Abstract
Let f be a newform of weight 2 on Γ0(N), and let A f be the corresponding optimal Abelian variety quotient of J 0(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.
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Kohel, D.R., Stein, W.A. (2000). Component Groups of Quotients of J 0(N). In: Bosma, W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722028_25
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DOI: https://doi.org/10.1007/10722028_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67695-9
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