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Elliptic geometry
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261	II. Algebraic Theory of Elliptic Curves In this chapter we sketch the general theory of elliptic curves from an algebraic viewpoint. This material is fairly standard, although some of our proofs may differ from the ones Add to Reading List Source URL: www.math.jussieu.fr Language: English - Date: 2004-09-20 07:25:40 Vector bundles Analytic number theory Elliptic curve Group theory Intersection number Canonical bundle Ample line bundle Combinatory logic Algebraic number field Abstract algebra Algebraic geometry Geometry
262	Journal de Th´eorie des Nombres de Bordeaux[removed]), 663–681 Computing the cardinality of CM elliptic curves using torsion points par Franc Add to Reading List Source URL: almira.math.u-bordeaux.fr Language: English - Date: 2009-01-22 09:21:14 Analytic number theory Polynomials Group theory Algebraic curves Differential geometry Elliptic curve Modular form Jet Resultant Abstract algebra Algebra Mathematics
263	ELLIPTIC FUNCTIONS AND ELLIPTIC CURVES (A Classical Introduction) Jan Nekov´ aˇ r Add to Reading List Source URL: www.math.jussieu.fr Language: English - Date: 2004-09-20 07:25:40 Angle Equations Euclidean plane geometry Pythagorean theorem Triangles Pythagorean triple Complex number Spectral theory of ordinary differential equations Envelope Geometry Mathematics Mathematical analysis
264	MATH CIRCLE - ELLIPTIC CURVES WEEKS 1 & 2 SAM LICHTENSTEIN 1. What is a curve? We started by considering the idea of a curve. This is just the set of points in the plane which satisfy a polynomial equation. For example, Add to Reading List Source URL: www.themathcircle.org Language: English - Date: 2007-10-20 22:29:22 Algebraic curves Diophantine equations Analytic number theory Elliptic curve Group theory Rational point Rational number Curve Infinite descent Mathematics Geometry Abstract algebra
265	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
266	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
267	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
268	Modelling Hyperbolic Geometry Robert D. Borgersen [removed] Supervisor: Dr. William Kocay February 14, 2005 Add to Reading List Source URL: robertborgersen.info Language: English - Date: 2008-10-06 13:34:40 Hyperbolic geometry Absolute geometry Parallel Euclidean geometry Axiom Line Triangle Elliptic geometry Dehn planes Geometry Elementary geometry Non-Euclidean geometry
269	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
270	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

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