Component Groups of Quotients of J0(N)

  title={Component Groups of Quotients of J0(N)},
  author={David R. Kohel and William A. Stein},
Let f be a newform of weight 2 on Γ0(N), and let Af be the corresponding optimal abelian variety quotient of J0(N). We describe an algorithm to compute the order of the component group of Af 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. 

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