Bielliptic curves and symmetric products
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- by Joe Harris and Joe Silverman PDF
- Proc. Amer. Math. Soc. 112 (1991), 347-356 Request permission
Abstract:
We show that the twofold symmetric product of a nonhyperelliptic, nonbielliptic curve does not contain any elliptic curves. Applying a theorem of Faltings, we conclude that such a curve defined over a number field $K$ has only finitely many points over all quadratic extensions of $K$. We illustrate our theory with the modular curves ${X_0}(N),{X_1}(N),X(N)$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 347-356
- MSC: Primary 11G30; Secondary 14H25
- DOI: https://doi.org/10.1090/S0002-9939-1991-1055774-0
- MathSciNet review: 1055774