A Quartic Cover of 37a1 and Its Regular S4-Closure
Arithmetic geometry
gen2
arithmetic
submitted
For the conductor-37 elliptic curve, we carry out a complete explicit programme: constructing the regular S4-closure of a degree-4 map, decomposing the Jacobian via rational idempotents into a genus-2…
Journal of Number Theory Submitted 39 Theorems Arithmetic geometry
Abstract
For the conductor-37 elliptic curve, we carry out a complete explicit programme: constructing the regular S4-closure of a degree-4 map, decomposing the Jacobian via rational idempotents into a genus-2 Jacobian, a resolvent elliptic curve, and a Prym threefold.
Keywords: elliptic curves, Galois covers, Jacobian decomposition, Prym varieties, ray class fields
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