A Formula for the Gr 6 ssencharacter of a Parametrized Elliptic Curve

  title={A Formula for the Gr 6 ssencharacter of a Parametrized Elliptic Curve},
  author={Robert Rumely},
The grossencharacter of an elliptic curve with complex multiplication is an important arithmetic invariant. Deuring [2] first proved its existence in showing that the zeta-function of the curve is a product of Hecke L-series. It is ramified precisely where the curve has bad reduction; at a “good” prime its value reduces to the Frobenius endomorphism. Its minimal field of definition is the smallest field over which the torsion points are abelian. In this paper we give a formula for the… CONTINUE READING

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