Overview of the SEA algorithm for computing cardinality of elliptic curves over finite fields.
Archive of posts filed under the Algebraic Geometry category.
A less very, very stupid way of counting points on elliptic curves
Sidestepping brute-force determination of the number of points over a finite field by construction of zeta functions.
Small defect types in Maple
Maple procedures for finding polynomials of a given trace and degree; hence for establishing the possible types of zeta function for small defect.
Rational points of curves over finite fields
Overview of a number-theoretic procedure to characterise zeta functions of curves over finite fields.
Elliptic Divisibility Sequences
EDS, their connection to elliptic curves and Maple procedures for working with them.
Curves with large Szpiro ratios
Number crunching on elliptic curves in search of high values of the Szpiro ratio.
As easy as abc
The abc conjecture and its connection to elliptic curves.
The Torsion subgroup of an Elliptic Curve
Yet more Maple code, this time for finding/classifying torsion points of an elliptic curve.
Implementing the Group Law Algorithm in Maple- finite fields
Extension of Maple code to finite fields.
Implementing the Group Law Algorithm in Maple- Examples
Sample problems from Silverman on the Elliptic curve group law.
