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2021 | OriginalPaper | Buchkapitel

Efficient Computation of BSD Invariants in Genus 2

verfasst von : Raymond van Bommel

Erschienen in: Arithmetic Geometry, Number Theory, and Computation

Verlag: Springer International Publishing

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Abstract

Recently, all Birch and Swinnerton-Dyer invariants, except for the order of

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-80914-0_6/510803_1_En_6_IEq1_HTML.gif

, have been computed for all curves of genus 2 contained in the L-functions and Modular Forms Database [LMFDB]. This report explains the improvements made to the implementation of the algorithm described in [vBom19] 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.

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Vorheriges Kapitel Elliptic Curves with Good Reduction Outside of the First Six Primes

Nächstes Kapitel Restrictions on Weil Polynomials of Jacobians of Hyperelliptic Curves

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Titel: Efficient Computation of BSD Invariants in Genus 2
verfasst von: Raymond van Bommel
Verlag: Springer International Publishing
Buch: Arithmetic Geometry, Number Theory, and Computation
Print ISBN: 978-3-030-80913-3

Electronic ISBN: 978-3-030-80914-0

Copyright-Jahr: 2021
DOI: https://doi.org/10.1007/978-3-030-80914-0_6

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