  We discuss abelian equivariant Iwasawa theory for elliptic curves over
$\mathbb{Q}$ at good supersingular primes and non-anomalous good ordinary
primes. Using Kobayashi's method, we construct equivariant Coleman maps, which
send the Beilinson-Kato element to the equivariant $p$-adic $L$-functions. Then
we propose equivariant main conjectures and, under certain assumptions, prove
one divisibility via Euler system machinery. As an application, we prove a case
of a conjecture of Mazur-Tate.
