Computing the Modular Degree of an Elliptic Curve

DOI10.1080/10586458.2002.10504701zbMath1162.11349OpenAlexW1981573829MaRDI QIDQ5472045

Mark Watkins

Publication date: 14 June 2006

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1057864659

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Arithmetic aspects of modular and Shimura varieties (11G18) Analytic computations (11Y35)

Related Items (18)

Critical and ramification points of the modular parametrization of an elliptic curve ⋮ On a conjecture of Watkins ⋮ Powers of 2 in modular degrees of modular abelian varieties ⋮ Watkins’s conjecture for elliptic curves with non-split multiplicative reduction ⋮ Remarks on a conjecture of Lang ⋮ On a special case of Watkins’ conjecture ⋮ Modular degrees of elliptic curves and some quotient of \(L\)-values ⋮ Congruences for newforms and the index of the Hecke algebra ⋮ Class numbers of real quadratic fields ⋮ RATIONAL TORSION ON OPTIMAL CURVES ⋮ Computing modular degrees using \(L\)-functions ⋮ \(L\)-functions of automorphic forms and combinatorics: Dyck paths. ⋮ A spectral proof of class number one ⋮ Elliptic curves of odd modular degree ⋮ Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups ⋮ A conjecture of Watkins for quadratic twists ⋮ An explicit lower bound for special values of Dirichlet \(L\)-functions. II ⋮ Algorithms for Chow-Heegner points via iterated integrals

Uses Software

• ecdata

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stickelberger elements and modular parametrizations of elliptic curves
• Arithmetic on elliptic curves with complex multiplication. II
• Heegner points and derivatives of \(L\)-series
• On the arithmetic of quaternion algebras. II
• Modular curves and the Eisenstein ideal
• Intersections over modular curves
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• The number of elliptic curves over \(\mathbb{Q}\) with conductor \(N\)
• Exponents of class groups and elliptic curves.
• Modular elliptic curves and Fermat's Last Theorem
• Hecke operators on \(\Gamma_0(m)\)
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• Modular Parametrizations of Elliptic Curves
• On the Holomorphy of Certain Dirichlet Series
• Elliptic Curves of Prime Conductor
• The special values of the zeta functions associated with cusp forms
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Values of symmetric square L-functions at 1
• Computing Periods of Cusp Forms and Modular Elliptic Curves
• Elliptische Kurven mit vorgeschriebenem Reduktionsverhalten. II
• The behavior of the Mordell-Weil group of elliptic curves
• Advanced Topics in Computional Number Theory
• Elliptische Kurven mit vorgeschriebenem Reduktionsverhalten. I
• Statistics of the random variable \(L(\text{sym}^2f,1)\)

This page was built for publication: Computing the Modular Degree of an Elliptic Curve