On Ito's observation on coefficients of the modular polynomial
type: Item
instance of: scholarly article
title: On Ito's observation on coefficients of the modular polynomial
zbMATH Open document ID: 0870.11023
author: Masanobu Kaneko
published in: Proceedings of the Japan Academy. Series A
publication date: 1996-12-01T00:00:00Z
review text: As a result of his extensive computation of the classical modular polynomial, \textit{H. Ito} [ibid. 71, 48-50 (1995; Zbl 0832.11017)] found interesting congruence properties among coefficients of the polynomial modulo the squares of a certain finite number of primes, and remarked that these primes are precisely the prime factors of the order of the simple group ``Monster''. In this note we give an explanation for his observation by employing the well-known fact that the set of primes in question is identical with the set of \(p\)'s with the proprty that all the \(j\)-invariants of supersingular elliptic curves in characteristic \(p\) belong to the prime field \(\mathbb{F}_p\).
Mathematics Subject Classification ID: 11F03
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 14H05
zbMATH DE Number: 952364
zbMATH Keywords: monster group
zbMATH Keywords: modular polynomial
zbMATH Keywords: coefficients
zbMATH Keywords: \(j\)-invariants of supersingular elliptic curves
MaRDI profile type: Publication
full work available at URL: pjaa.72.95
OpenAlex ID: W1995449121
cites work: Q4314331
cites work: \(p\)-adic cycles
cites work: Fibre Systems of Jacobian Varieties: (III. Fibre Systems of Elliptic Curves)
cites work: Q4049198
cites work: Computation of the modular equation
cites work: Q5670674
cites work: Q4104069
DOI: 10.3792/PJAA.72.95
description: scientific article; zbMATH DE number 952364