2 citations · 2 across the 7 of their papers we have counts for
7 papers
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…