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Authors
Affiliations
1 University of Cambridge, DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, GB
2 American University in Cairo, Mathematics and Actuarial Science Department, AUC Avenue, New Cairo, EG
Source
Journal of the Ramanujan Mathematical Society, Vol 31, No 4 (2016), Pagination: 359-383
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.