Supersingular primes for elliptic curves over real number fields

Noam D. Elkies

Displaying similar documents to “Supersingular primes for elliptic curves over real number fields”

Counting points on elliptic curves over finite fields

René Schoof (1995)

Journal de théorie des nombres de Bordeaux

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We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large ; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic...

Prime divisors of Lucas sequences

Pieter Moree, Peter Stevenhagen (1997)

Acta Arithmetica

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Artin's primitive root conjecture for quadratic fields

Hans Roskam (2002)

Journal de théorie des nombres de Bordeaux

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Fix an element $α$ in a quadratic field $K$ . Define $S$ as the set of rational primes $p$ , for which $α$ has maximal order modulo $p$ . Under the assumption of the generalized Riemann hypothesis, we show that $S$ has a density. Moreover, we give necessary and sufficient conditions for the density of $S$ to be positive.

A problem of Erdös concerning power residue sums.

P. Elliott (1967)

Acta Arithmetica

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Class number parity of a compositum of five quadratic fields

Michal Bulant (2002)

Acta Mathematica et Informatica Universitatis Ostraviensis

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A class of diophantine equations connected with certain elliptic curves over $Q (\sqrt{- 13})$

R. J. Stroeker (1979)

Compositio Mathematica

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An application of dihedral fields to representations of primes by binary quadratic forms

Pierre Kaplan, Kenneth Williams, Yoshihiko Yamamoto (1984)

Acta Arithmetica

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On the 2-primary part of K₂ of rings of integers in certain quadratic number fields

A. Vazzana (1997)

Acta Arithmetica

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1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of $K ₂_{E}$ . For quadratic fields whose discriminant has arbitrarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form $ℚ (\sqrt (p ₁ . . . p_{k}))$ , where the primes $p_{i}$ are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrelbrink which examines under what conditions the 4-rank of $K ₂_{E}$ is zero for such fields. In the course...

Fundamental domains for Shimura curves

David R. Kohel, Helena A. Verrill (2003)

Journal de théorie des nombres de Bordeaux

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We describe a process for defining and computing a fundamental domain in the upper half plane $ℋ$ of a Shimura curve $X_{0}^{D} (N)$ associated with an order in a quaternion algebra $A / 𝐐$ . A fundamental domain for $X_{0}^{D} (N)$ realizes a finite presentation of the quaternion unit group, modulo units of its center. We give explicit examples of domains for the curves $X_{0}^{6} (1), X_{0}^{15} (1), and X_{0}^{35} (1)$ . The first example is a classical example of a triangle group and the second is a corrected version of that appearing in the book of Vignéras [13], due...