Proceedings of the Japan Academy, Series A, Mathematical Sciences

Infinitely many elliptic curves of rank exactly two

Dongho Byeon and Keunyoung Jeong

Full-text: Open access

Abstract

In this note, we construct an infinite family of elliptic curves $E$ defined over $\mathbf{Q}$ whose Mordell-Weil group $E(\mathbf{Q})$ has rank exactly two under the parity conjecture.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 5 (2016), 64-66.

Dates
First available in Project Euclid: 28 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.pja/1461868542

Digital Object Identifier
doi:10.3792/pjaa.92.64

Mathematical Reviews number (MathSciNet)
MR3492814

Zentralblatt MATH identifier
1350.11064

Subjects
Primary: 11G05: Elliptic curves over global fields [See also 14H52]
Secondary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]

Keywords
Elliptic curve rank

Citation

Byeon, Dongho; Jeong, Keunyoung. Infinitely many elliptic curves of rank exactly two. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 5, 64--66. doi:10.3792/pjaa.92.64. https://projecteuclid.org/euclid.pja/1461868542


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References

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