Tetraelliptic modular curves X₁(N)

2023/05/10 by Jeon, Daeyeol · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2305.05851

Abstract

In this paper, we determine all tetraelliptic modular curves X₁(N) over \mathbb Q, and find some tetraelliptic maps ϕ_N from X₁(N) to elliptic curves for those tetraelliptic X₁(N). Also we will construct ϕ_N explicitly as rational functions. Moreover, we will show that all ϕ_N we found are Galois and find elliptic curves with torsion subgroup \mathbb Z/17\mathbb Z over cyclic quartic number fields by using the cyclic map ϕ₁₇.

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