Geodesic
The distribution of group structures on elliptic curves over finite prime fields
Documenta mathematica, Tome 11 (2006), pp. 119-142
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We determine the probability that a randomly chosen elliptic curve E/Fp​ over a randomly chosen prime field Fp​ has an l-primary part E(Fp​)[l∞] isomorphic with a fixed abelian l-group Hα,β(l)​=Z/lα×Z/lβ.
DOI : 10.4171/dm/206
Classification : 11, 20, 45, 80
Mots-clés : elliptic curves over finite fields, group structures, counting functions 
@article{10_4171_dm_206,
     author = {Ernst-Ulrich Gekeler},
     title = {The distribution of group structures on elliptic curves over finite prime fields},
     journal = {Documenta mathematica},
     pages = {119--142},
     year = {2006},
     volume = {11},
     doi = {10.4171/dm/206},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/206/}
}
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Ernst-Ulrich Gekeler. The distribution of group structures on elliptic curves over finite prime fields. Documenta mathematica, Tome 11 (2006), pp. 119-142. doi: 10.4171/dm/206

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