Publications (7)
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…
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 su…
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…
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 $Ï_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 $Ï_{E,l^{\infty}} \colon \Gal(\…
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 \[Ï_E \colon Gal(…