We show that there is a bound depending only on g, r and [K: Q] for the number of K-rational
points on a hyperelliptic curve C of genus g over a number field K such that the Mordell–Weil …

Let X be a curve of genus g≥ 2 over a number field F of degree d=[F: Q]. The conjectural
existence of a uniform bound N (g, d) on the number# X (F) of F-rational points of X is an …

We prove that when all hyperelliptic curves of genus $ n\geq 1$ having a rational
Weierstrass point are ordered by height, the average size of the 2-Selmer group of their …

We consider the family of hyperelliptic curves over $\mathbb {Q} $ of fixed genus along with
a marked rational Weierstrass point and a marked rational non-Weierstrass point. When …

By a hyperelliptic curve over Q, we mean a smooth, geometrically irreducible, complete
curve C over Q equipped with a fixed map of degree 2 to P^ 1 defined over Q. Thus any …

Let E/k be an elliptic curve over a number field. We obtain some quantitative refinements of
results of Hindry-Silverman, giving an upper bound for the number of k-rational torsion …

Consider the smooth projective models 𝐶 of curves 𝑦²= 𝑓 (𝑥) with 𝑓 (𝑥)∊ ℤ [𝑥] monic and
separable of degree 2𝑔+ 1. We prove that for 𝑔≥ 3, a positive fraction of these have only …

Given a curve X of the form yp= h (x) over a number field, one can use descents to obtain
explicit bounds on the Mordell-Weil rank of the Jacobian or to prove that the curve has no …

MAXIMAL RANKS AND INTEGER POINTS ON A FAMILY OF ELLIPTIC CURVES PG Walsh
University of Ottawa, Canada 1. Introduction There a Page 1 GLASNIK MATEMATICKI Vol …

We provide new upper bounds on N_q (g), the maximum number of rational points on a
smooth absolutely irreducible genus-g curve over F_q, for many values of q and g. Among …