On genus one curves of degree 5 with square-free discriminant
T Fisher, M Sadek - arXiv preprint arXiv:1406.6953, 2014 - arxiv.org
T Fisher, M Sadek
arXiv preprint arXiv:1406.6953, 2014•arxiv.orgWe 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.
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.
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.
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