Genus two curves with full -level structure and Tate–Shafarevich groups
N Bruin, EV Flynn, A Shnidman - Selecta Mathematica, 2023 - Springer
We give an explicit rational parameterization of the surface H 3 over Q whose points
parameterize genus 2 curves C with full 3-level structure on their Jacobian J. We use this …
parameterize genus 2 curves C with full 3-level structure on their Jacobian J. We use this …
Arithmetic of totally split modular Jacobians and enumeration of isogeny classes of prime level simple modular Abelian varieties
K Lui - 2019 - digital.lib.washington.edu
In this thesis, we aim to give algorithms for computing two key invariants of the modular
Jacobians $ J_0 (N) $. We first give methods for computing the rational torsion order of rank …
Jacobians $ J_0 (N) $. We first give methods for computing the rational torsion order of rank …
Galois extensions and a conjecture of Ogg
K Klosin, M Papikian - Proceedings of the American Mathematical Society, 2020 - ams.org
Let $ N= pq $ be a product of two distinct primes. There is an isogeny $ J_0 (N)^\mathrm
{new}\to J^ N $ defined over $\mathbf {Q} $ between the new quotient $ J_0 (N) $ and the …
{new}\to J^ N $ defined over $\mathbf {Q} $ between the new quotient $ J_0 (N) $ and the …