On genus one curves of degree 5 with square-free discriminant
Number Theory
2017-08-15 v1
Abstract
We study genus one curves of degree 5 defined by Pfaffians. We give new formulae for the invariants, and prove the equivalence of two different definitions of minimality. As an application we show that transformations between models with square-free discriminant are necessarily integral. This result is used by Bhargava and Shankar in their work on the average ranks of elliptic curves.
Keywords
Cite
@article{arxiv.1406.6953,
title = {On genus one curves of degree 5 with square-free discriminant},
author = {Tom Fisher and Mohammad Sadek},
journal= {arXiv preprint arXiv:1406.6953},
year = {2017}
}
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25 pages