A Functional Equation Originating from Elliptic Curves

A Functional Equation Originating from Elliptic Curves

Elliptic Curves from Sextics

Let N be the moduli space of sextics with 3 (3,4)-cusps. The quotient moduli space N/G is one-dimensional and consists of two components, Ntorus/G and Ngen/G. By quadratic transformations, they are transformed into one-parameter families Cs and Ds of cubic curves respectively. First we study the geometry of Nε/G, ε = torus, gen and their structure of elliptic fibration. Then we study the Mordel...

On Silverman's conjecture for a family of elliptic curves

Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...

Pseudorandom sequences from elliptic curves

In this article we will generalize some known constructions to produce pseudorandom sequences with the aid of elliptic curves. We will make use of both additive and multiplicative characters on elliptic curves.

Elliptic Nets and Elliptic Curves

Elliptic divisibility sequences are integer recurrence sequences, each of which is associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P1, . . . , Pn are points on E defined over K. To this information we associate an ...