1 citations · 1 across the 2 of their papers we have counts for
4 papers
New Rank Records For Elliptic Curves Having Rational Torsion
Noam D. Elkies, Zev Klagsbrun
We present rank-record breaking elliptic curves having torsion subgroups Z/2Z, Z/3Z, Z/4Z, Z/6Z, and Z/7Z.
On a local invariant of elliptic curves with a p-isogeny
Matthew Gealy, Zev Klagsbrun
An elliptic curve defined over a -adic field with a -isogeny comes equipped with an invariant that measures the valuation of the l…
On the Joint Distribution Of and in Quadratic Twist Families
Daniel Kane, Zev Klagsbrun
If is an elliptic curve with a point of order two, then work of Klagsbrun and Lemke Oliver shows that the distribution of $\dim_{\mathbb{F}_2}\mathrm{Sel}_ϕ(E^d/\mathbb{Q}) - \…
The Elkies Curve has Rank 28 Subject only to GRH
Zev Klagsbrun, Travis Sherman, James Weigandt
In 2006, Elkies presented an elliptic curve with 28 independent rational points. We prove that subject to GRH, this curve has Mordell-Weil rank equal to 28 and analytic rank at mos…