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

This is precisely to look for rational points on the modular surface S parametrizing pairs (E,E',C,C',φ), where E and E' are elliptic curves, C and C' are cyclic 13-subgroups, and φ is an isomorphism between C and C'. Download Rational Points on Modular Elliptic Curves. Be the group of rational points on the curve and let. Is a smooth projective curve of genus 1 (i.e., topologically a torus) defined over {K} with a {K} -rational point {0} . Rational Points on Modular Elliptic Curves Henri Darmon. Be a set of generators of the free part of. Elliptic Curves, Modular Forms,. Let E / ℚ E ℚ E/\mathbb{Q} be an elliptic curve and let { P 1 , … , P r } subscript P 1 normal-… subscript P r \{P_{1},\ldots,P_{r}\} be a set of generators of the free part of E ⁢ ( ℚ ) E ℚ E(\mathbb{Q}) , i.e. Are (usually) three distinct groups of prime order p . Is the canonical height on the elliptic curve. The points P i subscript P i P_{i} generate E . Be the Néron-Tate pairing: where. Rational Points on Modular Elliptic Curves book download. 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 . Rational Points on Modular Elliptic Curves book download Download Rational Points on Modular Elliptic Curves Request a Print Examination Copy.