Inversion of the j--function and testing complex multiplication

2020/11/18 by J. V. Armitage, Armitage, John
Computer Science · Mathematics · #Cryptography and Residue Arithmetic #Algebraic Geometry and Number Theory #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2011.09405

Abstract

We develop an algorithm to invert the j--function in quasilinear time, and apply this to testing whether an elliptic curve has complex multiplication.

Related

• Complex Multiplication Tests for Elliptic Curves
• An Algorithm for Numerically Inverting the Modular j-function
• On the j-invariant and the Legendre Representation of Elliptic Curves\n with Complex Multiplication
• Observations on the "values" of the elliptic modular function j(tau) at real quadratics
• Computing isolated coefficients of the j-function