Steinitz class of elliptic curves with complex multilication

【摘要】 <正> Let E be any elliptic curve having complex multiplication by the ring (?)k of integers of the quadratic number field Let H be the Hilbert class field of K. The Mordell-Weil group E(H) of H-rational points is a module over the Dedekind domain (?)K, its structure depends on its Steinitz class. Here the Steinits class is determined when D is any prime number. This result advances the result for the specific elliptic curves when D = 10. A general theorem on structure of modules over Dedekind domain is also proposed.更多还原

【Abstract】 Let E be any elliptic curve having complex multiplication by the ring (?)k of integers of the quadratic number field Let H be the Hilbert class field of K. The Mordell-Weil group E(H) of H-rational points is a module over the Dedekind domain (?)K, its structure depends on its Steinitz class. Here the Steinits class is determined when D is any prime number. This result advances the result for the specific elliptic curves when D = 10. A general theorem on structure of modules over Dedekind domain is also proposed.更多还原