Results 21 to 30 of about 2,036 (63)

CODIMENSION TWO CYCLES IN IWASAWA THEORY AND ELLIPTIC CURVES WITH SUPERSINGULAR REDUCTION

Forum of Mathematics, Sigma, 2019
A result of Bleher, Chinburg, Greenberg, Kakde, Pappas, Sharifi and Taylor has initiated the topic of higher codimension Iwasawa theory. As a generalization of the classical Iwasawa main conjecture, they prove a relationship between analytic objects (a ...
ANTONIO LEI, BHARATHWAJ PALVANNAN
doaj   +1 more source

COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES

Forum of Mathematics, Sigma, 2016
Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
doaj   +1 more source

A note on the Mordell-Weil rank modulo n [PDF]

, 2009
Conjecturally, the parity of the Mordell-Weil rank of an elliptic curve over a number field K is determined by its root number. The root number is a product of local root numbers, so the rank modulo 2 is conjecturally the sum over all places of K of a ...
Dokchitser, Tim, Dokchitser, Vladimir
core   +2 more sources

On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1

Proceedings of the London Mathematical Society, Volume 118, Issue 5, Page 1245-1276, May 2019., 2019
Abstract The main result of this paper is to extend from Q to each of the nine imaginary quadratic fields of class number 1 a result of [Serre, Duke Math. J. 54 (1987) 179–230] and [Mestre–Oesterlé, J. reine. angew. Math. 400 (1989) 173–184], namely that if E is an elliptic curve of prime conductor, then either E or a 2‐, 3‐ or 5‐isogenous curve has ...
John Cremona, Ariel Pacetti
wiley   +1 more source

An interesting family of curves of genus 1

International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 6, Page 431-434, 2000., 2000
We study the family of elliptic curves y2 = x3 − t2x + 1, both over ℚ(t) and over ℚ. In the former case, all integral solutions are determined; in the latter case, computation in the range 1 ≤ t ≤ 999 shows large ranks are common, giving a particularly simple example of curves which (admittedly over a small range) apparently contradict the once held ...
Andrew Bremner
wiley   +1 more source

Elliptic curve and k-Fibonacci-like sequence

Scientific African, 2023
In this paper, we will introduce a modified k-Fibonacci-like sequence defined on an elliptic curve and prove Binet’s formula for this sequence. Moreover, we give a new encryption scheme using this sequence.
Zakariae Cheddour, Abdelhakim Chillali, Ali Mouhib   +2 more
doaj  

On the torsion group of elliptic curves induced by D(4)-triples

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014
A D(4)-m-tuple is a set of m integers such that the product of any two of them increased by 4 is a perfect square. A problem of extendibility of D(4)-m-tuples is closely connected with the properties of elliptic curves associated with them. In this paper
Dujella Andrej, Mikić Miljen
doaj   +1 more source

A new family of elliptic curves with positive ranks arising from the Heron triangles [PDF]

, 2010
The aim of this paper is to introduce a new family of elliptic curves with positive ranks. These elliptic curves have been constructed with certain rational numbers, namely a, b, and c as sides of Heron triangles having rational areas $k$.
Izadi, F. A., Khoshnam, Foad, Nabardi, K.   +2 more
core  

Average Analytic Ranks of Elliptic Curves over Number Fields

Forum of Mathematics, Sigma
We give a conditional bound for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a number field K are modular and have L-functions which satisfy the ...
Tristan Phillips
doaj   +1 more source

New Rank Records For Elliptic Curves Having Rational Torsion [PDF]

arXiv, 2020
We present rank-record breaking elliptic curves having torsion subgroups Z/2Z, Z/3Z, Z/4Z, Z/6Z, and Z/7Z.
arxiv