Results 21 to 30 of about 566 (61)
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
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
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
Class number formulas via 2-isogenies of elliptic curves [PDF]
, 2012 A classical result of Dirichlet shows that certain elementary character sums compute class numbers of quadratic imaginary number fields. We obtain analogous relations between class numbers and a weighted character sum associated to a 2-isogeny of ...
McLeman, Cam, Rasmussen, Christopher
core +1 more source
Hyperelliptic curves, continued fractions, and Somos sequences [PDF]
, 2006 We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion.
van der Poorten, Alfred J.
core +3 more sources
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
The yoga of the Cassels-Tate pairing
, 2007 Cassels has described a pairing on the 2-Selmer group of an elliptic curve which shares some properties with the Cassels-Tate pairing.
Brown +7 more
core +2 more sources
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