Bianchi's elliptic quintic curves and several modular function fields of level ten

2025/10/31 by Kaneko, Masanobu, Kuwata, Masato
#11F01 (Primary) 14H52 #11F03 #11G05 (Secondary) #11G30 #14H42 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.27395

Abstract

We provide an explicit description of two torsion points on the classical Bianchi elliptic quintic curve in terms of Ramanujan's functions. As a byproduct, we describe generators and defining equations of several modular function fields of level 10 using those functions.

Citations

• Computing algebraic Belyi functions on Bring's curve
• An algorithm for computing the Weierstrass normal form of hyperelliptic curves

Related

• Ogg's conjectures over function fields
• y-coordinates of elliptic curves
• Cubic theta functions and modular forms of level six
• Quasi-modular forms attached to elliptic curves, I
• Equations of Bielliptic Modular Curves