The 2-class groups of cubic fields and 2-descents on elliptic curves
Mayumi Kawachi,Shin Nakano +1 more
About:
This article is published in Tohoku Mathematical Journal.The article was published on 1992-12-01 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Supersingular elliptic curve & Schoof's algorithm.read more
Citations
More filters
Journal ArticleDOI
Non-isotrivial elliptic surfaces with non-zero average root number
TL;DR: In this paper, the root number of an elliptic curve has been studied in the context of finding non-isotrivial 1-parameter families of elliptic curves whose root number does not average to zero.
Posted Content
Families of elliptic curves with non-zero average root number
TL;DR: In this article, the root number of an elliptic curve is computed for families of elliptic curves whose root number does not average to zero as the parameter varies in the dimension of the curve.
Journal Article
Families of elliptic curves with non-zero average root number
TL;DR: In this paper, the root number of an elliptic curve is computed for families of elliptic curves whose root number does not average to zero as the parameter varies in the dimension of the curve.
References
More filters
Book
The Arithmetic of Elliptic Curves
TL;DR: It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
Journal ArticleDOI
The simplest cubic fields
TL;DR: In this article, the cyclic cubic fields generated by x3 = ax2 + (a + 3)x + 1 are studied in detail, and the class numbers are al2 2 ways of the form A + 3B, which are relatively large and easy to compute.
Journal ArticleDOI
Class numbers of the simplest cubic fields
TL;DR: In this paper, Washington et al. gave a modified proof and an extension of a result of Uchida, showing how to obtain cyclic cubic fields with class number divisible by n, for any n.
Journal ArticleDOI
Arithmetic of elliptic curves upon quadratic extension
TL;DR: In this article, the authors studied variations in the rank of the Mordell-Weil group of an elliptic curve E defined over a number field F as one passes to quadratic extensions K of F. The parity of rank E(K) was shown to be the same as the parity of the local norm indices of Z.