The Computational and Theoretical Aspects of Elliptic Curves
This volume presents a collection of results related to the BSD conjecture, based on the first two India-China conferences on this topic. It provides an overview of the conjecture and a few special cases where the conjecture is proved. The broad theme of
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Zhibin Liang Chandrakant Aribam Editors
The Computational and Theoretical Aspects of Elliptic Curves
Mathematical Lectures from Peking University Editor-in-Chief Gang Tian, Princeton, NJ, USA
Mathematical Lectures from Peking University includes monographs, lecture notes, and proceedings based on research pursued and events held at Beijing International Center for Mathematical Research (BICMR). BICMR is a mathematical research institute sponsored by the national government of China. The center was created in 2005 by national government decree. Its goal is to build a world-class mathematical center for research and training young talents; to foster a new generation of leading world-class mathematicians in China; to support the application of mathematics in sciences and practical fields; to promote research and improve the level of mathematics education at Peking University, as well as all over China.
More information about this series at http://www.springer.com/series/11574
Zhibin Liang Chandrakant Aribam •
Editors
The Computational and Theoretical Aspects of Elliptic Curves
123
Editors Zhibin Liang Capital Normal University Beijing, China
Chandrakant Aribam Department of Mathematical Sciences Indian Institute of Science Education and Research Mohali Sahibzada Ajit Singh Nagar, Punjab, India
ISSN 2197-4209 ISSN 2197-4217 (electronic) Mathematical Lectures from Peking University ISBN 978-981-13-6663-5 ISBN 978-981-13-6664-2 (eBook) https://doi.org/10.1007/978-981-13-6664-2 Library of Congress Control Number: 2019932699 © Springer Nature Singapore Pte Ltd. 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Foreword
The Birch and Swinnerton-Dyer (BSD
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