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On the Manin constants of modular elliptic curves

  • Bas Edixhoven
Chapter
Part of the Progress in Mathematics book series (PM, volume 89)

Abstract

For M a positive integer, let X 0 (M) Q be the modular curve over Q classifying elliptic curves with a given cyclic subgroup of order M and let J 0(M)Q be the jacobian of X 0(M)Q. An elliptic curve E over Q is said to be modular if it is an isogeny factor (isogenics over Q) of some J 0(M)Q; the smallest M for which this happens is then called the level of E. The Shimura-Taniyama conjecture states that every elliptic curve E over Q is modular, and that the level of E equals the conductor of E. A modular elliptic curve of level M is called strong if there exists a closed immersion EJ 0(M)Q. It follows from the multiplicity one principle for modular forms that such an immersion is unique up to sign.

Keywords

Elliptic Curve Elliptic Curf Stable Model Springer Lecture Note Modular Curve 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Bas Edixhoven

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