Completely decomposable modular Jacobians
Number Theory
2025-08-04 v2
Abstract
We use recently developed algorithms and a new database of modular curves constructed for the L-functions and Modular Forms Database to enumerate completely decomposable modular Jacobians of level N < 240. In particular, we find examples in 13 previously unknown genera of Jacobian varieties isogenous to a product of elliptic curves over Q. The new genera are: 38, 68, 75, 76, 77, 78, 113, 135, 137, 157, 159, 169, and 409.
Keywords
Cite
@article{arxiv.2502.16007,
title = {Completely decomposable modular Jacobians},
author = {Jennifer Paulhus and Andrew V. Sutherland},
journal= {arXiv preprint arXiv:2502.16007},
year = {2025}
}
Comments
6 pages