The Jacobians of Non-Split Cartan Modular Curves

DOI10.1112/S0024611598000392zbMath0903.11019MaRDI QIDQ3839976

Imin Chen

Publication date: 11 November 1998

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

elliptic curvesisogenySelberg trace formulaJacobianscusp formsexplicit formulatrace of Hecke operatorsCartan modular curvesnon-split dihedral representation

Mathematics Subject Classification ID

Elliptic curves (14H52) Jacobians, Prym varieties (14H40) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Hecke-Petersson operators, differential operators (one variable) (11F25)

Related Items (22)

Jacobians of modular curves associated to normalizers of Cartan subgroups of level \(p^n\) ⋮ Quadratic points on non-split Cartan modular curves ⋮ Serre’s uniformity conjecture for elliptic curves with rational cyclic isogenies ⋮ Constraints on the automorphism group of a curve ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ Modular curves with many points over finite fields ⋮ Automorphisms of Cartan modular curves of prime and composite level ⋮ The automorphism group of the non-split Cartan modular curve of level 11 ⋮ ON THE AUTOMORPHISMS OF THE NONSPLIT CARTAN MODULAR CURVES OF PRIME LEVEL ⋮ A MODULI INTERPRETATION FOR THE NON-SPLIT CARTAN MODULAR CURVE ⋮ An explicit correspondence of modular curves ⋮ A bound for the torsion conductor of a non-CM elliptic curve ⋮ The generalized Fermat equation with exponents 2, 3, ⋮ Double covers of Cartan modular curves ⋮ Pairs of elliptic curves with maximal Galois representations ⋮ An exceptional isomorphism between modular curves of level 13 ⋮ Arithmetic of elliptic curves and diophantine equations ⋮ Functions and differentials on the non-split Cartan modular curve of level 11 ⋮ Explicit Chabauty-Kim for the split Cartan modular curve of level 13 ⋮ The modularity of elliptic curves over all but finitely many totally real fields of degree 5 ⋮ On relations between Jacobians of certain modular curves ⋮ Steinberg representation and idempotent relations

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