[PDF] Top 20 Elliptic curves and primality proving
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Elliptic curves and primality proving
... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ... Voir le document complet
44
Constructing elliptic curves over finite fields using double eta-quotients
... decades, elliptic curves over finite fields have become an important ingredient for different number theoretic ...the primality of an integer [13, ...construct curves whose orders satisfy ... Voir le document complet
15
A formalization of elliptic curves for cryptography
... ciphers and hash functions, the algorithm is the ...to proving the equivalence between a concrete program written for some platform and an abstract program given in the standard ...inspection ... Voir le document complet
127
Elliptic dimers on minimal graphs and genus 1 Harnack curves
... Fock’s elliptic weights ...thus proving a non-trivial extension of the genus 0 results of [Ken02, KO06] on isora- dial critical ...inverses, and describe the phase diagram of the model by deriving ... Voir le document complet
72
A note on integral points on elliptic curves
... Zagier and Elkies, of finding large integral points on elliptic ...solution and equating coefficients, we are led to suspect four extremal cases that still might have nonde- generate ...resultants ... Voir le document complet
15
Iwasawa theory for elliptic curves over imaginary quadratic fields
... Selpoo and Epoo) are equal. Thus, the results of Green- berg recalled in the proof of theorem 3.1 imply that for supersingular primes the A-rank of is always at least 2. We now turn to consider primes p of good ... Voir le document complet
26
A quantitative primitive divisor result for points on elliptic curves
... Landau and Serre. The type of elliptic divisibility sequence used in their result is a slight variant of the typical sequences considered, but their conjecture is stated for conventional elliptic ... Voir le document complet
27
Rational Equivalences on Products of Elliptic Curves in a Family
... of curves, as will be discussed in Section ...1 curves over U (Q) with S = 1, from which we obtain approximately 7 · 10 8 nontrivial clean pairs of rank 1 ... Voir le document complet
17
No $17$-torsion on elliptic curves over cubic number fields
... and may be 17}. (Actually in loc. cit. we made for some p’s the arithmetic assumption (called (*)~, there) that J1 (p)’s winding quotient has rank 0 over Q. This is now known to be true for every p, by Kato’s ... Voir le document complet
9
Good reduction of elliptic curves over imaginary quadratic fields
... an elliptic curve having good reduction everywhere satisfies the following conditions for every discrete valuation v of the ring of integers of k (see [2, ... Voir le document complet
10
Integral points on a certain family of elliptic curves
... Bombieri and Schmidt’s result in [3], where they showed that if N n is an upper bound for the number of solutions to the equations F (x, y) = 1, as F (x, y) varies over irreducible binary forms of degree n with ... Voir le document complet
22
Isogenies of elliptic curves over function fields
... for elliptic curves over number fields: inspired by classical work of Faltings and Silverman, Theorem ...two elliptic curves E 1, E2 defined over Q which are linked by an isogeny ϕ ... Voir le document complet
25
Equivalences between elliptic curves and real quadratic congruence function fields
... Note that Theorem 4.2 is also very important for the proof of this the- orem. For real quadratic congruence function fields of higher genus, there exists no direct relation between 6i = 6(ti) and i. We state the ... Voir le document complet
22
Explicit $L$-functions and a Brauer–Siegel theorem for Hessian elliptic curves
... upper and lower bounds that are enough to ensure that ...the curves Ed and we compute the relevant invari- ants: height, conductor, torsion subgroup and Tamagawa ...notation and tools ... Voir le document complet
27
Merel's theorem on the boundedness of the torsion of elliptic curves
... This will give a contradiction. 3 Two key facts make it possible to follow this strategy: first, there is a presen- tation of H 1 (X; Z) by generators and relations due to Manin [Man72] (see the section 3.3); ... Voir le document complet
15
$S$-integral points on elliptic curves - Notes on a paper of B. M. M. de Weger
... in elliptic logarithms due to David [2] and for linear forms in at most two q-adic elliptic logarithms due to Rémond and Urfels [6] one obtains the upper bound for N(P) analogously as ... Voir le document complet
10
On the cyclic torsion of elliptic curves over cubic number fields (II)
... third column list the dimension d i and multiplicity m i of each A i (we omit m i if m i = 1). The fourth column verifies non-vanishing of L-series at 1 (a mark T means L(A i , 1) 6= 0 is verified, otherwise we ... Voir le document complet
9
On uniform lower bound of the Galois images associated to elliptic curves
... regard elliptic curves as rational points on modular curves, and reduce Theorem ...an elliptic curve E/K does not satisfy ρ E,p (G K ) ⊇ (1 + p n(p) M 2 (Z p )) det=1 ... Voir le document complet
22
Counting elliptic curves of bounded Faltings height
... Silverman [341 has shown that the Faltings height for elliptic curves over number fields can be expressed in terms of the minimal discriminant and period of the ellip[r] ... Voir le document complet
50
Generalizations of monsky matrices for elliptic curves in legendre form
... those curves and use the matrices to find new results both on the generalized curves as well as on the congruent number ...an elliptic curve in Legendre ...columns and rows depend on ... Voir le document complet
146
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