Results 11 to 20 of about 51 (50)
L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces
Bulletin of the London Mathematical Society, Volume 52, Issue 2, Page 395-409, April 2020., 2020 Abstract We construct non‐trivial L‐equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L‐equivalence for curves (necessarily over non‐algebraically closed fields) and provide a new bit of evidence for the conjectural relationship between L ...
Evgeny Shinder, Ziyu Zhang
wiley +1 more source
GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS
Forum of Mathematics, Sigma, 2019 Given an elliptic curve $E$ over $\mathbb{Q}$, a celebrated conjecture of Goldfeld asserts that a positive proportion of its quadratic twists should have analytic rank 0 (respectively 1).
DANIEL KRIZ, CHAO LI
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STARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE
Forum of Mathematics, Pi, 2015 Let $E$ be an elliptic curve over $\mathbb{Q}$, and let ${\it\varrho}_{\flat }$ and ${\it\varrho}_{\sharp }$ be odd two-dimensional Artin representations for which ${\it\varrho}_{\flat }\otimes {\it\varrho}_{\sharp }$ is self-dual.
HENRI DARMON, ALAN LAUDER, VICTOR ROTGER
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Nonlinearities on particular elliptic curves subspaces and applications
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 Researching on mathematical models for cryptography means to, primary, define the optimal spaces and rules for which we can archive the maximum time to find the involved parameters of the keys and, in the same time, to optimise the time for key ...
Alsaedi Ramzi +2 more
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Growth of torsion groups of elliptic curves upon base change
, 2020 We study how the torsion of elliptic curves over number fields grows upon base change, and in particular prove various necessary conditions for torsion growth.
Najman, Filip +1 more
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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
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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
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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
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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
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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
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