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- W1488405559 abstract "Throughout this note, p denotes a fixed prime number and f denotes a fixed natural number prime to p . It is easy to see and more or less known that for any natural number n , there exists an elliptic curve over p whose j -invariant is of degree n over F p and whose endomorphism ring is isomorphic to an order of an imaginary quadratic field. In this note, we consider a more precise problem: for any natural number n, decide whether or not there exists an elliptic curve over p whose j-invariant is of degree n over F p and whose endomorphism ring is isomorphic to an order of an imaginary quadratic field with conductor f ." @default.
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- W1488405559 date "1985-09-01" @default.
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- W1488405559 title "A note on quadratic fields in which a fixed prime number splits completely" @default.
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- W1488405559 doi "https://doi.org/10.1017/s0027763000021498" @default.
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