19 citations · 43 across the 14 of their papers we have counts for
15 papers
Second derivatives of -adic -functions and the Shafarevich--Tate group of rank-two CM elliptic curves
Barinder S. Banwait
For an elliptic curve of rank two with complex multiplication, Coates, Liang and Sujatha gave a criterion for the vanishing of at a goo…
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 coefficients of the reduced minimal Weierstrass model of an elliptic curve are determined by the Diric…
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} $\V(E; σ)$ of abelian…
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…
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…
Torsion subgroups of elliptic curves over quadratic fields and a conjecture of Granville
Barinder S. Banwait, Maarten Derickx
We study the problem of determining the groups that can arise as the torsion subgroup of an elliptic curve over a fixed quadratic field, building on work of Kamienny-Najman, Krumm,…
Towards strong uniformity for isogenies of prime degree
Barinder S. Banwait, Maarten Derickx
Let be an elliptic curve over a number field of degree that admits a -rational isogeny of prime degree . We study the question of finding a uniform bound on t…
Modularity over implies modularity over
Barinder S. Banwait
We give an account of Mazur's proof that, for an elliptic curve over , if it admits a nonconstant mapping from defined over the complex numbers , for…
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…
Explicit isogenies of prime degree over number fields
Barinder S. Banwait, Maarten Derickx
We provide an explicit and algorithmic version of a theorem of Momose classifying isogenies of prime degree of elliptic curves over number fields, which we implement in Sage and PA…
Explicit isogenies of prime degree over quadratic fields
Barinder S. Banwait
Let be a quadratic field which is not an imaginary quadratic field of class number one. We describe an algorithm to compute the primes for which there exists an elliptic cu…
Examples of abelian surfaces failing the local-global principle for isogenies
Barinder S Banwait
We provide examples of abelian surfaces over number fields whose reductions at almost all good primes possess an isogeny of prime degree rational over the residue field,…
Del Pezzo surfaces over finite fields and their Frobenius traces
Barinder Banwait, Francesc Fité, Daniel Loughran
Let be a smooth cubic surface over a finite field . It is known that for some . Serre has asked wh…
Tetrahedral Elliptic Curves and the local-global principle for Isogenies
Barinder Singh Banwait, John Cremona
We study the failure of a local-global principle for the existence of -isogenies for elliptic curves over number fields . Sutherland has shown that over there is…