Computing the $p$-Selmer group of an elliptic curve

DOI10.1090/S0002-9947-00-02535-6zbMath0954.11022OpenAlexW1523310006MaRDI QIDQ4505933

Z. Djabri, Edward F. Schaefer, Nigel P. Smart

Publication date: 3 October 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02535-6

zbMATH Keywords

elliptic curvesMordell-Weil rankSelmer group

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52) Computational aspects of algebraic curves (14Q05)

Related Items

Descent on elliptic surfaces and arithmetic bounds for the Mordell-Weil rank, Visualising Sha[2 in Abelian surfaces], Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve, Computing the Rank of Elliptic Curves over Number Fields, Rational points and the elliptic Chabauty method., Descent via isogeny on elliptic curves with large rational torsion subgroups, GENERALIZED EXPLICIT DESCENT AND ITS APPLICATION TO CURVES OF GENUS 3, Explicit n-descent on elliptic curves, I. Algebra, How to do a 𝑝-descent on an elliptic curve, 3-Selmer groups for curves y 2 = x 3 + a, Explicit $n$-descent on elliptic curves III. Algorithms, Second $p$-descents on elliptic curves, Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian

Uses Software

• mwrank

Cites Work

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• 2-descent on the Jacobians of hyperelliptic curves
• Class groups and Selmer groups
• Galois properties of points of finite order of elliptic curves
• Implementing 2-descent for Jacobians of hyperelliptic curves
• Explicit 4-descents on an elliptic curve
• Constants for lower bounds for linear forms in the logarithms of algebraic numbers I. The general case
• Second descents for elliptic curves
• On the complexity of computing the 2-Selmer group of an elliptic curve
• Notes on elliptic curves. I.