Jacobians of genus one curves

Sang Yook An, Seog Young Kim, David C. Marshall, Susan H. Marshall, William G. McCallum, Alexander R. Perlis

Research output: Contribution to journalArticle

53 Scopus citations

Abstract

Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P1a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariant theory gives the curve’s jacobian in Weierstrass form and the covering map to its jacobian induced by the K-rational divisor at infinity. We give a unified account of all three cases.

Original languageEnglish (US)
Pages (from-to)304-315
Number of pages12
JournalJournal of Number Theory
Volume90
Issue number2
DOIs
StatePublished - Jan 1 2001

ASJC Scopus subject areas

  • Algebra and Number Theory

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    An, S. Y., Kim, S. Y., Marshall, D. C., Marshall, S. H., McCallum, W. G., & Perlis, A. R. (2001). Jacobians of genus one curves. Journal of Number Theory, 90(2), 304-315. https://doi.org/10.1006/jnth.2000.2632