Computing the cardinality of CM elliptic curves using torsion points
| dc.creator | Morain, F. | |
| dc.date | 2002-10-11 | |
| dc.date | 2004-07-23 | |
| dc.date.accessioned | 2026-07-07T04:51:51Z | |
| dc.date.available | 2026-07-07T04:51:51Z | |
| dc.description | Let E be an elliptic curve having complex multiplication by a given quadratic order of an imaginary quadratic field K. The field of definition of E is the ring class field Omega of the order. If the prime p splits completely in Omega, then we can reduce E modulo one the factors of p and get a curve Ep defined over GF(p). The trace of the Frobenius of Ep is known up to sign and we need a fast way to find this sign. For this, we propose to use the action of the Frobenius on torsion points of small order built with class invariants a la Weber, in a manner reminiscent of the Schoof-Elkies-Atkin algorithm for computing the cardinality of a given elliptic curve modulo p. We apply our results to the Elliptic Curve Primality Proving algorithm (ECPP). | |
| dc.description | Revised and shortened version, including more material using discriminants of curves and division polynomials | |
| dc.identifier | https://arxiv.org/abs/math/0210173 | |
| dc.identifier | http://arxiv.org/abs/math/0210173 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65257 | |
| dc.subject | Number Theory | |
| dc.subject | 11G15, 11G20 | |
| dc.title | Computing the cardinality of CM elliptic curves using torsion points | |
| dc.type | text |