The Arithmetic of Elliptic Curves

2009/01/01 by Joseph H. Silverman · 21 citations
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Arithmetic #Elliptic curve #Hessian form of an elliptic curve #History and Theory of Mathematics #Mathematics #Pure mathematics #Quarter period #Schoof's algorithm #Supersingular elliptic curve

paper · doi:10.1007/978-0-387-09494-6

crossref issued 2009/01/01 · crossref published 2009/01/01 · crossref published-print 2009/01/01 · openalex publication_date 2009/01/01 · crossref created 2009/04/18 · crossref deposited 2019/04/06 · openalex created_date 2025/10/10 · crossref indexed 2026/08/05 · openalex updated_date 2026/08/05

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• Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function)
• The existence of infinitely many supersingular primes for every elliptic curve over ?
• Twists of Elliptic Curves
• Computing twists of hyperelliptic curves
• Finding elliptic curves with a subgroup of prescribed size
• Elementary 3-descent with a 3-isogeny
• Logarithmic deformations of normal crossing Enriques surfaces in characteristic two
• Isogeny volcanoes
• Sato–Tate distributions of twists ofy2=x5−xandy2=x6+ 1
• On the Distribution of Atkin and Elkies Primes
• ON THE NON-VANISHING OF ELLIPTIC CURVE L-FUNCTIONS AT THE CENTRAL POINT
• MANY CUBIC SURFACES CONTAIN RATIONAL POINTS
• A formula for the Jacobian of a genus one curve of arbitrary degree
• On several families of elliptic curves with arbitrary large Selmer groups
• Strong Weil curves over Fq(T) with small conductor
• On the basepoint-free theorem for log canonical threefolds over the algebraic closure of a finite field
• Congruent elliptic curves and double struck upper Z Subscript p Superscript d Z p d ℤ_p^d-extensions
• The Brauer group of the moduli stack of elliptic curves
• Three consecutive almost squares
• Elements of given order in Tate–Shafarevichgroups of abelian varieties in quadratic twist families
• Complex multiplication [wikipedia]