An explicit theory of heights
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- by E. V. Flynn PDF
- Trans. Amer. Math. Soc. 347 (1995), 3003-3015 Request permission
Abstract:
We consider the problem of explicitly determining the naive height constants for Jacobians of hyperelliptic curves. For genus $> 1$, it is impractical to apply Hilbert’s Nullstellensatz directly to the defining equations of the duplication law; we indicate how this technical difficulty can be overcome by use of isogenies. The height constants are computed in detail for the Jacobian of an arbitrary curve of genus $2$, and we apply the technique to compute generators of $\mathcal {J}(\mathbb {Q})$, the Mordell-Weil group for a selection of rank $1$ examples.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 3003-3015
- MSC: Primary 11G10; Secondary 11G30, 14H25, 14K15
- DOI: https://doi.org/10.1090/S0002-9947-1995-1297525-9
- MathSciNet review: 1297525