isogeny
Let and be elliptic curves over a field . An isogeny between and is a finite morphism of varieties that preserves basepoints.
The two curves are called isogenous if there is an isogeny between them. This is an equivalence relation, symmetry being due to the existence of the dual isogeny. Every isogeny is an algebraic homomorphism and thus induces homomorphisms of the groups of the elliptic curves for -valued points.
Title | isogeny |
Canonical name | Isogeny |
Date of creation | 2013-03-22 12:52:07 |
Last modified on | 2013-03-22 12:52:07 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 8 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 14H52 |
Classification | msc 14A15 |
Classification | msc 14A10 |
Classification | msc 14-00 |
Synonym | isogenous |
Related topic | EllipticCurve |
Related topic | ArithmeticOfEllipticCurves |