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18.783 Elliptic Curves Lecture 1Andrew Sutherland The equation x2 b2 = 1 defines an ellipse. Like all conic sections, an ellipse is a curve of genus 0. Elliptic curves have
18.783 Elliptic Curves Lecture 1 Andrew Sutherland February 6, 2019 1 What is an elliptic curve? 2 2 The equation x + y = 1 defines an ellipse. a2 b2 An ellipse, like all…
18783 Elliptic Curves Lecture 1 Andrew Sutherland February 8 2017 What is an elliptic curve The equation x 2 a2 + y2 b2 = 1 defines an ellipse An ellipse like all conic sections…
Math 248B. Modular curves Contents 1. Introduction 1 2. The analytic Weierstrass family 2 3. M -curves and M -groups 4 4. The M -elliptic curve group law 6 5. Relative uniformization…
December 5, 2013 Families of Fast Elliptic Curves from Q-curves Benjamin Smith (INRIA & École polytechnique) E : y2 = x3 + Ax + B an ordinary elliptic curve over Fp,…
18783 Elliptic Curves Lecture #10 Spring 2019 03112019 10 Generic algorithms for the discrete logarithm problem We now consider generic algorithms for the discrete logarithm…
Elliptic curves in the modern age (3rd millennium) Jens Berlips Elliptic curves in the modern age (3rd millennium) Jens Berlips August 21, 2006 Copyright c© 2006 Jens Berlips.…
Modules over the noncommutative torus, elliptic curves and cochain quantization Francesco D’Andrea ( joint work with G. Fiore & D. Franco ) ((A⊗B) ⊗ C) ⊗D (A⊗B)…
Elliptic Curves of Odd Modular Degree Frank Calegari∗ Matthew Emerton† December 17 2007 1 Introduction Let E be an elliptic curve over Q of conductor N Since E is modular…
Elliptic Curves: complex multiplication, application, and generalization Marco Streng General Mathematics Colloquium Vrije Universiteit Amsterdam 17th October 2012 Marco…
Elliptic Curves: complex multiplication, application, and generalization Marco Streng Universiteit Leiden Mathematics Colloquium Universiteit Utrecht 12th December 2013 Marco…
18.783 Elliptic Curves Spring 2013 Lecture #10 03/12/2013 Andrew V. Sutherland 10.1 The discrete logarithm problem In its most standard form, the discrete logarithm problem…
ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION AND Λ-STRUCTURES Lance Rory Gurney July 2015 Thesis submitted for the degree Doctor of Philosophy of the Australian National…
Torsion points on elliptic curves and modular polynomial symmetries Semjon Adlaj CCRAS, Moscow, Russia The joined MSU-CCRAS Computer Algebra Seminar September 24, 2014 �A…
18783 Elliptic Curves Lecture 1 Andrew Sutherland February 3 2015 What is an elliptic curve The equation x 2 a2 + y2 b2 = 1 defines an ellipse An ellipse like all conic sections…
A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations W. Duke∗and E. Kowalski With an appendix by D. Ramakrishnan 1 Introduction…
Elliptic Curves: complex multiplication, application, and generalization Marco Streng Universiteit Leiden Mathematics Colloquium Universiteit Utrecht 12th December 2013 Marco…
SUPERSINGULAR ELLIPTIC CURVES, THETA SERIES AND WEIGHT TWO MODULAR FORMS Matthew Emerton Northwestern University This paper deals with two subjects and their interaction.…
Mahler’s measure and L-functions of elliptic curves at s = 3 David Boyd University of British Columbia SFU-UBC Number Theory Seminar David Boyd (UBC) Mahler measure and…
Supersingular Primes over Zp-extensions of Number Fields June 21, 2005 Abstract In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular