A028938 Negative of numerator of y-coordinate of (2n)*P where P is generator for rational points on curve y^2 + y = x^3 - x.

0, 3, -14, 69, 2065, -28888, 2616119, -332513754, 8280062505, 18784454671297, -10663732503571536, 8938035295591025771, 31636113722016288336230, -41974401721854929811774227, 754388827236735824355996347601

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..86

B. Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. 14 (1986), 207-259; see p. 225.

Formula

P=(0, 0), 2P=(1, 0); if kP=(a, b) then (k+1)P = (a' = (b^2-a^3)/a^2, b' = -1 - b*a'/a).

a(n) = A028942(2n). - Seiichi Manyama, Nov 19 2016

Example

4P = (2, -3).

Crossrefs

Cf. A028936, A028937, A028939 (denominator), A028942.

Sequence in context: A190725 A151325 A020065 * A038213 A261207 A161939

Adjacent sequences: A028935 A028936 A028937 * A028939 A028940 A028941

Keyword

sign,frac

Author

N. J. A. Sloane

Status

approved