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2008 On the Equation $Y^2 = X^5 + k$
Andrew Bremner
Experiment. Math. 17(3): 371-374 (2008).

Abstract

We show that there are infinitely many nonisomorphic curves $Y^2 = X^5 + k$, $k \in {\mathbb Z}$}, possessing at least twelve finite points $k>0$, and at least six finite points for $k<$. We also determine all rational points on the curve $Y^2=X^5-7$.

Citation

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Andrew Bremner. "On the Equation $Y^2 = X^5 + k$." Experiment. Math. 17 (3) 371 - 374, 2008.

Information

Published: 2008
First available in Project Euclid: 19 November 2008

zbMATH: 1210.11045
MathSciNet: MR2455707

Subjects:
Primary: 11D41
Secondary: 11D25 , 11G05 , 11G30

Keywords: Elliptic curve , Fifth powers , genus two curve

Rights: Copyright © 2008 A K Peters, Ltd.

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Vol.17 • No. 3 • 2008
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