Results 61 to 70 of about 4,714,881 (83)
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 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
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
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
, 2008 The first part of the paper gives a new proof of self-duality for Selmer groups: if A is an abelian variety over a number field K, and F/K is a Galois extension with Galois group G, then the Q_pG-representation naturally associated to the p-infinity ...
Grothendieck +6 more
core +2 more sources
When are Multiples of Polygonal Numbers again Polygonal Numbers?
, 2018 Euler showed that there are infinitely many triangular numbers that are three times other triangular numbers. In general, it is an easy consequence of the Pell equation that for a given square-free m > 1, the relation P=mP' is satisfied by infinitely ...
Chahal, Jasbir S. +2 more
core +1 more source
Sums of two biquadrates and elliptic curves of rank $\geq 4$ [PDF]
, 2012 If an integer $n$ is written as a sum of two biquadrates in two different ways, then the elliptic curve $y^2=x^3-nx$ has rank $\geq 3$. If moreover $n$ is odd and the parity conjecture is true, then it has even rank $\geq 4$.
Izadi, F. A., Khoshnam, F., Nabardi, K.
core
On the Mordell-Weil lattice of y 2 = x 3 + b x + t 3 n + 1 in characteristic 3. [PDF]
Res Number Theory, 2022 Leterrier G.
europepmc +1 more source
Orienteering with One Endomorphism. [PDF]
Mathematica (N Y), 2023 Arpin S +5 more
europepmc +1 more source
MULTIPLICATIVE SUBGROUPS OF J0(N) AND APPLICATIONS TO ELLIPTIC CURVES
Journal of the Institute of Mathematics of Jussieu, 2005 V. Vatsal
semanticscholar +1 more source