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Jacobians of Genus One Curves

✍ Scribed by Sang Yook An; Seog Young Kim; David C. Marshall; Susan H. Marshall; William G. McCallum; Alexander R. Perlis

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 122 KB
Volume: 90
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2632

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✦ Synopsis

Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P 1 , a 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.

2001 Academic Press

Given a curve C of genus one, there is an associated elliptic curve (E, O), where E is the jacobian of C, Jac(C), and O is the point on E corresponding to the trivial divisor class.

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