A028937 Denominator of x-coordinate of (2n)*P where P = (0,0) is the generator for rational points on the curve y^2 + y = x^3 - x.

1, 1, 1, 25, 16, 841, 16641, 4225, 13608721, 264517696, 12925188721, 5677664356225, 49020596163841, 158432514799144041, 62586636021357187216, 1870098771536627436025, 41998153797159031581158401, 15402543997324146892198790401

Offset

1,4

Links

Seiichi Manyama, Table of n, a(n) for n = 1..106

LMFDB, Elliptic Curve 37.a1 (Cremona label 37a1)

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) = A028941(2n). - Seiichi Manyama, Nov 19 2016

a(n) = a(-n) = b(n)*b(n+3) - b(n+1)*b(n+2) for all n in Z where b(n) = A006720(n). - Michael Somos, Mar 23 2022

Example

a(4) = 25 where 8P = (21/25, -69/125).

Prog

(PARI) a(n)=denominator(ellmul(E, [0, 0], 2*n)[1]) \\ Charles R Greathouse IV, Mar 23 2022

Crossrefs

Cf. A006720, A051138, A028936 (numerator), A028938, A028939, A028941.

Sequence in context: A339773 A040602 A281335 * A215537 A104790 A291429

Adjacent sequences: A028934 A028935 A028936 * A028938 A028939 A028940

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved