# Component Groups of Quotients of J_{0}(N)

**Abstract**

Let f be a newform of weight 2 on Gamma0(N), and let A_f
be the corresponding optimal abelian variety quotient of J0(N).
We describe an algorithm to compute the order of the component group
of A_f at primes p that exactly divide N. We give a table of
orders of component groups for all f of level N <= 127 and five
examples in which the component group is very large, as predicted
by the Birch and Swinnerton-Dyer conjecture.

This paper has appeared in Springer's Lecture Notes in
Computer Science series, hence is copyright Springer-Verlag.

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