Groupes de Selmer et corps cubiques. (Selmer group and cubic fields)

DOI10.1016/0022-314X(86)90075-2zbMath0601.14027MaRDI QIDQ1080908

Philippe Satgé

Publication date: 1986

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

elliptic curveSelmer group

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) Elliptic curves (14H52) Cubic and quartic extensions (11R16)

Related Items (21)

On central L-values and the growth of the 3-part of the Tate–Shafarevich group ⋮ Using elliptic curves to produce quadratic number fields of high three-rank ⋮ Three-descent and the Birch and Swinnerton-Dyer conjecture ⋮ Infinitely many elliptic curves of rank exactly two ⋮ The rank of a CM elliptic curve and a recurrence formula ⋮ Sylvester’s problem and mock Heegner points ⋮ Cube sums of the forms \(3p\) and \(3p^2\) ⋮ Cyclic cubic extensions of ℚ ⋮ The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k ⋮ Cube sums of the forms \(3p\) and \(3p^2\). II ⋮ GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS ⋮ A classical family of elliptic curves having rank one and the \(2\)-primary part of their Tate-Shafarevich group non-trivial ⋮ Explicit isogeny descent on elliptic curves ⋮ ON TWISTS OF THE FERMAT CUBIC x³ + y³ = 2 ⋮ \(3\)-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field ⋮ How to do a 𝑝-descent on an elliptic curve ⋮ 3-Selmer groups for curves y 2 = x 3 + a ⋮ Un analogue du calcul de Heegner. (An analogue of the Heegner calculus) ⋮ Tamagawa number divisibility of central \(L\)-values of twists of the Fermat elliptic curve ⋮ An explicit Gross–Zagier formula related to the Sylvester conjecture ⋮ Rank of elliptic curves and exponential sums

Cites Work

• The parity of the rank of the Mordell-Weil group
• The Diophantine equation \(ax^3+by^3+cz^3=0\)
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Arithmetic on Curves of Genus 1. I. On a conjecture of Selmer.
• Arithmetic on curves of genus 1. VIII. On conjectures of Birch and Swinnerton-Dyer.
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