Delbourgo, Daniel

$\Lambda$-adic Euler characteristics of elliptic curves

Doc. Math. (Bielefeld) Extra Vol. John H. Coates' Sixtieth Birthday, 301-323 (2006)


Let $E_{/\Bbb Q}$ be a modular elliptic curve, and $p>3$ a good ordinary or semistable prime. Under mild hypotheses, we prove an exact formula for the $\mu$-invariant associated to the weight-deformation of the Tate module of $E$. For example, at ordinary primes in the range $3<p<100$, the result implies the triviality of the $\mu$-invariant of $X_0(11)$.

Mathematics Subject Classification

11R23, 11F80, 11G05


Euler characteristics, Selmer groups, Tamagawa numbers