Results 31 to 40 of about 990 (79)
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
Torsion points with multiplicatively dependent coordinates on elliptic curves
, 2020 In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations.
Barroero, Fabrizio, Sha, Min
core +1 more source
The upper bound estimate of the number of integer points on elliptic curves y2=x3+p2rx
Journal of Inequalities and Applications, 2014 Let p be a fixed prime and r be a fixed positive integer. Further let N(p2r) denote the number of pairs of integer points (x,±y) on the elliptic curve E:y2=x3+p2rx with y>0.
Jin Zhang, Xiaoxue Li
semanticscholar +2 more sources
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
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
An exact upper bound estimate for the number of integer points on the elliptic curves y2=x3−pkx
Journal of Inequalities and Applications, 2014 Let p be a fixed prime and k be a fixed odd positive integer. Further let N(pk) denote the number of pairs of integer points (x,±y) on the elliptic curve E:y2=x3−pkx with y>0.
S. Gou, Xiaoxue Li
semanticscholar +2 more sources
Elliptic curves with torsion group $\Z /6\Z $ [PDF]
, 2015 We exhibit several families of elliptic curves with torsion group isomorphic to $ \Z/6\Z$ and generic rank at least $3$. Families of this kind have been constructed previously by several authors: Lecacheux, Kihara, Eroshkin and Woo.
Dujella, A., Peral, J. C., Tadić, P.
core +3 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
core +1 more source
Average Analytic Ranks of Elliptic Curves over Number Fields
Forum of Mathematics, SigmaWe 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
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