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This code verifies all computational claims made in the paper "Cubic and quartic points on modular curves using generalised symmetric Chabauty" by Josha Box, Stevan Gajovic and Pip Goodman.

Each file named "X0..." verifies all claims made about the relevant modular curve. They should be run with the files "ozmansiksek.m", "Qcurvetest.m" and either "Cubicsieve.m" or both "quarticsieve.m" and "X065quarticpts.m" in the same directory.

The calculations took the following time/memory when ran on the University of Bristol's CREAM cluster:

X053deg3.m - Total time: 695.470 seconds, Total memory usage: 270.72MB

X057deg3.m - Total time: 2317.210 seconds, Total memory usage: 260.22MB

X061deg3.m - Total time: 1103.970 seconds, Total memory usage: 309.50MB

X065deg4.m - Total time: 36980.750 seconds, Total memory usage: 911.34MB

X067deg3.m - Total time: 140788.739 seconds, Total memory usage: 20538.69MB

X073deg3.m - Total time: 12035.489 seconds, Total memory usage: 3592.66MB

About

A project started at the AWS 2020 to find cubic points on modular curves with infinitely many quadratic points. The main example is X_0(65).

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