Computing Isogenies at Singular Points of the Modular Polynomial

2024/02/03 by Mahaney, William E., Morrison, Travis
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.02038

Abstract

In this paper we present a method which, given a singular point (j₁, j₂) on Y₀(ℓ) with j₁, j₂ ≠ 0, 1728 and an elliptic curve E with j-invariant j₁, returns an elliptic curve \widetildeE with j-invariant j₂ that admits a normalized ℓ-isogeny ϕ\colon E→ \widetildeE. The isogeny ϕ can then be efficiently computed from E and \widetildeE using an algorithm of Bostan, Morain, Salvy, and Schost.

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