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We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank.
Finiteness of E(Q) and X(E, Q) for a class of Weil curves
V. Kolyvagin, · 1989
Earlier work this paper cites.
The arithmetic of elliptic curves
J. H. Silverman, · 1992
Earlier work this paper cites.
Modular elliptic curves and Fermat’s last theorem
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Earlier work this paper cites.
On the modularity of elliptic curves over ℚ \mathbb{Q} : wild 3-adic exercises
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Earlier work this paper cites.
T. Hastie, R. Tibshirani, and J. Friedman, The elements of statistical learning: data mining, inference, and prediction
2001
Earlier work this paper cites.
Oberwolfach Reports 4, no. 3, 1992–2005, Expanded version at arXiv:0709.2908
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available at https://johncremona.github.io/ecdata/
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Sage 10.3 Reference Manual
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Cited in the paper.
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