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- W1973707954 abstract "Fix a prime ℓ, and let 𝔽 q be a finite field with q ≡ 1 (mod ℓ) elements. If ℓ > 2 and q ≫ ℓ 1, we show that asymptotically (ℓ - 1) 2 /2ℓ 2 of the elliptic curves E/𝔽 q with complete rational ℓ-torsion are such that E/〈P〉 does not have complete rational ℓ-torsion for any point P ∈ E(𝔽 q ) of order ℓ. For ℓ = 2 the asymptotic density is 0 or 1/4, depending whether q ≡ 1 (mod 4) or 3 (mod 4). We also show that for any ℓ, if E/𝔽 q has an 𝔽 q -rational point R of order ℓ 2 , then E/〈ℓR〉 always has complete rational ℓ-torsion." @default.
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- W1973707954 date "2013-09-01" @default.
- W1973707954 modified "2023-10-16" @default.
- W1973707954 title "QUOTIENTS OF ELLIPTIC CURVES OVER FINITE FIELDS" @default.
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- W1973707954 doi "https://doi.org/10.1142/s1793042113500334" @default.
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