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October 2015 The rank and generators of Kihara’s elliptic curve with torsion $\mathbf{Z}/4\mathbf{Z}$ over $\mathbf{Q}(t)$
Andrej Dujella, Ivica Gusić, Petra Tadić
Proc. Japan Acad. Ser. A Math. Sci. 91(8): 105-109 (October 2015). DOI: 10.3792/pjaa.91.105

Abstract

For the elliptic curve $E$ over $\mathbf{Q}(t)$ found by Kihara, with torsion group $\mathbf{Z}/4\mathbf{Z}$ and rank $\geq 5$, which is the current record for the rank of such curves, by using a suitable injective specialization, we determine exactly the rank and generators of $E(\mathbf{Q}(t))$.

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Andrej Dujella. Ivica Gusić. Petra Tadić. "The rank and generators of Kihara’s elliptic curve with torsion $\mathbf{Z}/4\mathbf{Z}$ over $\mathbf{Q}(t)$." Proc. Japan Acad. Ser. A Math. Sci. 91 (8) 105 - 109, October 2015. https://doi.org/10.3792/pjaa.91.105

Information

Published: October 2015
First available in Project Euclid: 5 October 2015

zbMATH: 1341.11027
MathSciNet: MR3403940
Digital Object Identifier: 10.3792/pjaa.91.105

Subjects:
Primary: 11G05 , 14H52

Keywords: Elliptic curve , generators , mwrank , ‎rank‎ , specialization homomorphism , torsion

Rights: Copyright © 2015 The Japan Academy

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Vol.91 • No. 8 • October 2015
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