Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields
Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 409-417
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We show that, for most of the elliptic curves $\text{E}$ over a prime finite field ${{\mathbb{F}}_{p}}$ of $p$ elements, the discriminant $D\left( E \right)$ of the quadratic number field containing the endomorphism ring of $\text{E}$ over ${{\mathbb{F}}_{p}}$ is sufficiently large. We also obtain an asymptotic formula for the number of distinct quadratic number fields generated by the endomorphism rings of all elliptic curves over ${{\mathbb{F}}_{p}}$ .
Luca, Florian; Shparlinski, Igor E. Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields. Canadian mathematical bulletin, Tome 50 (2007) no. 3, pp. 409-417. doi: 10.4153/CMB-2007-039-2
@article{10_4153_CMB_2007_039_2,
author = {Luca, Florian and Shparlinski, Igor E.},
title = {Discriminants of {Complex} {Multiplication} {Fields} of {Elliptic} {Curves} over {Finite} {Fields}},
journal = {Canadian mathematical bulletin},
pages = {409--417},
year = {2007},
volume = {50},
number = {3},
doi = {10.4153/CMB-2007-039-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-039-2/}
}
TY - JOUR AU - Luca, Florian AU - Shparlinski, Igor E. TI - Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields JO - Canadian mathematical bulletin PY - 2007 SP - 409 EP - 417 VL - 50 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-039-2/ DO - 10.4153/CMB-2007-039-2 ID - 10_4153_CMB_2007_039_2 ER -
%0 Journal Article %A Luca, Florian %A Shparlinski, Igor E. %T Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields %J Canadian mathematical bulletin %D 2007 %P 409-417 %V 50 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-039-2/ %R 10.4153/CMB-2007-039-2 %F 10_4153_CMB_2007_039_2
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