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Rational points on elliptic curves John Tate, Joseph H. Silverman
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K

Count the number of minimisations of a genus one curve defined over a Henselian discrete valuation field. For example the supersingular primes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, and 71 are important to moonshine theory as factors of the size of the monster group and as special cases for elliptic curves modulo p. [math.NT/0606003] We consider the structure of rational points on elliptic curves in Weierstrass form. A little more difficult, I really enjoyed Silverman+Tate's Rational Points on Elliptic Curves and Stewart+Tall's Algebraic Number Theory. Here's what this looks like: Image001. Rational Points on Elliptic Curves - Google Books The theory of elliptic curves involves a blend of algebra,. The only rational solution of which is x = 0. Vector bundles over algebraic curves and counting rational points. 5,7 and 11 also have special significance because PSL(2,p) is “exceptional” for these primes. This number depends only on the Kodaira symbol of the Jacobian and on an auxiliary rational point. Home » Book » Elliptic Curves:. Thich corresponds to the points (0,1) and (0,-1) on the elliptic curve. Points on elliptic curves over Q which are not [0:1:0] have their last coordinate =1 but sometimes this is an int (not even an Integer) which breaks some code: sage: E=EllipticCurve('37a1') sage: [type(c) for c in E(0)] [