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

E is just a set of points fulfilling an equation that is quadratic in terms of y and cubic in x . Buy Book Elliptic Curves: Number Theory and Cryptography. The two groups G_1 and G_2 correspond to subgroups of K -rational points E(K) of an elliptic curve E over a finite field K with characteristic q different from p . Order of a pole is similar: b is a pole of order n if n is the largest integer, such that r(x)=\frac{s(x)}{(x-b . If you're interested in algebraic geometry from an elementary point of view, Tate and Silverman's Rational Points on Elliptic Curves is also worth checking out. What we now know as the Hasse-Weil theorem implies that the number N(p) of rational points of an elliptic curve over the finite field Z/pZ, where p is a prime, can differ from the mean value p+1 by at most twice the square root of p. [math.NT/0606003] We consider the structure of rational points on elliptic curves in Weierstrass form. Home » Book » Elliptic Curves:. Akhil Mathew - August 17, 2009. The most general definition of an elliptic curve, is. By introducting a special point O (point is a rational function. Theorem 5 (on page vi) of Diem's thesis states that the discrete logarithm problem in the group of rational points of an elliptic curves E( F_{p^n} ) can be solved in an expected time of \tilde{O}( q^{2 – 2/n} ) bit operations. Rational Points on Elliptic Curves - Google Books The theory of elliptic curves involves a blend of algebra,. Are (usually) three distinct groups of prime order p .