2 citations · 2 across the 7 of their papers we have counts for
8 papers · 1 filter
Congruence obstructions in the refined Koblitz conjecture
Sung Min Lee, Jacob Mayle, Rakvi
Let be an elliptic curve. Zywina's refinement of Koblitz's conjecture predicts that there are infinitely many primes of good reduction for which $\#E_p(\mathbb{F…
The possible adelic indices for elliptic curves admitting a rational cyclic isogeny
Kate Finnerty, Tyler Genao, Jacob Mayle +1
In the 1970s, Serre proved that the adelic index of a non-CM elliptic curve over a number field is finite. More recently, Zywina conjectured the complete set of adelic indices for…
Modular curves of prime-power level with infinitely many quadratic points
Michael Cerchia, Rakvi
We completely determine the open subgroups of of prime-power level that satisfy and $\operatorname{det}(H)=\wideha…
On Possible Genus 0 adelic Galois Images of non CM Elliptic Curves over
Rakvi
Let be an elliptic curve defined over / Associated to , there is an adelic Galois representation $ρ_E \colon {\rm Gal}(\bar{\mathbb{Q}}/\mathbb{Q}) \to {\rm GL}_…
On possibilities of 3-adic Galois images associated to isogeny-torsion graphs
Rakvi
Let be a non CM elliptic curve defined over $\Q$. There is an isogeny-torsion graph associated to and there is also a Galois representation $ρ_{E,l^{\infty}} \colon \Gal(\Q…
Serre curves relative to obstructions modulo 2
Jacob Mayle, Rakvi
We consider elliptic curves for which the image of the adelic Galois representation is as large as possible given a constraint on the image modulo 2. For suc…
Genus Modular curves of prime power level with a point defined over number fields other than $\Q$
Rakvi
Associated to an open subgroup of $\GL_2(\Zhat)$ satisfying conditions and $\det(G) \subsetneq (\Zhat)^{\times}$ there is a modular curve which is a smooth com…
A Classification of Genus 0 Modular Curves with Rational Points
Rakvi
Let be a non-CM elliptic curve defined over . Fix an algebraic closure of . We get a Galois representation \[ρ_E \colon Gal(\…