Title: Computing Cassels-Tate pairing for genus 2 and beyond with good elements

Abstract: In this talk we will see an implementation of the Cassels-Tate pairing assuming the existence of elements which I call "good" in the 2-Selmer Group of the Jacobian of odd-degree hyperelliptic curves. We will see examples of computation of the pairing for genus 2,3 and 4 curves where the good elements exist. Furthermore, I will report on joint work with Tim Evink on computation of the Cassels-Tate pairing on a family of genus curves of the form y^2 = x(x^2-p^2)(x^2-4p^2), where p is an odd prime, using the existence of good elements.