There Are No Points of Order 11 on Elliptic Curves over Q
نویسنده
چکیده
Lemma 1. Let k be a field and let (a, b, c), (α, β, γ) ∈ P(k) be distinct points. Then there is a unique line through these points, and it is given by the equation: ∣∣∣∣∣ x y z a b c α β γ ∣∣∣∣∣ = 0 . Two lines given by equations ux+ vy+wz = 0 and u′x+ v′y+w′z = 0 coincide if and only if the points (u, v, w) and (u′, v′, w′) coincide as points in P(k). Two distinct lines in P(k) intersect in precisely 1 point.
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