LinQuadChab

(Linear) quadratic Chabauty for integral points on even degree hyperelliptic curves

Code for the algorithms described in ``Linear Quadratic Chabauty'' by Stevan Gajović and Steffen Müller. References below are to this paper.

Main files

• LinQCQ.sage implements the linear quadratic Chabauty method described in Section 3 for the case of genus 2 curves over the rationals.
• LinQCRQF.sage implements the linear quadratic Chabauty method described in Section 4 for the case of genus 2 curves over real quadratic fields.
• ex1Q.sage checks the example in §4.4.
• ex1_qcrqnf.sage checks the example in §5.3.

Dependencies

You need Sage and Magma. Moreover, you need

• the file phts_hyp.sage from https://github.com/StevanGajovic/heights_above_p;
• Jennifer Balakrishnan's code for even degree Coleman integrals from from https://github.com/jbalakrishnan/AWS. Follow the instructions given there.
• the files JSearch.m, g2-jac.m and add.m from https://homepages.warwick.ac.uk/staff/S.Siksek/progs/chabnf/, due to Samir Siksek. In the file JSearch.m, you need to comment out lines 203 and line 261.

---