Some Heuristics about Elliptic Curves
Watkins, Mark
Experiment. Math., Tome 17 (2008) no. 1, p. 105-125 / Harvested from Project Euclid
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We give some heuristics for counting elliptic curves with certain properties. In particular, we rederive the Brumer-McGuinness heuristic for the number of curves with positive/negative discriminant up to {\small$X$}, which is an application of lattice-point counting. We then introduce heuristics that allow us to predict how often we expect an elliptic curve $E$ with even parity to have $L(E,1)=0$. We find that we expect there to be about $c_1X^{19/24}(\log X)^{3/8}$ curves with $|\Delta|
Publié le : 2008-05-15
Classification:  Elliptic curves,  asymptotic count,  vanishing $L$-function,  14H52,  14G10 
@article{1227031901,
     author = {Watkins, Mark},
     title = {Some Heuristics about Elliptic Curves},
     journal = {Experiment. Math.},
     volume = {17},
     number = {1},
     year = {2008},
     pages = { 105-125},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1227031901}
}

Watkins, Mark. Some Heuristics about Elliptic Curves. Experiment. Math., Tome 17 (2008) no. 1, pp.  105-125. http://gdmltest.u-ga.fr/item/1227031901/