On the modularity of elliptic curves over q

Author: vjdo

August undefined, 2024

WebEvery elliptic curve over Q can be written in the form y 2 = x 3 + a x + b where a, b ∈ Z with discriminant Δ = − 16 ( 4 a 3 + 27 b 2) ≠ 0. So the number of elliptic curves of discriminant D is bounded above by number of nontrivial pairs ( a, b) ∈ Z 2 such that D = − 16 ( 4 a 3 + 27 b 2). Let D ∈ Z, D ≠ 0 be given. WebMODULARITY OF ELLIPTIC CURVES 2 The Modularity Theorem is known to hold today without the semistability as-sumption: every elliptic curve over Q is modular. In this form it apparently origi-nated as a conjecture in 1955 and became known as the Shimura-Taniyama-Weil 2 conjecture. It later became clear that it is an instance of the much more …

The modularity of elliptic curves over all but finitely many totally ...

WebWe study mirror symmetric pairs of Calabi--Yau manifolds over finite fields. In particular we compute the number of rational points of the manifolds as a function of ... http://sweet.ua.pt/apacetti/papers/Mod.pdf how to take leech off ark

PROVING MODULARITY FOR A GIVEN ELLIPTIC CURVE OVER …

WebKey words: elliptic curves, modular forms, Q-curves. Let E be an elliptic curve deﬁned over Q and without complex multiplication. is called a Q-curve if it is isogenous to each … Web25 de jan. de 2024 · Abstract: In this paper, we establish the modularity of every elliptic curve $E/F$, where $F$ runs over infinitely many imaginary quadratic fields, including … WebElliptic Curves over Finite Fields elliptic curves over finite fields in the previous section we developed the theory of elliptic curves geometrically. for. Skip to document. Ask an … how to take length in sql

Finiteness of elliptic curves of a given conductor - MathOverflow

18.783 Elliptic Curves Spring 2013 Lecture #25 05/14/2013

WebLet E be a [modular] elliptic curve over Q of prime conductor p. Then there is an elliptic curve E0=Q isogenous to E with minimal discriminant E0= p. Remarks: I Serre’s result was conditional on his conjecture on modularity of Galois representations (now a Theorem) I Mestre and Oesterle made the result conditional ‘only’ on´ WebKaneko and Sakai [11] recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be … ready to be used meaningWebBreuil, Christophe, Brian Conrad, Fred Diamond, and Richard L. Taylor. 2001. On the modularity of elliptic curves over Q: Wild 3-adic exercises. Journal of the American … how to take levitra 20 mg 1.2

"WebWintenberger [11, Theorem 9.1], we now know that modularity of an abelian variety over Q is equivalent to the property of being of GL 2-type. The abelian varieties of GL 2-type are not absolutely simple in general: they factor up to ... all elliptic curves over Q are strongly modular. Over number elds all CM elliptic curves are modular, and Elkies " - On the modularity of elliptic curves over q

On the modularity of elliptic curves over q

(PDF) On the modularity of elliptic curves over the cyclotomic ...

Web15 de mai. de 2001 · Pairs of mod~3 and mod~5 representations arising from elliptic curves. For an elliptic curve E0 over Q , we study the mod 3 representations, … WebAn elliptic curve E over a number field K is said to be potentially modular if there is a finite extension L / K such that E becomes modular over L. This notion of potential modularity has been much studied by Richard Taylor and his coauthors, and turns out to be almost as good for most purposes as knowing modularity over K.

Did you know?

Web4 de nov. de 2014 · 1.1 Summary of results. One of the great achievements of modern number theory is the proof by Breuil, Conrad, Diamond and Taylor [] of the … Web11 de abr. de 2024 · Download a PDF of the paper titled Ideal class groups of division fields of elliptic curves and everywhere unramified rational points, by Naoto Dainobu

Web27 de out. de 2000 · Elliptic functions and equations of modular curves. Lev Borisov, Paul Gunnells, Sorin Popescu. Let be a prime. We show that the space of weight one … Web=Qis an elliptic curve, then Eis modular. Theorem B. If ˆ : Gal(Q=Q) !GL 2(F 5) is an irreducible continuous representation with cyclotomic determinant, then ˆis modular. We …

Webelliptic curves over Q(√ 2) and Q(√ 17), and there are various other works [1], [26], which establish modularity under local assumptions on the curve Eand the ﬁeld K. In this paper, we prove modularity of all elliptic curves over all real quadratic ﬁelds. Theorem 1. Let Ebe an elliptic curve over a real quadratic ﬁeld K. Then Eis modular. WebN2 - A Q-curve is an elliptic curve over a number field K which is geometrically isogenous to each of its Galois conjugates. K. Ribet [17] asked whether every Q-curve is modular, …

Web17 de jan. de 2024 · The method is to use some automorphy lifting theorems and study non-cusp points on some specific elliptic curves by Iwasawa theory for elliptic curves. Since … ready to be offeredWebOn the modularity of elliptic curves over $\mathbf{Q}$: Wild $3$-adic exercises. By Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor. Abstract. We … how to take legal action against scammersWeb19 de mai. de 2024 · ON THE MODULARITY OFELLIPTIC CURVES OVER THE CYCLOTOMIC Zp-EXTENSION OF SOMEREAL QUADRATIC FIELDS XINYAO ZHANG Abstract. The modularity of ellipticcurves always intrigues number... ready to be on boardhttp://math.stanford.edu/~conrad/ ready to be richWebOf course, the themes Lozano-Robledo addresses in Elliptic Curves, Modular Forms, and Their L-Functions are deep and sophisticated; considerable mathematical background is … ready to be sentWebIn this paper, we establish the modularity of every elliptic curve E/F, where Fruns over inﬁnitely many imaginary quadratic ﬁelds, including Q(√ −d) for d= 1,2,3,5. Recall that the modular curve X0(15) is an elliptic curve of rank zero over Q– it is the curve with … ready to be picked crosswordWeb24 de nov. de 2016 · Then, any elliptic curve over K is modular. A number of developments of modularity lifting theorems enable us to prove that elliptic curves with … how to take legal action against nhs