This construction enables us to prove some results on the maximum number of rational points on an absolutely ir- reducible projective algebraic curve defined over F q of

Alp Bassa, Elisa Lorenzo García, Christophe Ritzenthaler and René Schoof.. Documents Mathématiques série dirigée par

The minimum and maximum number of rational points on jacobian surfaces over finite fields..

Instead of considering elliptic curves over number fields of degree d, one might consider abelian varieties over Q of dimension d.. Restriction of scalars a la Weil

bound for the number of rational points on irreducible (possibly singular or non-absolutely irreducible) curves lying on an abelian surface over a finite

Although the method we develop here can be applied to any toric surface, this paper solely focuses on the projective plane and Hirzeburch surfaces, which are the only minimal

Rational torsion points on elliptic curves over number fields (after Kamienny and Mazur). S´eminaire

Some of these bounds turn out to be asymptotically optimal when g → ∞ , meaning that they converge to the lower bound from the generalized Brauer–Siegel theorem for function

In this paper, the word curve stands for a reduced abso- lutely irreducible algebraic projective curve defined over the finite field I~q with q elements.. The

If it is the case, the corresponding isogeny class contains the product of elliptic curves of trace −m and these curves have q+1+m ≥ 3+1+3 = 7 rational points, thus at least

Toute utilisation commer- ciale ou impression systématique est constitutive d’une infraction pénale.. Toute copie ou impression de ce fichier doit contenir la présente mention

Kenku, Rational torsion points on elliptic curves defined over quadratic fields,

There are many other studies of the Galois images associated to elliptic curves over number fields or rational points on modular curves in [2,4,6,7,10-17,19,21].. Several

The conclusion is that rational points usually arise from cusps or elliptic curves with complex multiplication.. There are a finite number of

In this section we explain how to count the number of points on an elliptic curve .E, when the endomorphism ring of E is known.. In this case there is an extremely

Rene Schoof gave a polynomial time algorithm for counting points on elliptic curves i.e., those of genus 1, in his ground-breaking paper [Sch85].. Subsequent improvements by Elkies

We use an algorithm which, for a given genus g and a given field size q, returns the best upper order Weil bound for the number of F q -rational points of a genus g curve, together

The distribution of the number of points modulo an integer on elliptic curves over finite fields.. Wouter Castryck and Hendrik Hubrechts January