On the Average Number of 2-Selmer Elements of Elliptic Curves over with Two Marked Points
JA Thorne - Documenta Mathematica, 2019 - ems.press
We consider elliptic curves over global fields of positive characteristic with two distinct
marked non-trivial rational points. Restricting to a certain subfamily of the universal one, we …
marked non-trivial rational points. Restricting to a certain subfamily of the universal one, we …
Diagonals of rational functions: from differential algebra to effective algebraic geometry
We show that the results we had previously obtained on diagonals of 9-and 10-parameter
families of rational functions in three variables x, y, and z, using creative telescoping …
families of rational functions in three variables x, y, and z, using creative telescoping …
Counting models of genus one curves
M Sadek - … Proceedings of the Cambridge Philosophical Society, 2011 - cambridge.org
Let C be a soluble smooth genus one curve over a Henselian discrete valuation field. There
is a unique minimal Weierstrass equation defining C up to isomorphism. In this paper we …
is a unique minimal Weierstrass equation defining C up to isomorphism. In this paper we …
On genus one curves of degree 5 with square-free discriminant
T Fisher, M Sadek - arXiv preprint arXiv:1406.6953, 2014 - arxiv.org
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 …
invariants, and prove the equivalence of two different definitions of minimality. As an …