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.

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

Author

N. J. A. Sloane, Jan 27 2022

Keywords

• sign
• frac

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.

Crossrefs

Cf. A028940-A028943, A350622-A350625.

Programs

PARI

See A350622.