No 17 -torsion on elliptic curves over cubic number fields

Pierre Parent

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 3, page 831-838
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Parent, Pierre. "No $17$-torsion on elliptic curves over cubic number fields." Journal de théorie des nombres de Bordeaux 15.3 (2003): 831-838. <http://eudml.org/doc/249113>.

@article{Parent2003,
abstract = {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.},
author = {Parent, Pierre},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {elliptic curve; rational point; modular curve},
language = {eng},
number = {3},
pages = {831-838},
publisher = {Université Bordeaux I},
title = {No $17$-torsion on elliptic curves over cubic number fields},
url = {http://eudml.org/doc/249113},
volume = {15},
year = {2003},
}

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
PB - Université Bordeaux I
VL - 15
IS - 3
SP - 831
EP - 838
AB - 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.
LA - eng
KW - elliptic curve; rational point; modular curve
UR - http://eudml.org/doc/249113
ER -

References

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  1. [1] C. Deninger, E. Nart, Formal groups and L-series. Comment. Math. Helvetici65 (1990), 318-333. Zbl0741.14026MR1057247
  2. [2] T. Honda, On the theory of commutative formal groups. J. Math. Soc. Japan22 (1970), 213-246. Zbl0202.03101MR255551
  3. [3] N. Ishii, F. Momose, Hyperelliptic modular curves. Tsukuba J. Math.15 no. 2 (1991), 413-423. Zbl0771.14008MR1138196
  4. [4] S. Kamienny, Torsion points on elliptic curves over all quadratic fields. Duke Math. J.53 no. 1 (1986), 157-162. Zbl0599.14029MR835802
  5. [5] K. Kato, p-adic Hodge theory and values of zeta-functions of modular forms. To appear in Astérisque. Zbl1142.11336MR2104361
  6. [6] B. Mazur, Modular curves and the Eisenstein ideal. Publications mathématiques de l'I.H.E.S.47 (1977), 33-186. Zbl0394.14008MR488287
  7. [7] P. Parent, Torsion des courbes elliptiques sur les corps cubiques. Ann. Inst. Fourier50 (2000), 723-749. Zbl0971.11030MR1779891

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