A note on the growth of Mordell-Weil ranks of elliptic curves in cyclotomic $\mathbf {Z}_p$-extensions

Kazuo Matsuno

doi:10.3792/pjaa.79.101

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May 2003 A note on the growth of Mordell-Weil ranks of elliptic curves in cyclotomic $\mathbf {Z}_p$-extensions

Kazuo Matsuno

Proc. Japan Acad. Ser. A Math. Sci. 79(5): 101-104 (May 2003). DOI: 10.3792/pjaa.79.101

Abstract

In this note, we exhibit some examples of elliptic curves whose Mordell-Weil ranks grow in lower layer of the cyclotomic $\mathbf{Z}_p$-extension over the rationals.

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Kazuo Matsuno. "A note on the growth of Mordell-Weil ranks of elliptic curves in cyclotomic $\mathbf {Z}_p$-extensions." Proc. Japan Acad. Ser. A Math. Sci. 79 (5) 101 - 104, May 2003. https://doi.org/10.3792/pjaa.79.101