -11, 18, 3466)
(1, -13, -35, -831)
(1, -13, -68, -402)
(1, -15, 54, 438)
(1, -17, 0, -2)
(1, -18, -104, -628)
(1, -18, -150, -720)
(1, -2, -24, -589)
(1, -2, 0, -125)
(1, -2, 0, -52)
(1, -2, 186, 1456)
(1, -22, -128, -801)
(1, -27, 10, 110)
(1, -5, -36, -682)
(1, -6, -56, -460)
(1, -6, 0, -12)
(1, -7, -418, 3594)
(1, -8, 12, 104)
(1, -8, 132, 1048)
(1, -9, 0, -6)
(1, 11, 13, -351)
(1, 12, -644, 512)
(1, 15, 24, -618)
(1, 16, 72, 496)
(1, 191, 17, -159)
(1, 2, -4, -348)
(1, 2, -8, -321)
(1, 22, -42, 1024)
(1, 247, 240, 874)
(1, 30, -6, 48)
(1, 330, 640, 2399)
(1, 35, 148, 762)
(1, 3734, 200, 435)
(1, 39, 153, 825)
(1, 4, -6, -40)
(1, 4, 0, 40)
(1, 40, -12, 152)
(1, 5, -38, -162)
(1, 5, 2, 138)
(1, 52, 222, 304)
(1, 6, -2, 32)
(1, 60, 54, 288)
(1, 67, 285, 449)
(1, 688, 30, 160)
(1, 79, 129, 625)
(1, 8, 10, -72)
(1, 8, 2, -24)
(1, 816, 190, -544)
(1, 82, -54, -128)
(1, 93, 570, 3558)
(100, 1025, -850, -816)
(100, 624, -128, 2861)
(121, -1040, -90, 784)
(121, -1821, -60, 258)
(121, -574, -52, 804)
(121, 1046, 8, 1659)
(121, 1208, 110, -2112)
(121, 202, -1188, -3916)
(144, -2655, -612, -3128)
(16, -335, 66, 1052)
(16, -415, 143, 2217)
(16, 113, 56, 696)
(16, 129, -62, 236)
(16, 185, 8, -168)
(16, 401, -98, 396)
(16, 57, -282, 684)
(16, 673, -270, -292)
(16, 89, -65, 465)
(16, 945, 3556, -3208)
(169, 1174, 240, 1244)
(169, 2375, 8, 3702)
(169, 950, -598, 4368)
(196, -159, -32, -2428)
(25, -129, -776, -4114)
(25, -166, -592, -3084)
(25, -50, -600, -2996)
(25, -676, 164, 2064)
(25, 114, -24, 519)
(25, 119, -56, 234)
(25, 121, 6, 886)
(25, 134, -130, 480)
(25, 1371, 205, -3535)
(25, 169, -66, 514)
(25, 284, 574, 3504)
(25, 41, 22, 1014)
(25, 459, 1701, -951)
(25, 601, -138, 2054)
(25, 631, 2577, 4049)
(25, 736, 3006, 256)
(289, -2036, -438, 1976)
(36, 153, -450, 1000)
(36, 289, 268, 2260)
(36, 865, -314, 184)
(361, -3105, -39, -183)
(361, 1635, -1211, -2407)
(4, -11, -225, -551)
(4, -27, 15, 2985)
(4, -39, -858, 4080)
(4, -55, -44, -1812)
(4, -56, 36, 341)
(4, -7, -52, -3084)
(4, -79, -670, -3048)
(4, 1, -150, -200)
(4, 153, -110, -280)
(4, 1593, -3782, -2584)
(4, 16, 0, 197)
(4, 21, 7, 185)
(4, 225, 24, -444)
(4, 232, -60, 37)
(4, 25, -6, 128)
(4, 25, 0, 116)
(4, 369, -138, -192)
(4, 40, 132, 1013)
(4, 41, 100, -1428)
(4, 49, 120, -3236)
(4, 645, -801, -1719)
(4, 721, 2496, 2180)
(4, 73, 24, -652)
(4, 77, -17, 129)
(49, -1046, -12, -76)
(49, -19, 170, 2550)
(49, 1149, -230, 2486)
(49, 176, -800, 480)
(49, 186, -264, -3660)
(49, 219, -75, 9)
(49, 235, -84, 518)
(49, 380, 322, -3192)
(49, 410, -122, 1152)
(529, -412, -206, 3048)
(64, -127, -352, -528)
(64, 313, -630, 3700)
(64, 3217, -1542, -2764)
(81, -1188, -234, -608)
(81, -729, 0, -2714)
(81, 1510, -458, 1408)
(81, 16, 160, 3616)
(81, 175, -111, 1377)
(81, 187, -332, 274)
(81, 445, 138, 4122)
(81, 544, 118, 2896)
(9, -125, -476, -2894)
(9, -135, -1458, -3182)
(9, -171, 306, 2626)
(9, -221, -20, -506)
(9, -224, -138, -2256)
(9, -230, 54, 768)
(9, -236, 172, 3088)
(9, -26, -120, -501)
(9, -26, -168, -789)
(9, -41, -455, -2999)
(9, -54, 0, -425)
(9, 10, -56, -89)
(9, 10, -80, -4169)
(9, 106, -378, -1536)
(9, 115, 21, 393)
(9, 1219, 37, -647)
(9, 13, 10, 370)
(9, 144, -72, 1744)
(9, 1723, 588, -3714)
(9, 18, -72, -188)
(9, 28, 0, 600)
(9, 34, -138, -192)
(9, 34, 10, 2176)
(9, 43, -12, 186)
(9, 63, 9, 313)
(9, 70, 4, 76)
(9, 76, -188, -656)
(9, 76, 30, -528)
(9, 94, 0, 204)
# <1 6 5 22 22 8 0> <100> <-q>
(0, 1, 0, 0)
(0, 1, 1, 8)
(1, 0, 0, 4)
(1, 1, 0, -8)
(1, 1, 0, 24)
(18, -2, 11, -58)
(4, -7, 6, 16)
(4, -9, 17, 16)
(4, 57, -10, 16)
# <0 0 0 0 0 0 0> <100>

The polynomial must have degree at least 5.

#

Usage: j-points 'a_0 a_1 ... a_d' max_height
                [-n num_primes1] [-M num_primes2] [-N num_primes3]
                [-p num_primes] [-s size] [-t threads] [-f format]
                [-w bound4] [-c constants] [-1] [-q] [-a]
# <1 2 3 4 5> <100>

The polynomial must have degree at least 5.

# <1 2 3 4 5 6 7 8> <100>

Too many coefficients.

# <1 2 3 4 5 6 7> <0>

Incorrect height argument.
  Height must be in [1, 3037000499].

# <1 2 3 4 5 6 7> <3037000500>

Incorrect height argument.
  Height must be in [1, 3037000499].

# <1 2 3 4 5 6 7> <100> <-x>

Wrong syntax for optional arguments:


Usage: j-points 'a_0 a_1 ... a_d' max_height
                [-n num_primes1] [-M num_primes2] [-N num_primes3]
                [-p num_primes] [-s size] [-t threads] [-f format]
                [-w bound4] [-c constants] [-1] [-q] [-a]
# <1 2 3 4 5 6 7> <100> <-n>

Wrong syntax for optional arguments:


Usage: j-points 'a_0 a_1 ... a_d' max_height
                [-n num_primes1] [-M num_primes2] [-N num_primes3]
                [-p num_primes] [-s size] [-t threads] [-f format]
                [-w bound4] [-c constants] [-1] [-q] [-a]
# <1 2 3 4 5 6 7> <100> <-p> <0>

Wrong syntax for optional arguments:


Usage: j-points 'a_0 a_1 ... a_d' max_height
                [-n num_primes1] [-M num_primes2] [-N num_primes3]
                [-p num_primes] [-s size] [-t threads] [-f format]
                [-w bound4] [-c constants] [-1] [-q] [-a]
# <1 2 3 4 5 6 7> <100> <-s> <0>

Wrong syntax for optional arguments:


Usage: j-points 'a_0 a_1 ... a_d' max_height
                [-n num_primes1] [-M num_primes2] [-N num_primes3]
                [-p num_primes] [-s size] [-t threads] [-f format]
                [-w bound4] [-c constants] [-1] [-q] [-a]
# <21 116 171 128 55 12 1> <100> <-n> <3> <-M> <6> <-N> <9> <-c> <AND=0.63,SIZE=756,TEST2=5.6,TTEST=2> | grep -v '^This is j-points'


Please acknowledge use of the program in published work.


y^2 = x^6 + 12 x^5 + 55 x^4 + 128 x^3 + 171 x^2 + 116 x + 21

max. Height = 100
Sieving in the tube of the bound on the fourth coordinate:
about 3.38 words per row, 0.12 cells of the analysis per row.
0 primes used for the first stage of sieving,
6 primes used for the first two stages together,
9 primes used for all three stages together.
Constants of the cost model set by -c: AND=0.63 SIZE=756 TEST2=5.6 TTEST=2
Sieving primes:
 First stage: 
 Second stage: 13, 7, 23, 17, 19, 11
 Third stage: 59, 61, 41
Probabilities: Min(181) = 0.349499, Cut2(11) = 0.571751, Cut3(41) = 0.392348, Max(3) = 0.925926

(0, 0, 1, -19)
(1, -4, 4, -91)
(0, 1, -2, 38)
(0, 1, -2, 26)
(1, -6, -1, -24)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -2, -5, 64)

64586 candidates survived the first stage,
48082 candidates survived the second stage,
2528 candidates survived the third stage.

Found 8 rational points on K lifting to J.
# <2 0 5 0 4 0 1> <100>

The polynomial must be squarefree.

# <1 178 817 -274 16 1> <60> <-q> <-f> <<%ld:%ld:%ld:%ld>\t\\\n> | cat; echo
<0:1:-6:36>	\
<0:1:-2:4>	\
<0:1:0:0>	\
<0:1:4:16>	\
<1:-17:0:-2>	\
<1:-9:0:-6>	\
<1:-6:0:-12>	\
<1:-2:0:-52>	\
<1:4:-6:-40>	\
<1:4:0:40>	\
<1:6:-2:32>	\
<1:8:2:-24>	\
<1:30:-6:48>	\

# <21 116 171 128 55 12 1> <60> <-q> <-w> <20>
(0, 0, 1, -19)
# <21 116 171 128 55 12 1> <20> <-q> <-w> <500>
(0, 0, 1, -19)
(0, 1, -2, 26)
(0, 1, -2, 38)
(1, -12, 17, -300)
(1, -2, -5, 64)
(1, -2, 3, -112)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -4, 4, -91)
(1, -4, 5, -116)
(1, -6, -1, -24)
(1, -6, 7, -136)
(3, -14, 3, -117)
(3, -6, 1, -160)
(5, -14, 3, -232)
# <1 178 817 -274 16 1> <60> <-q> <-a> <-w> <100000>
(0, 1, -17, 289)
(0, 1, -2, 4)
(0, 1, -6, 36)
(0, 1, -9, 81)
(0, 1, 0, 0)
(0, 1, 4, 16)
(0, 16, 100, 625)
(0, 81, 252, 784)
(1, -10, -28, -852)
(1, -11, 18, 3466)
(1, -13, -35, -831)
(1, -15, 54, 438)
(1, -17, 0, -2)
(1, -2, -24, -589)
(1, -2, 0, -125)
(1, -2, 0, -52)
(1, -27, 10, 110)
(1, -5, -36, -682)
(1, -6, -56, -460)
(1, -6, 0, -12)
(1, -8, 12, 104)
(1, -9, 0, -6)
(1, 0, 0, 7104)
(1, 11, 13, -351)
(1, 15, 24, -618)
(1, 2, -4, -348)
(1, 2, -8, -321)
(1, 22, -42, 1024)
(1, 30, -6, 48)
(1, 4, -6, -40)
(1, 4, 0, 40)
(1, 40, -12, 152)
(1, 5, -38, -162)
(1, 5, 2, 138)
(1, 6, -2, 32)
(1, 60, 54, 288)
(1, 8, 10, -72)
(1, 8, 2, -24)
(100, 1025, -850, -816)
(16, 25, 6, 24364)
(169, -845, -6084, -32822)
(1764, 5488, 0, 84981)
(196, -192, 112, 9989)
(25, -475, 850, 46974)
(25, -50, -600, -2996)
(25, 41, 22, 1014)
(2500, 15625, 0, 70156)
(289, -4913, 0, -5470)
(36, 153, -450, 1000)
(4, -27, 15, 2985)
(4, -32, 48, 23557)
(4, -55, -44, -1812)
(4, -56, 36, 341)
(4, -7, -52, -3084)
(4, 16, 0, 197)
(4, 21, 7, 185)
(4, 232, -60, 37)
(4, 25, -6, 128)
(4, 25, 0, 116)
(4, 40, 132, 1013)
(484, 2057, -6050, -5568)
(49, -539, 882, 7190)
(81, -729, 0, -2714)
(9, -171, 306, 2626)
(9, -54, 0, -425)
(9, 10, -56, -89)
(9, 13, 10, 370)
(9, 144, -72, 1744)
(9, 18, -72, -188)
(9, 28, 0, 600)
(9, 34, 10, 2176)
(9, 43, -12, 186)
(9, 63, 9, 313)
# <21 116 171 128 55 12 1> <100> <-w> <50> <-n> <3> <-M> <6> <-N> <9> <-c> <AND=0.63,SIZE=756,TEST2=5.6,TTEST=2> | grep -v '^This is j-points'


Please acknowledge use of the program in published work.


y^2 = x^6 + 12 x^5 + 55 x^4 + 128 x^3 + 171 x^2 + 116 x + 21

max. Height = 100
Bound on the fourth coordinate = 50
Sieving in the tube of the bound on the fourth coordinate:
about 3.38 words per row, 0.12 cells of the analysis per row.
0 primes used for the first stage of sieving,
6 primes used for the first two stages together,
9 primes used for all three stages together.
Constants of the cost model set by -c: AND=0.63 SIZE=756 TEST2=5.6 TTEST=2
Sieving primes:
 First stage: 
 Second stage: 13, 7, 23, 17, 19, 11
 Third stage: 59, 61, 41
Probabilities: Min(181) = 0.349499, Cut2(11) = 0.571751, Cut3(41) = 0.392348, Max(3) = 0.925926

(0, 0, 1, -19)
(0, 1, -2, 38)
(0, 1, -2, 26)
(1, -6, -1, -24)
(1, -4, -3, 28)
(1, -4, 1, -44)

64385 candidates survived the first stage,
47969 candidates survived the second stage,
2522 candidates survived the third stage.

Found 6 rational points on K lifting to J.
# <0 -1 2 -1 3 1 1> <100> <-n> <3> <-M> <6> <-N> <9> <-c> <AND=0.63,SIZE=756,TEST2=5.6,TTEST=2> | grep -v '^This is j-points'


Please acknowledge use of the program in published work.


y^2 = x^6 + x^5 + 3 x^4 - x^3 + 2 x^2 - x

max. Height = 100
The search runs on y^2 = x^5 + 2 x^4 + x^3 + 3 x^2 - x + 1
(the curve under x -> 1/x and x -> -x), a monic quintic, and the points are
transformed back.

Sieving in the tube of the bound on the fourth coordinate:
about 3.87 words per row, 0.12 cells of the analysis per row.
0 primes used for the first stage of sieving,
6 primes used for the first two stages together,
9 primes used for all three stages together.
Constants of the cost model set by -c: AND=0.63 SIZE=756 TEST2=5.6 TTEST=2
Sieving primes:
 First stage: 
 Second stage: 5, 11, 13, 7, 17, 3
 Third stage: 37, 53, 23
Probabilities: Min(163) = 0.336737, Cut2(3) = 0.777778, Cut3(23) = 0.370757, Max(3) = 0.777778

(0, 0, 4, -11)
(0, 1, 0, 0)

7787 candidates survived the first stage,
6645 candidates survived the second stage,
297 candidates survived the third stage.

Found 2 rational points on K lifting to J.
# <0 -1 2 -1 3 1 1> <60> <-q> <-a>
(0, 0, 4, -11)
(0, 1, 0, 0)
# <0 -1 2 -1 3 1 1> <300> <-q> <-1>
(0, 0, 4, -11)
# <21 116 171 128 55 12 1> <100> <-c> <FOO=1>

The argument of -c must be NAME=value, or several of them separated
by commas, with a positive value and one of the names
 AND SIZE WORD TEST2 BIT ROW3 TEST3 EXACT ROW CELL TWORD TTEST TROW RROW REXCL RCUT RANGE PASS TABLE INIT.

# <21 116 171 128 55 12 1> <100> <-c> <CELL=1e6,AND=0.45,SIZE=756,TEST2=5.6,TTEST=2> | grep -v '^This is j-points'


Please acknowledge use of the program in published work.


y^2 = x^6 + 12 x^5 + 55 x^4 + 128 x^3 + 171 x^2 + 116 x + 21

max. Height = 100
11 primes used for the first stage of sieving,
11 primes used for the first two stages together,
15 primes used for all three stages together.
Constants of the cost model set by -c: AND=0.45 SIZE=756 TEST2=5.6 CELL=1e+06 TTEST=2
Sieving primes:
 First stage: 7, 13, 11, 5, 17, 19, 23, 29, 3, 31, 37
 Second stage: 
 Third stage: 59, 61, 41, 53
Probabilities: Min(181) = 0.349499, Cut1(37) = 0.457011, Cut3(53) = 0.406221, Max(3) = 0.925926

(0, 0, 1, -19)
(1, -4, 4, -91)
(0, 1, -2, 38)
(0, 1, -2, 26)
(1, -6, -1, -24)
(1, -4, -3, 28)
(1, -4, 1, -44)
(1, -2, -5, 64)

3451 candidates survived the first stage,
3633 candidates survived the second stage,
108 candidates survived the third stage.

Found 8 rational points on K lifting to J.
