A028936 -id:A028936 - cp's OEIS frontend

A028939 a(n) = denominator of y-coordinate of (2n)*P where P is the generator for rational points on the curve y^2 + y = x^3 - x.

1, 1, 1, 125, 64, 24389, 2146689, 274625, 50202571769, 4302115807744, 1469451780501769, 13528653463047586625, 343216282443844010111, 63061816101171948456692661, 495133617181351428873673516736

Offset: 1

N. J. A. Sloane

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

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.

Cf. A028936, A028937, A028938 (numerator), A028943.

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) = A028943(2n). - Seiichi Manyama, Nov 19 2016

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.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

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

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.

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

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

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

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.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

			4P = (2, -3).

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.

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

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

cp's OEIS Frontend

A028939 a(n) = denominator of y-coordinate of (2n)*P where P is the generator for rational points on the curve y^2 + y = x^3 - x.

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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.

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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.

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