Elliptic curves over function fields with a large set of integral points
نویسندگان
چکیده
منابع مشابه
Elliptic Curves with Large Rank over Function Fields
We produce explicit elliptic curves over Fp(t) whose Mordell-Weil groups have arbitrarily large rank. Our method is to prove the conjecture of Birch and Swinnerton-Dyer for these curves (or rather the Tate conjecture for related elliptic surfaces) and then use zeta functions to determine the rank. In contrast to earlier examples of Shafarevitch and Tate, our curves are not isotrivial. Asymptoti...
متن کاملHigher Heegner points on elliptic curves over function fields
Let E be a modular elliptic curve defined over a rational function field k of odd characteristic. We construct a sequence of Heegner points on E, defined over a Zp -tower of finite extensions of k, and show that these Heegner points generate a group of infinite rank. This is a function field analogue of a result of C. Cornut and V. Vatsal.
متن کاملHeegner points and elliptic curves of large rank over function fields
This note presents a connection between Ulmer’s construction [Ulm02] of non-isotrivial elliptic curves over Fp(t) with arbitrarily large rank, and the theory of Heegner points (attached to parametrisations by Drinfeld modular curves, as sketched in section 3 of the article [Ulm03] appearing in this volume). This ties in the topics in section 4 of [Ulm03] more closely to the main theme of this p...
متن کاملRanks of elliptic curves over function fields
We present experimental evidence to support the widely held belief that one half of all elliptic curves have infinitely many rational points. The method used to gather this evidence is a refinement of an algorithm due to the author which is based upon rigid and crystalline cohomology.
متن کاملIntegral Points on Elliptic Curves Defined by Simplest Cubic Fields
CONTENTS Introduction 1. Elliptic Curves Defined by Simplest Cubic Fields 2. Linear Forms in Elliptic Logarithms 3. Computation of Integral Points 4. Tables of Results 5. General Results about Integral Points on the Elliptic Curves y2 = x3 + mx2 (m+3)x + 1 References Let f(X) be a cubic polynomial defining a simplest cubic field in the sense of Shanks. We study integral points on elliptic curve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2013
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa161-4-3