Geodesic
Small discriminants of complex multiplication fields of elliptic curves over finite fields
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 381-388.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves $E$ over a prime finite field $\mathbb {F}_p$ of $p$ elements, such that the discriminant $D(E)$ of the quadratic number field containing the endomorphism ring of $E$ over $\mathbb {F}_p$ is small. For almost all primes we also obtain a similar unconditional bound. These lower bounds complement an upper bound of F. Luca and I. E. Shparlinski (2007).
DOI : 10.1007/s10587-015-0183-4
Classification : 11G20, 11N32, 11R11
Keywords: elliptic curve; complex multiplication field; Frobenius discriminant 
@article{10_1007_s10587_015_0183_4,
     author = {Shparlinski, Igor E.},
     title = {Small discriminants of complex multiplication fields of elliptic curves over finite fields},
     journal = {Czechoslovak Mathematical Journal},
     pages = {381--388},
     publisher = {mathdoc},
     volume = {65},
     number = {2},
     year = {2015},
     doi = {10.1007/s10587-015-0183-4},
     mrnumber = {3360434},
     zbl = {06486954},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0183-4/}
}
TY  - JOUR
AU  - Shparlinski, Igor E.
TI  - Small discriminants of complex multiplication fields of elliptic curves over finite fields
JO  - Czechoslovak Mathematical Journal
PY  - 2015
SP  - 381
EP  - 388
VL  - 65
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0183-4/
DO  - 10.1007/s10587-015-0183-4
LA  - en
ID  - 10_1007_s10587_015_0183_4
ER  - 
%0 Journal Article
%A Shparlinski, Igor E.
%T Small discriminants of complex multiplication fields of elliptic curves over finite fields
%J Czechoslovak Mathematical Journal
%D 2015
%P 381-388
%V 65
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0183-4/
%R 10.1007/s10587-015-0183-4
%G en
%F 10_1007_s10587_015_0183_4
Shparlinski, Igor E. Small discriminants of complex multiplication fields of elliptic curves over finite fields. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 381-388. doi : 10.1007/s10587-015-0183-4. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0183-4/

Cité par Sources :