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Elliptic curves
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511	Rational Divisors in Rational Divisor Classes N. Bruin?1 and E.V. Flynn??2 1 2 Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Vector bundles Divisor Canonical bundle Ample line bundle Riemann–Roch theorem Algebraic curves Linear system of divisors Greatest common divisor Elliptic curve Abstract algebra Algebraic geometry Algebra
512	The Arithmetic of Hyperelliptic Curves E. V. Flynn∗ , Mathematical Institute, University of Oxford Abstract We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in partic Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:37 Elliptic curve Kummer surface Algebraic number field Hyperelliptic curve Hyperelliptic curve cryptography Trace Zero Cryptography Abstract algebra Algebraic geometry Algebraic curves
513	APPLICATION OF COVERING TECHNIQUES TO FAMILIES OF CURVES E.V. FLYNN AND J. REDMOND Abstract. Much success in finding rational points on curves has been obtained by using Chabauty’s Theorem, which applies when the genus Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Algebraic curves Elliptic curves Analytic number theory Group theory Diophantine geometry Abelian variety Modular curve Genus of a multiplicative sequence Isogeny Abstract algebra Algebraic geometry Algebra
514	CYCLES OF QUADRATIC POLYNOMIALS AND RATIONAL POINTS ON A GENUS 2 CURVE E. V. FLYNN, BJORN POONEN, AND EDWARD F. SCHAEFER Abstract. It has been conjectured that for N sufficiently large, there are no quadratic polynomials Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Algebraic curves Field theory Analytic number theory Algebraic number theory Vector bundles Elliptic curve Algebraic number field Polynomial Ample line bundle Abstract algebra Algebra Mathematics
515	EXHIBITING SHA[2] ON HYPERELLIPTIC JACOBIANS N. BRUIN AND E.V. FLYNN Abstract. We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves, with an emphasis on the theory and prac Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Niels Henrik Abel Abelian variety Elliptic curve Rational point Abelian group Hyperelliptic curve cryptography Imaginary hyperelliptic curve Abstract algebra Algebraic curves Algebra
516	Heegner points and Sylvester’s conjecture Samit Dasgupta and John Voight Abstract. We consider the classical Diophantine problem of writing positive integers n as the sum of two rational cubes, i.e. n = x3 + y 3 for x, Add to Reading List Source URL: people.ucsc.edu Language: English - Date: 2008-09-13 15:52:13 Algebraic number theory Elliptic curves Number theory Group theory Heegner point Modular form Birch and Swinnerton-Dyer conjecture Prime number Classical modular curve Abstract algebra Mathematics Analytic number theory
517	N -COVERS OF HYPERELLIPTIC CURVES N. BRUIN AND E.V. FLYNN Abstract. For a hyperelliptic curve C of genus g with a divisor class of order n = g + 1, we shall consider an associated covering collection of curves Dδ , each Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Algebraic curves Hyperelliptic curve Elliptic curve Curve Symbol Algebraic number field Imaginary hyperelliptic curve Abstract algebra Geometry Mathematics
518	Journal de Théorie des Nombres de Bordeaux 00 (XXXX), 000–000 Non-trivial X Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2009-08-31 00:19:33 Field theory Group theory Elliptic curves Finite fields Abstract algebra Algebraic number theory Algebraic number field
519	Descent via Isogeny in Dimension 2 E. V. Flynn, Mathematical Institute, University of Oxford Abstract A technique of descent via 4-isogeny is developed on the Jacobian of a curve of genus 2 of the form: Y 2 = q1 (X)q2 (X Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:37 Analytic number theory Algebraic curves Elliptic curve Group theory Symbol Abelian variety Quadratic form Constructible universe Classical modular curve Algebraic geometry Abstract algebra Algebra
520	CANONICAL HEIGHTS ON THE JACOBIANS OF CURVES OF GENUS 2 AND THE INFINITE DESCENT E.V. FLYNN AND N.P. SMART Abstract. We give an algorithm to compute the canonical height on a Jacobian of a curve of genus 2. The computati Add to Reading List Source URL: people.maths.ox.ac.uk Language: English - Date: 2006-07-08 18:57:36 Algebraic number theory Analytic number theory Elliptic curve Group theory Kummer surface Algebraic number field P-adic number Prime number Abstract algebra Mathematics Field theory

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