The maximal rank of elliptic Delsarte surfaces
نویسنده
چکیده
Shioda described in his article [6] a method to compute the Lefschetz number of a Delsarte surface. In one of his examples he uses this method to compute the rank of an elliptic curve over kptq. In this article we find all elliptic curves over kptq for which his method is applicable. For these curves we also compute the maximal Mordell-Weil rank.
منابع مشابه
Elliptic Curves with Bounded Ranks in Function Field Towers
We study the arithmetic structure of elliptic curves over k(t), where k is an algebraically closed field. In [Shi86] Shioda shows how one may determine rank of the Néron-Severi group of a Delsarte surface–a surface that may be defined by four monomial terms. To this end, he describes an explicit method of computing the Lefschetz number of a Delsarte surface. He proves the universal bound of 56 ...
متن کاملOn the rank of certain parametrized elliptic curves
In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.
متن کاملElliptic 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 کاملComplete characterization of the Mordell-Weil group of some families of elliptic curves
The Mordell-Weil theorem states that the group of rational points on an elliptic curve over the rational numbers is a finitely generated abelian group. In our previous paper, H. Daghigh, and S. Didari, On the elliptic curves of the form $ y^2=x^3-3px$, Bull. Iranian Math. Soc. 40 (2014), no. 5, 1119--1133., using Selmer groups, we have shown that for a prime $p...
متن کاملThree lectures on elliptic surfaces and curves of high rank
Three lectures on elliptic surfaces and curves of high rank Noam D. Elkies Over the past two years we have improved several of the (Mordell–Weil) rank records for elliptic curves over Q and nonconstant elliptic curves over Q(t). For example, we found the first example of a curve E/Q with 28 independent points P i ∈ E(Q) (the previous record was 24, by R. Martin and W. McMillen 2000), and the fi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 81 شماره
صفحات -
تاریخ انتشار 2012