DEGREE OF ISOGENIES OF FLLIPTIC CURVES WITH COMPLEX MULTIPLICATION

Let E be an elliptic curve over with complex multiplication. Suppose that E is defined over F= (j(E)). We study possible degrees of F-isogenies of E.

Bengamin notes Class field theory E. Artin;J. Tate
Proc. London Math. Soc. v.28 Modular invariants expressible in terms of quadratic and cubic irrationalities W. E. H. Berwick
Lecture notes in math. no.476 Modular functions of one variables Ⅳ B. J. Birch;W. Kyuk (ed.)
Primes of the form x²+ny² D. Cox
Compositio Math. v.58 A remark about isogenies of elliptic curves over quadratic fields G. Frey
Israel J. Math. v.85 Curves with infinitely many points of fixed degree G. Frey
Lecture notes in math. no.776 Arithmetic on elliptic curves with complex multiplication B. Gross
Invent. Math. v.84 Heegner points and derivatives of L-series B. Gross;D. Zagier
Math. Proc. Cambridge Philos. Soc. v.87 The modular curves $X_0(65)\;and\;X_0(91)$ and rational isogeny M. A. Kenku
Publ. Math. IHES v.47 Modular curves and the Eisenstein ideal B. Mazur
Invent. Math. v.44 Rational isogenies of prome degree B. Mazur
Compositio Math. v.97 isogenies of prome degree over number fields F. Momose
Bull. Amer. Math. Soc. v.81 Diophantine equations and modular curves A. Ogg
J. of Number Theory v.33 Rational torsion in complex-multiplication elliptic curves J. L. Parish
Invent. Math. v.15 Proprietes galoisiennes des points d'ordre fini des courbes elliptiques J. P. Serre
The arithmetic of elliptic curves J. H. Silverman
Advanced topics in the arithmetic of elliptic curves J. H. Silverman
A course of modern analysis E. T. Whittaker