Counting elliptic curves with prescribed torsion over imaginary quadratic fields
Allechar Serrano López (University of Utah)
Abstract: A generalization of Mazur's theorem, proved by Kamienny, states that there are 26 possibilities for the torsion subgroup of an elliptic curve over quadratic extensions of the rational numbers. We prove that if $G$ is isomorphic to one of these subgroups then the elliptic curves up to height $X$ whose torsion is isomorphic to $G$ is on the order of $X^{\frac{1}{d}}$ where $d>1$.
number theory
Audience: researchers in the discipline
POINT: New Developments in Number Theory
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Organizers: | Jessica Fintzen*, Karol Koziol*, Joshua Males*, Aaron Pollack, Manami Roy*, Soumya Sankar*, Ananth Shankar*, Vaidehee Thatte*, Charlotte Ure* |
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