Results 11 to 20 of about 548 (39)
Transactions of the London Mathematical Society, 2019 Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E over Q when ...
Harris B. Daniels +2 more
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Non‐vanishing theorems for central L‐values of some elliptic curves with complex multiplication
Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1531-1578, December 2020., 2020 Abstract The paper uses Iwasawa theory at the prime p=2 to prove non‐vanishing theorems for the value at s=1 of the complex L‐series of certain quadratic twists of the Gross family of elliptic curves with complex multiplication by the field K=Q(−q), where q is any prime ≡7mod8.
John Coates, Yongxiong Li
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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
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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 +3 more
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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
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COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES
Forum of Mathematics, Sigma, 2016 Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
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Elliptic Curves over Totally Real Cubic Fields are Modular [PDF]
, 2019 We prove that all elliptic curves defined over totally real cubic fields are modular. This builds on previous work of Freitas, Le Hung and Siksek, who proved modularity of elliptic curves over real quadratic fields, as well as recent breakthroughs due to
Derickx, Maarten +2 more
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On Serre's uniformity conjecture for semistable elliptic curves over totally real fields [PDF]
, 2015 Let $K$ be a totally real field, and let $S$ be a finite set of non-archimedean places of $K$. It follows from the work of Merel, Momose and David that there is a constant $B_{K,S}$ so that if $E$ is an elliptic curve defined over $K$, semistable outside
Anni, Samuele, Siksek, Samir
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, 2018 We prove that there exist infinitely many rationals a, b and c with the property that a^2-1, b^2-1, c^2-1, ab-1, ac-1 and bc-1 are all perfect squares.
Dujella, Andrej +3 more
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On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1
Proceedings of the London Mathematical Society, Volume 118, Issue 5, Page 1245-1276, May 2019., 2019 Abstract The main result of this paper is to extend from Q to each of the nine imaginary quadratic fields of class number 1 a result of [Serre, Duke Math. J. 54 (1987) 179–230] and [Mestre–Oesterlé, J. reine. angew. Math. 400 (1989) 173–184], namely that if E is an elliptic curve of prime conductor, then either E or a 2‐, 3‐ or 5‐isogenous curve has ...
John Cremona, Ariel Pacetti
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