"Amicable Pairs and Aliquot Cycles for Elliptic Curves Over Number Fiel" by Jim Brown, David Heras et al.
 

Amicable Pairs and Aliquot Cycles for Elliptic Curves Over Number Fields

Document Type

Article

Publication Date

1-1-2016

Description

Let E/ℚ be an elliptic curve. Silverman and Stange define primes p and q to be an elliptic, amicable pair if #E(Fp) = q and #E(Fq) = p. More generally, they define the notion of aliquot cycles for elliptic curves. Here, we study the same notion in the case that the elliptic curve is defined over a number field K. We focus on proving the existence of an elliptic curve E/K with aliquot cycle (p1,⋯, pn) where the pi are primes of K satisfying mild conditions.

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