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Principal polarizations on products of elliptic curves

Herbert Lange
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Abstract

An abelian variety admits only a finite number of isomorphism classes of principal polarizations. The paper gives an interpretation of this number in terms of class numbers of definite Hermitian forms in the case of a product of elliptic curves without complex multiplication. In the case of a self-product of an elliptic curve, as well as in the two-dimensional case, classical class number computations can be applied to determine this number.

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Herbert Lange. 2005-08-24. Principal polarizations on products of elliptic curves. https://arxiv.org/abs/math/0508458

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