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A350624
a(n) = numerator of the Y-coordinate of n*P where P is the generator [0,0] for rational points on the curve y^2 + y = x^3 + x^2.
1
0, -1, -2, 3, 1, -28, -99, 20, -931, -10527, 76400, 71117, -7705242, -97805561, 317884519, -6053168484, -584285903929, 17516504939480, 21171512841831, -20045208029885441, -987005650468865600, 26826505806361752519, -24519007717765931978, -338107738763085297600203, 37652404140584119758794769, 262883121764561512399492, -470660250581978416129759599211, -103603683448954712692908522816060, 17053994466435658069907361489699701
OFFSET
1,3
COMMENTS
We can take P = P[1] = [x_1, y_1] = [0,0]. Then P[n] = P[1]+P[n-1] = [x_n, y_n] for n >= 2. Sequence gives numerators of the y_n.
REFERENCES
D. Husemoller, Elliptic Curves, Springer, 1987, p. 28.
A. W. Knapp, Elliptic Curves, Princeton, 1992, p. 64.
PROG
(PARI) See A350622.
CROSSREFS
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Jan 27 2022
STATUS
approved