Un analogue du calcul de Heegner. (An analogue of the Heegner calculus)

DOI10.1007/BF01389425zbMath0616.14023MaRDI QIDQ1821163

Philippe Satgé

Publication date: 1987

Published in: Inventiones Mathematicae (Search for Journal in Brave)

zbMATH Keywords

modular formsHeegner pointscubic twists of an elliptic curveinfinitely many rational points

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) Special algebraic curves and curves of low genus (14H45) Elliptic curves (14H52) Automorphic forms, one variable (11F12)

Related Items (10)

Sums of two rational cubes with many prime factors ⋮ Sylvester’s problem and mock Heegner points ⋮ Cube sums of the forms \(3p\) and \(3p^2\) ⋮ Binomial squares in pure cubic number fields ⋮ Cube sum problem for integers having exactly two distinct prime factors ⋮ MANY CUBIC SURFACES CONTAIN RATIONAL POINTS ⋮ Cube sums of the forms \(3p\) and \(3p^2\). II ⋮ Ranks of Elliptic Curves in Families of Quadratic Twists ⋮ A classical family of elliptic curves having rank one and the \(2\)-primary part of their Tate-Shafarevich group non-trivial ⋮ ON TWISTS OF THE FERMAT CUBIC x³ + y³ = 2

Cites Work

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• Groupes de Selmer et corps cubiques. (Selmer group and cubic fields)
• Heegner points and derivatives of \(L\)-series
• On the arithmetic of special values of L functions
• Modular curves and the Eisenstein ideal
• The Diophantine equation \(ax^3+by^3+cz^3=0\)
• Diophantine analysis and modular forms
• Diophantine Equations with Special Reference To Elliptic Curves

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