Engineering↗
Atkin-Morain Elliptic Curve Primality Proving
ECPP: using complex multiplication to construct curves of known order, avoiding point counting entirely.
Every page in the KEVOS library tagged Complex Multiplication. 4 pages.
ECPP: using complex multiplication to construct curves of known order, avoiding point counting entirely.
The link between curves with complex multiplication and class groups of imaginary quadratic orders, and the Hilbert class polynomial.
Isogenies as maps of curves respecting the group law, and the two possible endomorphism rings over a field of characteristic zero.
Complex multiplication, isogenies, the relation between CM curves and imaginary quadratic orders, Hilbert and Weber class polynomials, and the CM method for curve construction.