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March 2019 Local torsion primes and the class numbers associated to an elliptic curve over $\mathbb Q$
Toshiro Hiranouchi
Hiroshima Math. J. 49(1): 117-127 (March 2019). DOI: 10.32917/hmj/1554516039

Abstract

Using the rank of the Mordell-Weil group $E(\mathbb {Q})$ of an elliptic curve $E$ over $\mathbb Q$, we give a lower bound of the class number of the number field $\mathbb {Q}(E[p^{n}])$ generated by $p^n$-division points of $E$ when the curve $E$ does not possess a $p$-adic point of order $p: E(\mathbb {Q}_p)[p]=0$.

Citation

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Toshiro Hiranouchi. "Local torsion primes and the class numbers associated to an elliptic curve over $\mathbb Q$." Hiroshima Math. J. 49 (1) 117 - 127, March 2019. https://doi.org/10.32917/hmj/1554516039

Information

Received: 8 November 2017; Revised: 13 October 2018; Published: March 2019
First available in Project Euclid: 6 April 2019

zbMATH: 07090065
MathSciNet: MR3936649
Digital Object Identifier: 10.32917/hmj/1554516039

Subjects:
Primary: 11R29
Secondary: 11G05

Rights: Copyright © 2019 Hiroshima University, Mathematics Program

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Vol.49 • No. 1 • March 2019
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