Michael Stoll
Mathematisches Institut
Universität Bayreuth
95440 Bayreuth, Germany

Genus 2 Curves Data Files


The files in this directory contain data on genus 2 curves with small odd discriminant and small coefficients. All these curves have good reduction mod 2, and one can show that every curve with good reduction mod 2 has a model

y2 + h(x) y = f0(x) + 2 f(x) ,
where (h(x), f0(x)) is some pair in a list of 160 pairs of polynomials with 0-1-coefficients of degrees (≤3, ≤6), and f(x) is some polynomial with integral coefficients. The Magma code for producing the lists is given below.

curves-with-small-odd-discriminant.txt

This file contains all curves as above with f with coefficients bounded by 5 in absolute value and discriminant at most 114 (obtained by calling FindCurves(5, 11^4)). The curves are sorted

  1. by absolute value of the discriminant
  2. by their Euler factor at 2
  3. by isomorphism classes.
See the README file for more information.

small-curves-with-more-info.txt

This file contains the first bunch of curves (up to discriminant 4000), together with additional arithmetic information — Mordell-Weil rank, torsion subgroup, number of rational points, plus conductor and reduction types (up to disc. 1205; thanks to Qing Liu's genus2reduction program).

See the README file for the Magma code for the search.

Michael Stoll,  Dec 08, 2013