Singular moduli, modular polynomials, and the index of the closure of \({\mathbb{Z}}[j(\tau)]\) in \({\mathbb{Q}}(j(\tau))\)

DOI10.1007/BF01446429zbMath0642.12014MaRDI QIDQ1101511

David R. Dorman

Publication date: 1989

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

Full work available at URL: https://eudml.org/doc/164502

zbMATH Keywords

elliptic modular functionmodular polynomial

Mathematics Subject Classification ID

Quadratic extensions (11R11) Families, moduli of curves (algebraic) (14H10) Modular and automorphic functions (11F03) Special algebraic curves and curves of low genus (14H45) Class field theory (11R37) Iwasawa theory (11R23)

Related Items (7)

Hilbert class polynomials and traces of singular moduli ⋮ Class invariants for quartic CM fields ⋮ Singular values of principal moduli ⋮ On a conjecture of Chen and Yui: Fricke groups ⋮ ON DISCRIMINANTS OF MINIMAL POLYNOMIALS OF THE RAMANUJAN CLASS INVARIANTS ⋮ Class polynomials for nonholomorphic modular functions ⋮ CONGRUENCE PROPERTIES OF BORCHERDS PRODUCT EXPONENTS

Cites Work

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• Heegner points and derivatives of \(L\)-series
• Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
• Good reduction of abelian varieties
• Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
• Special values of the elliptic modular function and factorization formulae.
• The Field Generated by the Discriminant of the Class Invariants of an Imaginary Quadratic Field
• Elliptic Curves with Good Reduction Everywhere

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