Two-cover descent on plane quartics with rational bitangents: electronic resources

routines.m: Magma file containing the code used to compute the electronic data. Example of its usage in Magma:

> Attach("routines.m");
> Process([-8,-29,7,-7,-24,3]);
[*
    [ -8, -29, 7, -7, -24, 3 ],
    294931966187744840908800000,
    {},
    0, 0, 10, true
*]

[ -8, -29, 7, -7, -24, 3 ]

Moduli point: it describes the seven points in the plane (1:0:0),(0:1:0),(0:0:1),(1,1,1),(-8:-7:1),(-29:-24:1),(7:3:1)

294931966187744840908800000

The square of this is the absolute value of the discriminant of the quartic model we compute.

{}

The set of primes at which this curve has local obstructions

0

The number of rational contact points of the bitangents

0

The size of the two-Selmer set

10

The rank of the two-Selmer group (or at least a lower bound on it)

true

A flag indicating whether the computation of the rank of the two-Selmer group resulted in the actual rank or only in a lower bound.

data6.txt: Data set A in the article. File with 81070 lines, each describing the output of Process called on the vectors with entries from [-6..6] describing data in general position.

data40.txt: Data set B in the article. File with 70000 lines, each describing the output of Process called on a vector with randomly chosen entries from [-40..40].