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A028943
Denominator of y coordinate of n*P where P is the generator [0,0] for rational points on curve y^2+y = x^3-x.
11
1, 1, 1, 1, 8, 1, 27, 125, 343, 64, 12167, 24389, 205379, 2146689, 30959144, 274625, 3574558889, 50202571769, 553185473329, 4302115807744, 578280195945297, 1469451780501769, 238670664494938073, 13528653463047586625
OFFSET
1,5
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 x_n. - N. J. A. Sloane, Jan 27 2022
REFERENCES
A. W. Knapp, Elliptic Curves, Princeton 1992, p. 77.
LINKS
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).
EXAMPLE
5P = (1/4, -5/8).
PROG
(PARI) See A028940.
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
STATUS
approved