Quadratic Points on Modular Curves
Number Theory
2018-08-16 v3
Abstract
In this paper we determine the quadratic points on the modular curves X_0(N), where the curve is non-hyperelliptic, the genus is 3, 4 or 5, and the Mordell--Weil group of J_0(N) is finite. The values of N are 34, 38, 42, 44, 45, 51, 52, 54, 55, 56, 63, 64, 72, 75, 81. As well as determining the non-cuspidal quadratic points, we give the j-invariants of the elliptic curves parametrized by those points, and determine if they have complex multiplication or are quadratic \Q-curves.
Cite
@article{arxiv.1806.08192,
title = {Quadratic Points on Modular Curves},
author = {Ekin Ozman and Samir Siksek},
journal= {arXiv preprint arXiv:1806.08192},
year = {2018}
}
Comments
Some improvements and corrections suggested by the referee are incorporated. Magma programs used to generate the data are now available with this arXiv version