On elliptic curves with complex multiplication and root numbers

Wan Lee, Myungjun Yu

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1 Citation (Scopus)

Abstract

Let E/F be an elliptic curve defined over a number field F. Suppose that E has complex multiplication over F¯, i.e. EndF¯(E) ⊗ is an imaginary quadratic field. With the aid of CM theory, we find elliptic curves whose quadratic twists have a constant root number.

Original languageEnglish
Pages (from-to)827-842
Number of pages16
JournalInternational Journal of Number Theory
Volume17
Issue number4
DOIs
Publication statusPublished - 2021 May

Bibliographical note

Funding Information:
The first author is grateful to Korea Institute for Advanced Study (KIAS) for hospitality. The second author was supported by a KIAS Individual Grant (SP075201) via the Center for Mathematical Challenges at KIAS. He was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1C1C1A01007604).

Funding Information:
We are grateful to Karl Rubin for helpful discussions. We also thank David Rohrlich for answering our questions concerning the root numbers. We thank the anonymous referee for many comments to improve the exposition of our paper. The first author is grateful to Korea Institute for Advanced Study (KIAS) for hospitality. The second author was supported by a KIAS Individual Grant (SP075201) via the Center for Mathematical Challenges at KIAS. He was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1C1C1A01007604).

Publisher Copyright:
© 2021 World Scientific Publishing Company.

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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