On pairs of 17-congruent elliptic curves
Number Theory
2021-06-04 v1
Abstract
We compute explicit equations for the surfaces Z(17,1) and Z(17,3) parametrising pairs of -congruent elliptic curves. We find that each is a double cover of the same elliptic K3-surface. We use these equations to exhibit the first non-trivial example of a pair of symplectically 17-congruent elliptic curves over the rationals. We also compute the corresponding genus 2 curve whose Jacobian has a -splitting.
Keywords
Cite
@article{arxiv.2106.02033,
title = {On pairs of 17-congruent elliptic curves},
author = {Tom Fisher},
journal= {arXiv preprint arXiv:2106.02033},
year = {2021}
}
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24 pages