Results 11 to 20 of about 990 (79)

Orienting supersingular isogeny graphs

Journal of Mathematical Cryptology, 2020
We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs.
Colò Leonardo, Kohel David
doaj   +1 more source

Models of hyperelliptic curves with tame potentially semistable reduction

Transactions of the London Mathematical Society, Volume 7, Issue 1, Page 49-95, December 2020., 2020
Abstract Let C be a hyperelliptic curve y2=f(x) over a discretely valued field K. The p‐adic distances between the roots of f(x) can be described by a completely combinatorial object known as the cluster picture. We show that the cluster picture of C, along with the leading coefficient of f and the action of Gal(K¯/K) on the roots of f, completely ...
Omri Faraggi, Sarah Nowell
wiley   +1 more source

Different approach on elliptic curves mathematical models study and their applications

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
In a research project in which a group of mathematical researchers is involved, it was necessary to create a system of nonlinear equations defined over a particular nonsupersingular elliptic space.
Alsaedi Ramzi, Dhifli Abdelwahab, Ghanmi Abdeljabbar   +2 more
doaj   +1 more source

Conductor and discriminant of Picard curves

Journal of the London Mathematical Society, Volume 102, Issue 1, Page 368-404, August 2020., 2020
Abstract We describe normal forms and minimal models of Picard curves, discussing various arithmetic aspects of these. We determine all so‐called special Picard curves over Q with good reduction outside 2 and 3, and use this to determine the smallest possible conductor a special Picard curve may have.
Irene I. Bouw, Angelos Koutsianas, Jeroen Sijsling, Stefan Wewers   +3 more
wiley   +1 more source

Torsion subgroups of rational Mordell curves over some families of number fields

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022
Mordell curves over a number field K are elliptic curves of the form y2 = x3 + c, where c ∈ K \ {0}. Let p ≥ 5 be a prime number, K a number field such that [K : ℚ] ∈ {2p, 3p}.
Gužvić Tomislav, Roy Bidisha
doaj   +1 more source

L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces

Bulletin of the London Mathematical Society, Volume 52, Issue 2, Page 395-409, April 2020., 2020
Abstract We construct non‐trivial L‐equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L‐equivalence for curves (necessarily over non‐algebraically closed fields) and provide a new bit of evidence for the conjectural relationship between L ...
Evgeny Shinder, Ziyu Zhang
wiley   +1 more source

Base change for Elliptic Curves over Real Quadratic Fields [PDF]

, 2014
Let E be an elliptic curve over a real quadratic field K and F/K a totally real finite Galois extension. We prove that E/F is modular.Comment: added a short proof of Proposition 2.1 and a few more small changes to improve ...
Dieulefait, Luis, Freitas, Nuno
core   +4 more sources

Right triangles with algebraic sides and elliptic curves over number fields [PDF]

, 2009
Given any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem.
Girondo, Ernesto, Gonzalez-Diez, Gabino, Gonzalez-Jimenez, Enrique, Steuding, Jorn, Steuding, Rasa   +4 more
core   +3 more sources

Toroidal and Annular Dehn Fillings [PDF]

, 1997
Suppose that M is a hyperbolic 3‐manifold which admits two Dehn fillings M(r1) and M(r2) such that M(r1) contains an essential annulus, and M(r2) contains an essential torus. It is known that Δ = Δ (r1, r2) ⩽ 5.
C. Gordon, Ying‐Qing Wu
semanticscholar   +1 more source

GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS

Forum of Mathematics, Sigma, 2019
Given an elliptic curve $E$ over $\mathbb{Q}$, a celebrated conjecture of Goldfeld asserts that a positive proportion of its quadratic twists should have analytic rank 0 (respectively 1).
DANIEL KRIZ, CHAO LI
doaj   +1 more source