2 citations · 2 across the 7 of their papers we have counts for
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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…
Uniform bounds on the level of cyclotomic division fields of elliptic curves
Sam Allen, Tyler Genao
In this paper, we prove that for each number field there exists a uniform bound on the prime levels of elliptic curves for which . Under the Generaliz…
A uniform bound on the smallest surjective prime of an elliptic curve
Tyler Genao, Jacob Mayle, Jeremy Rouse
Let be an elliptic curve without complex multiplication. A well-known theorem of Serre asserts that the -adic Galois representation is surj…
Uniform polynomial bounds on torsion from rational geometric isogeny classes
Abbey Bourdon, Tyler Genao
In 1996, Merel showed there exists a function such that for any elliptic curve defined over a number field of degree , one h…
New isogenies of elliptic curves over number fields
Tyler Genao
Using Galois representations, we analyze fields of definition of cyclic isogenies on elliptic curves to prove the following uniformity result: for any number field which has no…
Growth of torsion groups of elliptic curves upon base change from number fields
Tyler Genao
Given a number field that contains no Hilbert class field of any imaginary quadratic field, we show that under GRH there exists an effectively computable constant $B:=B(F_0)\…
Polynomial bounds on torsion from a fixed geometric isogeny class of elliptic curves
Tyler Genao
We show there exist polynomial bounds on torsion of elliptic curves which come from a fixed geometric isogeny class. More precisely, for an elliptic curve defined over a numb…