Surjectivity of mod l Representations Attached to Elliptic Curves and Congruence Primes
Canadian mathematical bulletin, Tome 45 (2002) no. 3, pp. 337-348

Voir la notice de l'article provenant de la source Cambridge University Press

For a modular elliptic curve $E/\mathbb{Q}$ , we show a number of links between the primes $\ell $ for which the mod $\ell $ representation of $E/\mathbb{Q}$ has projective dihedral image and congruence primes for the newform associated to $E/\mathbb{Q}$ .
DOI : 10.4153/CMB-2002-036-3
Mots-clés : 11G05, 11F80, torsion points of elliptic curves, Galois representations, congruence primes, Serre tori, grossencharacters, non-split Cartan
Chen, Imin. Surjectivity of mod l Representations Attached to Elliptic Curves and Congruence Primes. Canadian mathematical bulletin, Tome 45 (2002) no. 3, pp. 337-348. doi: 10.4153/CMB-2002-036-3
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[1] [1] Breuil, C., Conrad, B., Diamond, F. and Taylor, R., On the modularity of elliptic curves over Q: wild 3-adic exercises. J. Amer.Math. Soc., to appear. Google Scholar

[2] [2] Chen, I., On Siegel's modular curve of level 5 and the class number one problem. J. Number Theory (2) 74(1999). Google Scholar

[3] [3] Cohn, P. M., Algebra, Volume 2. John Wiley & Sons, second edition, 1982. Google Scholar

[4] [4] Cremona, J. E., Algorithms for modular elliptic curves. Cambridge University Press, second edition, 1997. Google Scholar

[5] [5] Kraus, A., Une remarque sur les points de torsion des courbes elliptiques. C. R. Acad. Sci. Paris S érie I Math. 321 (1995), 321–1995. Google Scholar

[6] [6] Mazur, B., Rational isogenies of prime degree. Invent.Math. 44 (1978), 44–1978. Google Scholar

[7] [7] Miyake, T., Modular Forms. Springer-Verlag, 1989. Google Scholar

[8] [8] Momose, F., Galois action on some ideal section points of the abelian variety associated with a modular form and its application. Nagoya Math. J. 91 (1983), 91–1983. Google Scholar

[9] [9] Momose, F., Rational points on the modular curves X split(p). Compositio Math. 52 (1984), 52–1984. Google Scholar

[10] [10] Ribet, K., On l-adic representations attached to modular forms. Invent.Math. 28 (1975), 28–1975. Google Scholar

[11] [11] Ribet, K., On modular representations of Gal(Q j Q) arising from modular forms. Invent.Math. 100 (1990), 100–1990. Google Scholar

[12] [12] Serre, J. P., Corps locaux. Number VIII in Publications de l'Université de Nancago, Hermann, Paris, deuxifieme edition, 1968. Google Scholar

[13] [13] Serre, J. P., Propriétés galoisiennes des points d'ordrefini des courbes elliptiques. Invent.Math. 15 (1972), 15–1972. Google Scholar

[14] [14] Serre, J. P., Sur les représentations modulaires de degré 2 de Gal(Q/Q). Duke Math. J. (1) 54 (1987), 54–1987. Google Scholar

[15] [15] Weil, A., On a certain type of characters of the idfiele-class groups of an algebraic number-field. In: Proceedings of the international symposium of algebraic number theory, Tokyo & Nikko, 1955, Tokyo, 1956, Science Council of Japan, 1–7. Google Scholar

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