Solvability of small curves of genus 2

by Nils Bruin and Michael Stoll

Supporting data: files.zip (2.7Mb). Contains:

AllCurves.m (22Mb): Contains all square free polynomials of degree 5 or 6 with integer coordinates between -3 and 3, grouped by isomorphism classes of the curves y² = f (x) they define.
BSD-data.txt (13K): Lists the BSD data for the 47 curves with (conjectural) non-trivial SHA[2]
DescentObstruction.m (1007Kb): Contains all curves (up to isomorphism) that have no 2-covers with points everywhere locally.
LocalObstruction.m (976Kb): Contains all curves (up to isomorphism) that have a local obstruction to having a rational point.
MWSieve-rank*.m (1K-193K): For *=0,1,2,3,4 these files list the Mordell-Weil sieve data that proves that the curves have no rational points.
Solvable.m (4.4Mb): Contains all curves (up to isomorphism) with a rational point
Unres.m (46Kb): The remaining curves.

The files are in a machine-readable format for MAGMA. The data can easily be made readable for any other standard computer algebra system, usually by substituting Magma's particular delimiter symbols. For instance, in UNIX, one can use: cat file.m ¦ tr \<\{>\} \[\[\]\] > file.maple and some minimal editing of the files to make the files readable for, say, Maple.