Small exponent point groups on elliptic curves

Florian Luca; James McKee; Igor E. Shparlinski

Small exponent point groups on elliptic curves

Florian Luca, James McKee, Igor E. Shparlinski

School of Computing

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Let E be an elliptic curve defined over F_q, the finite field of q elements. We show that for some constant ƞ > 0 depending only on q, there are infinitely many positive integers n such that the exponent of E(F_qⁿ), the group of F_qⁿ-rational points on E, is at most qⁿ exp (−n^{ƞ/ log log n}). This is an analogue of a result of R. Schoof on the exponent of the group E(F_p) of F_p-rational points, when a fixed elliptic curve E is defined over ℚ and the prime p tends to infinity.

Original language	English
Pages (from-to)	471-476
Number of pages	6
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	18
Issue number	2
Publication status	Published - 2006

Cite this

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AU - McKee, James

AU - Shparlinski, Igor E.

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AB - Let E be an elliptic curve defined over Fq, the finite field of q elements. We show that for some constant ƞ > 0 depending only on q, there are infinitely many positive integers n such that the exponent of E(Fqn), the group of Fqn-rational points on E, is at most qn exp (−nƞ/ log log n). This is an analogue of a result of R. Schoof on the exponent of the group E(Fp) of Fp-rational points, when a fixed elliptic curve E is defined over ℚ and the prime p tends to infinity.

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JO - Journal de Theorie des Nombres de Bordeaux

JF - Journal de Theorie des Nombres de Bordeaux

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ER -

Small exponent point groups on elliptic curves

Abstract

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