Elements of order 4 of the Hilbert kernel in quadratic number fields
Elements of Quaternions [Book]
Elimination theory for the ring of algebraic integers.
Elliptic Carmichael numbers and elliptic Korselt criteria
Elliptic curves and class fields of real quadratic fields: Algorithms and evidence.
Elliptic curves and continued fractions.
Elliptic curves and local -factors
Elliptic curves and -extensions
Elliptic curves and special values of L-series.
Elliptic curves associated with simplest quartic fields
We are studying the infinite family of elliptic curves associated with simplest cubic fields. If the rank of such curves is 1, we determine the whole structure of the Mordell-Weil group and find all integral points on the original model of the curve. Note however, that we are not able to find them on the Weierstrass model if the parameter is even. We have also obtained similar results for an infinite subfamily of curves of rank 2. To our knowledge, this is the first time that so much information...
Elliptic curves of high rank with nontrivial torsion group over .
Elliptic curves over function fields with a large set of integral points
We construct isotrivial and non-isotrivial elliptic curves over with an arbitrarily large set of separable integral points. As an application of this construction, we prove that there are isotrivial log-general type varieties over with a Zariski dense set of separable integral points. This provides a counterexample to a natural translation of the Lang-Vojta conjecture to the function field setting. We also show that our main result provides examples of elliptic curves with an explicit and arbitrarily...
Elliptic curves with and counterexamples to local-global divisibility by 9
We give a family of elliptic curves, depending on two nonzero rational parameters and , such that the following statement holds: let be an elliptic curve and let be its 3-torsion subgroup. This group verifies if and only if belongs to .Furthermore, we consider the problem of the local-global divisibility by 9 for points of elliptic curves. The number 9 is one of the few exceptional powers of primes, for which an answer to the local-global divisibility is unknown in the case of such...
Elliptic curves with a rational point of finite order.
Elliptic curves with all quadratic twists of positive rank
Elliptic curves with bounded ranks in function field towers
Elliptic curves with complex multiplication and Galois module structure.
Elliptic Curves With Complex Multiplication and the Conjecture of Birch and Swinnerton-Dyer.
Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.
Let p be a prime number, p ≠ 2,3 and Fp the finite field with p elements. An elliptic curve E over Fp is a projective nonsingular curve of genus 1 defined over Fp. Each one of these curves has an isomorphic model given by an (Weierstrass) equation E: y2 = x3 + Ax + B, A,B ∈ Fp with D = 4A3 + 27B2 ≠ 0. The j-invariant of E is defined by j(E) = 1728·4A3/D.The aim of this note is to establish some results concerning the cardinality of the group of points on elliptic curves over Fp with j-invariants...
Elliptic curves with non-trivial 2-adic Iwasawa μ-invariant