The elliptic threefold y^2=x^3+16s^6+16t^6-32(t^3s^3+t^3+s^3)+16

TL;DR

This paper introduces a method to compute the rank of a specific elliptic curve over a function field, utilizing a generalized approach to calculate certain cohomological invariants of nodal hypersurfaces.

Contribution

It extends existing techniques to determine the rank of elliptic curves over function fields by generalizing a method for computing cohomology of nodal hypersurfaces.

Findings

Successfully computes the rank of the given elliptic curve.

Provides a generalized method applicable to similar elliptic curves.

Enhances understanding of the relationship between hypersurface cohomology and elliptic curve ranks.

Abstract

We present a method to calculate the rank of $E(\oQ(s,t))$ for the elliptic curve mentioned in the title. This method uses a generalization of a method from Van Geemen and Werner to calculate $h^4(Y)$ for nodal hypersurfaces $Y$.