A028940
a(n) = numerator of the X-coordinate of n*P where P is the generator [0,0] for rational points on the curve y^2 + y = x^3 - x.
Original entry on oeis.org
0, 1, -1, 2, 1, 6, -5, 21, -20, 161, 116, 1357, -3741, 18526, 8385, 480106, -239785, 12551561, -59997896, 683916417, 1849037896, 51678803961, -270896443865, 4881674119706, -16683000076735, 997454379905326
Offset: 1
4P = P[4] = [2, -3].
P[1] to P[16] are [0, 0], [1, 0], [-1, -1], [2, -3], [1/4, -5/8], [6, 14], [-5/9, 8/27], [21/25, -69/125], [-20/49, -435/343], [161/16, -2065/64], [116/529, -3612/12167], [1357/841, 28888/24389], [-3741/3481, -43355/205379], [18526/16641, -2616119/2146689], [8385/98596, -28076979/30959144], [480106/4225, 332513754/274625]. - _N. J. A. Sloane_, Jan 27 2022
- A. W. Knapp, Elliptic Curves, Princeton 1992, p. 77.
-
\\ from N. J. A. Sloane, Jan 27 2022. To get the first 40 points P[n].
\\ define curve E
E = ellinit([0,0,1,-1,0]) \\ y^2+y = x^3-x
P = vector(100)
P[1] = [0,0]
for(n=2, 40, P[n] = elladd(E, P[1], P[n-1]))
P
A350625
a(n) = denominator 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.
Original entry on oeis.org
1, 1, 1, 1, 8, 27, 1, 343, 1331, 8000, 6859, 658503, 6967871, 7645373, 1054977832, 19270387241, 549554511871, 199279038321, 537149706740569, 17795935051712000, 238963978065144151, 27915217583090079761, 3036108535167687186689, 338086202776927409397159
Offset: 1
- D. Husemoller, Elliptic Curves, Springer, 1987, p. 28.
- A. W. Knapp, Elliptic Curves, Princeton, 1992, p. 64.
A350623
a(n) = denominator of the X-coordinate of n*P where P is the generator [0,0] for rational points on the curve y^2 + y = x^3 + x^2.
Original entry on oeis.org
1, 1, 1, 1, 4, 9, 1, 49, 121, 400, 361, 7569, 36481, 38809, 1036324, 7187761, 67092481, 34117281, 6607901521, 68162766400, 385083543601, 9202249657441, 209674135856641, 4853089476046161, 7099336433764, 2600282294202480889, 60193393235277536641, 1371165544633857017809
Offset: 1
- D. Husemoller, Elliptic Curves, Springer, 1987, p. 28.
- A. W. Knapp, Elliptic Curves, Princeton, 1992, p. 64.
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.
Original entry on oeis.org
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
- D. Husemoller, Elliptic Curves, Springer, 1987, p. 28.
- A. W. Knapp, Elliptic Curves, Princeton, 1992, p. 64.
Showing 1-4 of 4 results.
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