#### DOCUMENTA MATHEMATICA, Vol. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 301-323

Daniel Delbourgo

Lambda-Adic Euler Characteristics of Elliptic Curves

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 $X_0(11)$.

2000 Mathematics Subject Classification: 11G40; also 11F33, 11R23, 11G05

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