Efficient computation of BSD invariants in genus 2

Abstract

Recently, all Birch and Swinnerton-Dyer invariants, except for the order of Sha, have been computed for all curves of genus 2 contained in the L-functions and Modular Forms Database. This report explains the improvements made to the implementation of the algorithm described in arXiv:1711.10409 that were needed to do the computation of the Tamagawa numbers and the real period in reasonable time. We also explain some of the more technical details of the algorithm, and give a brief overview of the methods used to compute the special value of the $L$-function and the regulator.