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►Algebraic curves of the form
, where is a nonsingular polynomial of degree 3 or 4 (see McKean and Moll (1999, §1.10)), are elliptic curves, which are also considered in §23.20(ii).
…For any two points and on this curve, their sum
, always a third point on the curve, is defined by the Jacobi–Abel addition law
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►An algebraic curve that can be put either into the form
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►
always has the form
(Mordell’s Theorem: Silverman and Tate (1992, Chapter 3, §5)); the determination of , the rank of , raises questions of great difficulty, many of which are still open.
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