Invariant theory for the elliptic normal quintic. I: Twists of \(X(5)\)

DOI10.1007/s00208-012-0850-9zbMath1304.11045arXiv1110.3520OpenAlexW2007663230MaRDI QIDQ2377011

Tom A. Fisher

Publication date: 26 June 2013

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.3520

zbMATH Keywords

elliptic curvesHeisenberg groupSelmer groupsgenus one modelinvariants and covariants

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Arithmetic ground fields for curves (14H25) Actions of groups on commutative rings; invariant theory (13A50) Algebraic number theory computations (11Y40)

Related Items (9)

Global methods for the symplectic type of congruences between elliptic curves ⋮ On genus one curves of degree 5 with square-free discriminant ⋮ On families of 9-congruent elliptic curves ⋮ Families of elliptic curves with the same mod 8 representations ⋮ Explicit moduli spaces for congruences of elliptic curves ⋮ L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces ⋮ A formula for the Jacobian of a genus one curve of arbitrary degree ⋮ On families of 7- and 11-congruent elliptic curves ⋮ Visibility of 4-covers of elliptic curves

Uses Software

• Magma
• ecdata

Cites Work

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• Minimisation and reduction of 5-coverings of elliptic curves
• The Magma algebra system. I: The user language
• Geometric syzygies of elliptic normal curves and their secant varieties
• A quintic of genus 1 that contradicts the Hasse principle
• A rank 2 vector bundle on P\(^4\) with 15,000 symmetries
• The Hessian of a genus one curve
• On families of 9-congruent elliptic curves
• The invariants of a genus one curve
• Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
• Mod 2 and mod 5 icosahedral representations
• On the reduction theory of binary forms
• Visualizing Elements in the Shafarevich—Tate Group
• Mod $2$ representations of elliptic curves
• Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero
• Explicit n-descent on elliptic curves, I. Algebra
• Algorithmic Number Theory
• Moduli of abelian varieties

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