A relation between embedding degrees and class numbers of binary quadratic forms
نویسندگان
چکیده
منابع مشابه
A relation between embedding degrees and class numbers of binary quadratic forms
In this paper, we describe a relation between the embedding degree of an elliptic curve over a prime field Fp and the inertial degree of the primes above p in a certain ring class field. From this relation, we conclude that the embedding degree divides the class number of a group of binary quadratic forms of a fixed discriminant.
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Notation: Z the set of integers, N the set of positive integers, [x] the greatest integer not exceeding x, ( a m) the Legendre-JacobiKronecker symbol, ordpm the nonnegative integer α such that pα | m but pα+1 m, (a, b) the greatest common divisor of a and b, (a, b, c) the form ax2 + bxy + cy2, [a, b, c] the equivalence class containing the form (a, b, c), H(d) the form class group of discrimina...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2014
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2014-02831-7