39 citations · 80 across the 5 of their papers we have counts for
6 papers
Large Algebraic Integers
Denis Simon, Lea Terracini
An algebraic integer is said large if all its real or complex embeddings have absolute value larger than . An integral ideal is said \emph{large} if it admits a large generator.…
Computing the trace of an algebraic point on an elliptic curve
Nicolas Mascot, Denis Simon
We present a simple and efficient algorithm to compute the sum of the algebraic conjugates of a point on an elliptic curve.
Plane Curves With Minimal Discriminant
Denis Simon, Martin Weimann
We give lower bounds for the degree of the discriminant with respect to y of separable polynomials f in K[x,y] over an algebraically closed field of characteristic zero. Depending…
Explicit n-descent on elliptic curves. III. Algorithms
John Cremona, Tom Fisher, Cathy O'Neil +2
This is the third in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as curves of degree n in P^{n-1}. The m…
Explicit n-descent on elliptic curves, II. Geometry
John Cremona, Tom Fisher, Cathy O'Neil +2
This is the second in a series of papers in which we study the n-Selmer group of an elliptic curve. In this paper, we show how to realize elements of the n-Selmer group explicitly…
Explicit n-descent on elliptic curves, I. Algebra
John Cremona, Tom Fisher, Cathy O'Neil +2
This is the first in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as genus one normal curves of degree n.…