Journal of the Ramanujan Mathematical Society
Volume 31, Issue 4, December 2016 pp. 359–383.
On genus one curves of degree 5 with square-free discriminant
Authors:
Tom~Fisher and Mohammad~Sadek
Author institution:University of Cambridge, DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK
Summary:
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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