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- René Schoof
- 1985

In this paper we present a deterministic algorithm to compute the number of F^-points of an elliptic curve that is defined over a finite field Fv and which is given by a Weierstrass equation. The… (More)

- René Schoof
- 1995

- René Schoof
- J. Comb. Theory, Ser. A
- 1987

Abstract We determine the number of projectively inequivalent nonsingular plane cubic curves over a finite field F q with a fixed number of points defined over F q . We count these curves by counting… (More)

It is proved that any finite extension of a finite field has a normal basis consisting of primitive roots. Introduction. Let q be a prime power, q > 1. We denote by F9 a finite field of q elements.… (More)

- René Schoof
- Math. Comput.
- 2003

The class numbers hl+ of the real cyclotomic fields Q(ζl + + ζl+-1) are notoriously hard to compute. Indeed, the number hl+ is not known for a single prime l ≥ 71. In this paper we present a table of… (More)

- René Schoof
- 2008

Shanks's infrastructure algorithm and Buchmann's algorithm for computing class groups and unit groups of rings of integers of algebraic number fields are most naturally viewed as computations inside… (More)

- René Schoof
- 1986

Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für… (More)

- René Schoof
- 1980

To make flashlamps in which the filler material has sharply bent foil shreds, which are buckled, the shreds are sucked through a supply tube by an air flow, preferably of about 3 at and accelerated… (More)

We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and several… (More)

- René Schoof
- 1991

Let E denote an elliptic curve over Q without complex multiplication. It is shown that the exponents of the groups E(F p ) grow at least as fast as \( \frac{{\sqrt {P} \log \;p}}{{{{(\log \;\log… (More)