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2011 Elliptic nets and elliptic curves
Katherine Stange
Algebra Number Theory 5(2): 197-229 (2011). DOI: 10.2140/ant.2011.5.197


An elliptic divisibility sequence is an integer recurrence sequence associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P1,,Pn are points on E defined over K. To this information we associate an n-dimensional array of values in K satisfying a nonlinear recurrence relation. Arrays satisfying this relation are called elliptic nets. We demonstrate an explicit bijection between the set of elliptic nets and the set of elliptic curves with specified points. We also obtain Laurentness/integrality results for elliptic nets.


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Katherine Stange. "Elliptic nets and elliptic curves." Algebra Number Theory 5 (2) 197 - 229, 2011.


Received: 28 April 2010; Revised: 16 September 2010; Accepted: 17 October 2010; Published: 2011
First available in Project Euclid: 21 December 2017

zbMATH: 1277.11063
MathSciNet: MR2833790
Digital Object Identifier: 10.2140/ant.2011.5.197

Primary: 11B37 , 11G05 , 11G07
Secondary: 11B39 , 14H52

Keywords: Elliptic curve , elliptic divisibility sequence , elliptic net , Laurentness , recurrence sequence

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.5 • No. 2 • 2011
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