About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 55. Chapters: Elliptic curves, Theta functions, Schoof's algorithm, Jacobian curve, Abelian variety, Hessian form of an elliptic curve, Counting points on elliptic curves, Period mapping, Montgomery curve, Tripling-oriented Doche-Icart-Kohel curve, Timeline of abelian varieties, Metaplectic group, Twisted Edwards curve, Sato-Tate conjecture, Doubling-oriented Doche-Icart-Kohel curve, Congruent number, Complex multiplication, Dual abelian variety, Twisted Hessian curves, Theta representation, Abelian integral, Table of costs of operations in elliptic curves, Arithmetic of abelian varieties, Tate module, Supersingular elliptic curve, Equations defining abelian varieties, Tate's algorithm, Jacobi triple product, Picard group, Weil pairing, Poncelet's porism, Elliptic curve primality proving, Schottky problem, Theta divisor, Mordell-Weil theorem, Heegner point, Abelian variety of CM-type, Theta characteristic, Jacobian variety, Semistable abelian variety, Twists of curves, Albanese variety, Jacobi theta functions, Nagell-Lutz theorem, Prym variety, Conductor of an abelian variety, Riemann form, Ramanujan theta function, Torelli theorem, Fourier-Mukai transform, Coble hypersurface, Complex torus, Appell-Humbert theorem, Jacobi form, Eisenstein ideal, Lemniscatic elliptic function, Equianharmonic, Bogomolov conjecture, Modular elliptic curve, Q-theta function, J-line, Kummer variety. Excerpt: In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety - that is, it has a multiplication defined algebraically with respect to which it is a (necessarily commutative) group - and O serves as the identity element. Often the curve itself, without O specified, is called an elliptic curve. Any elliptic curve can be written as a plan...
