Mon premier blog

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

Here's what this looks like: Image001. The problem is therefore reduced to proving some curve has no rational points. Thich corresponds to the points (0,1) and (0,-1) on the elliptic curve. The first proposition is that an elliptic curve $y^2 = x^3 + A x + B$, with $A,B \in Z$, $A \geq 0$, cannot contain a rational torsion point of order 5 or 7. Whose rational points are precisely isomorphism classes of elliptic curves over {{\mathbb Q}} together with a rational point of order 13. Silverman, Joseph H., Tate, John, Rational Points on Elliptic Curves, 1992 63. An upper bound is established for certain exponential sums on the rational points of an elliptic curve over a residue class ring ZN , N=pq for two distinct odd primes p and q. Devlin, Keith, The Joy of Sets – Fundamentals of Contemporary Set Theory, 1993 64. 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'. Then there is a constant B(d) depending only on d such that, if E/K is an elliptic curve with a K -rational torsion point of order N , then N < B(d) . Position: Location: Field of Science: Science - Math - Number Theory - Elliptic Curves and Modular Forms. From the formula for doubling a point we get that. Kinsey, L.Christine, Topology of Surfaces, 1993 65. The only rational solution of which is x = 0. Graphs of curves y2 = x3 − x and y2 = x3 − x + 1. Website / Blog: www.math.rutgers.edu/~tunnell/math574.html. Name: Institution: Rational Points on Elliptic Curves. Theorem (Uniform Boundedness Theorem).Let K be a number field of degree d . In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O.