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arXiv · 2502.16007

Completely decomposable modular Jacobians

Jennifer Paulhus·Andrew V. Sutherland
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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.

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Jennifer Paulhus, Andrew V. Sutherland. 2025-02-21. Completely decomposable modular Jacobians. https://arxiv.org/abs/2502.16007

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