The Splitting of Primes in Division Fields of Elliptic Curves
Duke, W. ; Tóth, Á.
Experiment. Math., Tome 11 (2002) no. 3, p. 555-565 / Harvested from Project Euclid
We give a global description of the Frobenius for the division fields of an elliptic curve E that is strictly analogous to the cyclotomic case. This is then applied to determine the splitting of a prime p in a subfield of such a division field. These subfields include a large class of nonsolvable quintic extensions and our application provides an arithmetic counterpart to Klein's "solution" of quintic equations using elliptic functions. A central role is played by the discriminant of the ring of endomorphisms of the reduced curve modulo p.
Publié le : 2002-05-14
Classification:  Elliptic curves,  division fields,  quintic expressions,  11G,  11R,  11G05,  11R32
@article{1057864664,
     author = {Duke, W. and T\'oth, \'A.},
     title = {The Splitting of Primes in Division Fields of Elliptic Curves},
     journal = {Experiment. Math.},
     volume = {11},
     number = {3},
     year = {2002},
     pages = { 555-565},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1057864664}
}
Duke, W.; Tóth, Á. The Splitting of Primes in Division Fields of Elliptic Curves. Experiment. Math., Tome 11 (2002) no. 3, pp.  555-565. http://gdmltest.u-ga.fr/item/1057864664/