Uniform bounds for the number of rational points of families of curves of genus 2
نویسندگان
چکیده
We construct an infinite family {Ca,b}a,b∈Q of curves of genus 2 defined over Q, with two independent morphisms to a family of elliptic curves {Ea,b}a,b∈Q. When any of these elliptic curves Ea,b has rank 1 over Q, we obtain (modulo a conjecture of S. Lang, proved for special cases) a uniform bound for the number of rational points of the curve Ca,b, and an algorithm which finds all the rational points of the curve Ca,b.
منابع مشابه
Uniform bounds on the number of rational points of a family of curves of genus 2∗
We exhibit a genus–2 curve C defined over Q(T ) which admits two independent morphisms to a rank–1 elliptic curve defined over Q(T ). We describe completely the set of Q(T )–rational points of the curve C and obtain a uniform bound for the number of Q–rational points of a rational specialization Ct of the curve C for a certain (possibly infinite) set of values t ∈ Q. Furthermore, for this set o...
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