CM elliptic curve
= CM elliptic curve
{c}
An <elliptic curve> with <complex multiplication> is called a CM elliptic curve. Distinguish geometric <endomorphisms> from <endomorphisms> defined over the base <field>. In characteristic zero, adjoining the <imaginary quadratic field> selected by the tangent action makes all geometric <endomorphisms> defined over the base. Good split primes have <ordinary reduction>; good inert primes have <supersingular reduction>.