Results 21 to 30 of about 548 (39)
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
Criteria for irreducibility of mod p representations of Frey curves [PDF]
, 2014 Let K be a totally real Galois number field and let A be a set of elliptic curves over K. We give sufficient conditions for the existence of a finite computable set of rational primes P such that for p not in P and E in A, the representation on E[p] is ...
Freitas, Nuno, Siksek, Samir
core +3 more sources
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
Upper bound for the height of S-integral points on elliptic curves [PDF]
, 2012 We establish new upper bounds for the height of the S-integral points of an elliptic curve. This bound is explicitly given in terms of the set S of places of the number field K involved, but also in terms of the degree of K, as well as the rank, the ...
Bosser, Vincent, Surroca, Andrea
core +4 more sources
Figurate primes and Hilbert's 8th problem
, 2014 In this paper, by using the theory of elliptic curves, we discuss several Diophantine equations related with the so-called figurate primes. Meanwhile, we raise several conjectures related with figurate primes and Hilbert's 8th problem, including Goldbach'
Cai, Tianxin +2 more
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On the rank of the fibers of elliptic K3 surfaces [PDF]
, 2013 Let $X$ be an elliptic K3 surface endowed with two distinct Jacobian elliptic fibrations $\pi_i$, $i=1,2$, defined over a number field $k$. We prove that there is an elliptic curve $C\subset X$ such that the generic rank over $k$ of $X$ after a base ...
Salgado, Cecilia
core
On the Euler characteristics of signed Selmer groups
, 2019 Let $p$ be an odd prime number, and $E$ an elliptic curve defined over a number field with good reduction at every prime of $F$ above $p$. In this short note, we compute the Euler characteristics of the signed Selmer groups of $E$ over the cyclotomic ...
Ahmed, Suman, Lim, Meng Fai
core +1 more source
Constructing families of moderate-rank elliptic curves over number fields [PDF]
, 2017 We generalize a construction of families of moderate rank elliptic curves over $\mathbb{Q}$ to number fields $K/\mathbb{Q}$. The construction, originally due to Steven J.
Mehrle, David +4 more
core
On the largest element in D(n)-quadruples
, 2019 Let $n$ be a nonzero integer. A set of nonzero integers $\{a_1,\ldots,a_m\}$ such that $a_ia_j+n$ is a perfect square for all $1\leq ...
Dujella, Andrej, Petričević, Vinko
core +1 more source
CM relations in fibered powers of elliptic families
, 2017 Let $E_\lambda$ be the Legendre family of elliptic curves. Given $n$ linearly independent points $P_1,\dots , P_n \in E_\lambda\left(\overline{\mathbb{Q}(\lambda)}\right)$ we prove that there are at most finitely many complex numbers $\lambda_0$ such ...
André +10 more
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