Explicit moduli spaces for congruences of elliptic curves

2018/04/26 by Fisher, Tom · 1 citation
#11F80 #11G05 #14J27 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1804.10195

Abstract

We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil lattice and the geometric Picard number.

Cited by

• Determining the rational points on a curve of genus 2 and Mordell-Weil rank 1

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• Congruences of elliptic curves arising from non-surjective mod N Galois representations
• Some explicit elliptic modular surfaces
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• Elliptic Surfaces
• On families of 13-congruent elliptic curves