Attachment 'mjfound_1.txt'

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   1 179 -12*a + 5 [1,0,0,-5,3,-5,-4,1,5,7,1,2,-3,-6,-4,8,-11,-10,10,12,0,12,4,4] [a, -a - 1, 1, 15*a - 26, 35*a - 57]
   2 205 13*a - 9 [3,-4,'?',4,0,-2,4,-4,-6,-8,-6,10,'?','?',4,12,2,6,4,-2,-4,-16,-8,-6] [a, a, 1, -8*a - 16, 25*a + 2]
   3 404 -18*a + 10 ['?',0,-2,-4,6,-1,2,4,-4,9,-11,-5,3,-2,-5,6,1,-6,-12,-16,6,-8,9,12] [a + 1, 1, a, -17*a - 11, -57*a - 36]
   4 445 19*a - 12 [1,2,'?',-6,0,0,4,-8,-2,-10,4,0,2,10,4,0,-2,14,8,-16,-4,-12,'?','?'] [a + 1, -a + 1, a, 21*a - 38, -53*a + 83]
   5 484 22 ['?',-3,4,13,'?','?',7,7,-3,-3,-5,-5,-8,-8,-12,-12,5,5,-7,-7,4,4,7,7] [a + 1, 1, 0, -2*a - 2, -16*a - 12]
   6 495 -3*a + 24 [3,'?','?',-2,'?','?',4,0,-2,2,4,-8,-10,2,0,4,-6,-10,-8,0,-16,4,14,-10] [a + 1, a + 1, 1, 10*a - 12, 15*a - 23]
   7 505 -a + 23 [0,1,'?',9,-6,5,8,7,0,-6,-8,2,-9,0,-14,5,0,-5,13,-1,-8,-6,-18,-1] [0, a + 1, 1, 132*a - 211, 879*a - 1421]
   8 539 -21*a + 7 [-3,-1,-1,'?','?','?',-3,-6,-4,-1,-4,-4,8,5,-7,11,-14,13,-2,4,-10,5,6,-9] [a + 1, a + 1, a, -11*a - 8, 10*a + 6]
   9 539 -21*a + 7 [3,-1,-1,'?','?','?',3,-6,8,-1,-4,-4,-4,5,-1,5,-2,-11,10,-8,14,-13,6,-9] [a + 1, a, a + 1, 228*a - 367, 1927*a - 3117]
  10 539 21*a - 7 [-3,2,2,'?','?','?',6,6,2,2,8,-10,8,-10,8,2,4,-14,-8,-8,-4,-4,12,0] [a + 1, a, 1, a - 11, -22*a + 8]
  11 545 21*a - 8 [1,2,'?',2,0,2,6,0,2,2,-8,-4,2,-2,6,0,2,2,-2,-10,-14,-8,-6,2] [a, 1, a, 19*a - 34, 61*a - 99]
  12 209 a - 15 [-2,2,4,-12,'?','?','?','?',7,1,-5,-2,-11,-3,-3,10,8,-2,12,-13,4,-10,-14,10] [0, -a + 1, a, 69*a - 112, 371*a - 601]
  13 580 22*a - 6 ['?',3,'?',-4,1,-4,2,7,'?','?',-10,3,-12,-5,6,-14,10,13,2,-6,-14,-7,7,-18] [a, -a - 1, a, -23*a - 12, -45*a - 29]
  14 599 -a + 25 [-1,2,2,8,6,-4,-4,6,2,-2,0,2,0,-8,6,12,-8,6,-8,-14,-16,2,-2,6] [1, -a, 1, 46*a - 78, 204*a - 326]
  15 599 a - 25 [-1,2,2,11,-3,5,2,0,2,1,-3,-1,6,-5,-12,3,1,-12,-2,7,11,5,-2,-15] [a, 1, 0, -7*a - 5, -16*a - 11]
  16 620 2*a - 26 ['?',4,'?',-9,1,-3,6,5,-2,7,'?','?',8,-4,6,3,-5,-14,14,-5,-14,10,10,-9] [1, a, 1, -7*a - 7, -19*a - 13]
  17 639 -3*a + 27 [2,'?',1,2,0,3,0,-6,3,6,-3,-2,-9,2,-5,10,-5,-6,'?','?',4,10,-2,10] [0, -a, a + 1, 138*a - 223, 960*a - 1555]
  18 639 -3*a + 27 [-1,'?',4,-4,0,0,0,6,6,-6,0,-2,0,-10,-2,4,-2,-12,'?','?',16,-14,10,-2] [a, a - 1, a, -13*a - 13, -43*a - 19]
  19 649 23*a - 8 [-2,-1,-2,-4,'?','?',-5,0,0,-9,3,-6,-3,0,'?','?',5,7,2,10,-6,-1,2,10] [0, -a, a + 1, 4*a - 5, -4*a + 4]
  20 649 -a + 26 [-1,2,4,8,'?','?',-4,0,2,-2,-8,-10,4,2,'?','?',-8,0,0,6,-8,-10,10,14] [a, a, 1, 4*a - 7, 4*a - 8]
  21 684 24*a - 6 ['?','?',0,-2,-2,4,'?','?',6,8,4,-4,2,0,2,-2,-14,-10,6,-14,4,0,-2,0] [1, a, 0, 9*a - 14, 13*a - 23]
  22 239 -a + 16 [1,-1,1,-6,3,-5,5,-2,0,-2,1,-4,-2,9,14,11,5,-14,-6,-8,-3,2,-4,9] [1, a + 1, a + 1, -103*a - 67, -720*a - 448]
  23 784 28 ['?',-3,-4,'?',3,3,8,8,1,1,-2,-2,-6,-6,10,10,0,0,0,0,7,7,-8,-8] [0, 0, 0, -8*a - 8, -16*a - 12]
  24 796 6*a + 26 ['?',-2,3,-4,3,3,-7,-4,-9,6,-10,-7,0,3,6,0,11,5,12,6,-4,-13,6,6] [1, 1, 0, -5*a - 1, -9*a - 6]
  25 820 26*a - 18 ['?',4,'?',12,0,-2,4,4,10,-8,2,2,'?','?',-12,12,10,-2,-12,-10,-4,16,-16,10] [a + 1, 0, a + 1, -61*a - 36, -297*a - 182]
  26 836 2*a - 30 ['?',-5,-3,2,'?','?','?','?',-7,8,-5,5,-4,-10,-10,-4,-6,-2,12,1,11,11,0,3] [a, a + 1, 1, 3*a - 7, -2*a + 8]
  27 855 -6*a - 27 [1,'?','?',2,0,4,'?','?',-2,-6,8,0,2,-2,0,-8,-2,14,12,-12,-8,-8,-6,-10] [1, a, a, 3*a - 8, 6*a - 9]
  28 909 -27*a + 15 [-1,'?',-1,2,3,2,7,3,9,2,-1,4,5,-12,10,4,-10,1,14,0,-4,0,3,-6] [a + 1, a + 1, 1, 13*a - 31, 26*a - 83]
  29 961 31 [2,-3,3,-3,-6,6,-1,-4,8,8,'?','?',9,-6,-13,-4,-4,8,-8,-5,10,-14,-10,14] [0, 0, a + 1, 8*a + 5, -a - 3]
  30 244 -14*a + 8 ['?',5,0,8,3,-4,-6,6,-8,9,0,-3,-10,0,-10,1,'?','?',-7,-10,-13,8,-4,13] [1, a + 1, 1, -16*a + 3, -29*a - 25]
  31 979 -28*a + 13 [3,4,0,4,'?','?',4,-2,-10,-2,0,-4,0,-10,-4,-4,6,12,8,4,4,14,'?','?'] [a + 1, -a, a, -44*a - 32, -178*a - 107]
  32 979 6*a - 35 [3,-1,2,6,'?','?',2,-5,-1,1,-4,8,0,-2,0,-3,-10,-5,3,8,4,4,'?','?'] [a, -1, 0, 33*a - 53, 99*a - 160]
  33 284 -2*a + 18 ['?',2,0,-2,4,-2,6,2,4,0,-8,-8,-6,-10,2,0,-10,8,'?','?',12,4,-10,-6] [a, a, 0, -2*a - 7, -9*a - 10]
  34 380 -4*a - 18 ['?',2,'?',0,2,4,'?','?',4,-2,4,0,-12,2,-4,0,-2,6,0,-8,-6,-16,6,-14] [1, -a, 1, -61*a - 36, -245*a - 145]
  35 395 2*a + 19 [1,4,'?',4,2,-2,0,0,6,-4,-4,0,-6,2,4,12,-10,-14,-6,4,'?','?',0,0] [1, 0, 0, 2*a - 7, 3*a - 8]
  36 396 -18*a + 6 ['?','?',3,-11,'?','?',7,-7,0,-7,-1,6,-5,2,11,4,-5,-12,5,12,-14,-14,10,-11] [a, -1, 0, a - 4, -2*a - 7]
  37 404 18*a - 10 ['?',4,2,-4,-2,-1,-2,0,0,3,-1,5,-1,-6,-9,14,7,-10,-4,-8,-10,-8,17,0] [1, 0, a, 38*a - 60, 135*a - 219]

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  • [get | view] (2011-05-02 04:23:25, 3563.5 KB) [[attachment:Birch-Conjectures_Concerning_Elliptic_Curves.pdf]]
  • [get | view] (2011-08-08 23:54:03, 1.7 KB) [[attachment:Curves_1000-2000_MISSING_corrected_aps.txt]]
  • [get | view] (2011-08-10 18:18:53, 0.7 KB) [[attachment:Curves_2000_Missing_8-10-11.txt]]
  • [get | view] (2011-08-10 18:03:07, 19.1 KB) [[attachment:Curves_FOUND_8-10-11.txt]]
  • [get | view] (2011-08-10 18:07:58, 0.7 KB) [[attachment:Curves_MISSING_8-10-11.txt]]
  • [get | view] (2011-07-23 07:22:33, 146.8 KB) [[attachment:FindingCurvesAPs.pdf]]
  • [get | view] (2011-06-22 23:09:59, 154.0 KB) [[attachment:Prime_Isogenies_Over_Number_Fields.pdf]]
  • [get | view] (2011-05-02 04:18:24, 2380.7 KB) [[attachment:Tate-The_Arithmetic_of_Elliptic_Curves.pdf]]
  • [get | view] (2011-06-30 15:16:53, 791.8 KB) [[attachment:Updated Table]]
  • [get | view] (2011-06-21 22:30:45, 80.3 KB) [[attachment:minimal_model.pdf]]
  • [get | view] (2011-07-28 21:29:16, 4.3 KB) [[attachment:mjfound_1.txt]]
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