7 papers
Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves
Barinder S. Banwait, Xiaoyu Huang, Kyu-Hwan Lee +3
We investigate the extent to which the reduced minimal Weierstrass coefficients of an elliptic curve over may be computed from it's Frobenius traces. Decision tree mod…
On the Identification of Elliptic Curves That Admit Infinitely Many Twists Satisfying the Birch-Swinnerton-Dyer Conjecture
Barinder S. Banwait, Xiaoyu Huang
Recent work of Burungale-Skinner-Tian-Wan established the first infinite families of quadratic twists of non-CM elliptic curves over for which the strong Birch-Swinner…
A formal proof of the Ramanujan--Nagell theorem in Lean 4
Barinder S. Banwait
We present a complete formalization, in the Lean interactive theorem prover with the Mathlib library, of the Ramanujan--Nagell theorem: the only integer solutions to the Diophantin…
On the Visibility category of the Shafarevich--Tate group
Barinder S. Banwait, Jerson Caro, Shiva Chidambaram
Given an elliptic curve over $\Q$ and a nontrivial element of its Shafarevich--Tate group $\Sha(E)$, we introduce the \textbf{Visualization category} $\V(E; Ï)$ of abelia…
Cyclic isogenies of elliptic curves over fixed quadratic fields
Barinder S. Banwait, Filip Najman, Oana Padurariu
Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cyclic isogenies of elliptic curves over . Although more than 40 years ha…
Machine Learning Approaches to the Shafarevich-Tate Group of Elliptic Curves
Angelica Babei, Barinder S. Banwait, AJ Fong +2
We train machine learning models to predict the order of the Shafarevich-Tate group of an elliptic curve over . Building on earlier work of He, Lee, and Oliver, we show…