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22 Introduction to Rational Points on Plane Curves
B Q
O π
P R = −P − Q
T(O)
for the line L(P, Q) through P, Q ∈ C and the tangent line L(P) to C through
P ∈ C.
We return in 10(3.5) to elliptic curves as intersections of two quadrics in projec-
tive three space, and as quartic curves in 4(3.2).
