Completely decomposable modular Jacobians
Jennifer Paulhus, Andrew V. Sutherland
TL;DR
This paper employs advanced algorithms and a new database to identify modular Jacobians that are completely decomposable into elliptic curves, discovering new examples across multiple genera.
Contribution
It introduces a novel computational approach and database to enumerate completely decomposable modular Jacobians, revealing previously unknown genera over Q.
Findings
Identified 13 new genera with completely decomposable Jacobians
Found examples in genera 38, 68, 75, 76, 77, 78, 113, 135, 137, 157, 159, 169, 409
Expanded the known landscape of modular Jacobians decomposable into elliptic curves
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Nonlinear Waves and Solitons