no. 3
No 17-torsion on elliptic curves over cubic number fields
Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 831-838.

On achève de dresser la liste des nombres premiers de torsion de courbes elliptiques sur les corps de nombres cubiques, en montrant que 17 n’en fait pas partie.

We complete our previous determination of the torsion primes of elliptic curves over cubic number fields, by showing that 17 is not one of those.

@article{JTNB_2003__15_3_831_0,
     author = {Parent, Pierre},
     title = {No $17$-torsion on elliptic curves over cubic number fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {831--838},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {3},
     year = {2003},
     mrnumber = {2142238},
     zbl = {1072.11037},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2003__15_3_831_0/}
}
TY  - JOUR
AU  - Parent, Pierre
TI  - No $17$-torsion on elliptic curves over cubic number fields
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2003
SP  - 831
EP  - 838
VL  - 15
IS  - 3
PB  - Université Bordeaux I
UR  - http://www.numdam.org/item/JTNB_2003__15_3_831_0/
LA  - en
ID  - JTNB_2003__15_3_831_0
ER  - 
%0 Journal Article
%A Parent, Pierre
%T No $17$-torsion on elliptic curves over cubic number fields
%J Journal de théorie des nombres de Bordeaux
%D 2003
%P 831-838
%V 15
%N 3
%I Université Bordeaux I
%U http://www.numdam.org/item/JTNB_2003__15_3_831_0/
%G en
%F JTNB_2003__15_3_831_0
Parent, Pierre. No $17$-torsion on elliptic curves over cubic number fields. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 831-838. http://www.numdam.org/item/JTNB_2003__15_3_831_0/

[1] C. Deninger, E. Nart, Formal groups and L-series. Comment. Math. Helvetici 65 (1990), 318-333. | MR | Zbl

[2] T. Honda, On the theory of commutative formal groups. J. Math. Soc. Japan 22 (1970), 213-246. | MR | Zbl

[3] N. Ishii, F. Momose, Hyperelliptic modular curves. Tsukuba J. Math. 15 no. 2 (1991), 413-423. | MR | Zbl

[4] S. Kamienny, Torsion points on elliptic curves over all quadratic fields. Duke Math. J. 53 no. 1 (1986), 157-162. | MR | Zbl

[5] K. Kato, p-adic Hodge theory and values of zeta-functions of modular forms. To appear in Astérisque. | Numdam | MR | Zbl

[6] B. Mazur, Modular curves and the Eisenstein ideal. Publications mathématiques de l'I.H.E.S. 47 (1977), 33-186. | Numdam | MR | Zbl

[7] P. Parent, Torsion des courbes elliptiques sur les corps cubiques. Ann. Inst. Fourier 50 (2000), 723-749. | Numdam | MR | Zbl