\\ Table of all j's for which there exists SOME elliptic curve \\ over E/Fp of j-invariant j for which |E(Fp)| = p. jap1=vector(997); jap1[5] = [4]; jap1[7] = [0, 3]; jap1[11] = [6]; jap1[13] = [2, 9]; jap1[17] = [3]; jap1[19] = [0, 4, 6]; jap1[23] = [4, 16]; jap1[29] = [4, 8]; jap1[31] = [10, 24]; jap1[37] = [0, 16, 35]; jap1[41] = [10]; jap1[43] = [18, 23, 25, 32, 33]; jap1[47] = [13, 21]; jap1[53] = [3, 31, 36]; jap1[59] = [29, 45]; jap1[61] = [0, 7, 21, 23, 59]; jap1[67] = [2, 26]; jap1[71] = [3, 39, 61]; jap1[73] = [11, 14, 40, 67]; jap1[79] = [6, 13, 28, 40, 62, 71]; jap1[83] = [12, 26, 63]; jap1[89] = [35, 45, 69, 81]; jap1[97] = [30, 54, 71, 81, 91]; jap1[101] = [16, 99]; jap1[103] = [18, 33, 53, 74, 82, 87]; jap1[107] = [8, 60]; jap1[109] = [48, 62, 88, 102]; jap1[113] = [3, 22, 26, 55, 69, 82]; jap1[127] = [0, 23, 70, 79, 92]; jap1[131] = [68, 88, 102, 114, 125]; jap1[137] = [7, 8, 95]; jap1[139] = [2, 50, 61, 109]; jap1[149] = [8, 16, 50, 70]; jap1[151] = [40, 75, 96, 99, 125]; jap1[157] = [15, 53, 122, 133]; jap1[163] = [12, 50, 56, 80, 112, 124, 131, 144]; jap1[167] = [79, 94, 134, 158]; jap1[173] = [31, 39, 76, 82, 161]; jap1[179] = [15, 20, 54, 59]; jap1[181] = [60, 61, 83, 124]; jap1[191] = [22, 77, 153, 163]; jap1[193] = [56, 91, 100, 101, 109, 120]; jap1[197] = [16, 59, 93, 99, 116]; jap1[199] = [23, 81, 102, 168]; jap1[211] = [44, 56, 59, 99, 163, 174]; jap1[223] = [9, 13, 25, 143, 161, 183, 204, 206, 222]; jap1[227] = [87, 150, 162]; jap1[229] = [47, 76, 83, 89, 130, 142, 151, 171]; jap1[233] = [42, 47, 106, 182, 188, 198, 220]; jap1[239] = [72, 95, 127, 146]; jap1[241] = [33, 39, 66, 77, 105, 164, 210, 215, 223]; jap1[251] = [59, 163, 196, 227]; jap1[257] = [97, 124, 129, 163]; jap1[263] = [4, 66, 154, 176, 249]; jap1[269] = [49, 148, 158, 169, 257, 258, 262]; jap1[271] = [0, 7, 26, 200, 246, 255, 269]; jap1[277] = [11, 27, 137, 156, 174, 179, 264, 268]; jap1[281] = [28, 98, 153, 179, 257]; jap1[283] = [28, 46, 119, 123, 193, 270, 276, 280]; jap1[293] = [6, 9, 64, 74, 123, 247, 254]; jap1[307] = [98, 132, 138, 142]; jap1[311] = [54, 129, 251, 273]; jap1[313] = [20, 24, 26, 84, 92, 167, 212, 233, 235, 238, 250, 260, 261, 263, 278]; jap1[317] = [48, 66, 82, 147, 152, 291]; jap1[331] = [0, 21, 36, 44, 98, 99, 195, 226, 236, 246]; jap1[337] = [90, 171, 272, 296, 305, 325]; jap1[347] = [100, 117, 237, 275]; jap1[349] = [20, 91, 104, 136, 168, 209, 246, 262, 272, 281, 284, 306]; jap1[353] = [5, 9, 12, 157]; jap1[359] = [24, 176, 189, 304]; jap1[367] = [39, 63, 161, 236, 276]; jap1[373] = [40, 73, 98, 141, 196, 198, 246, 258, 275, 285, 319, 352]; jap1[379] = [2, 12, 122, 134, 141, 261, 282, 292, 298, 307, 341, 355]; jap1[383] = [5, 17, 64, 74, 76, 174, 239, 253, 272, 324, 330]; jap1[389] = [58, 381, 382, 383]; jap1[397] = [0, 75, 121, 156, 233, 247, 264, 266, 312]; jap1[401] = [84, 115, 140, 173, 273, 400]; jap1[409] = [133, 141, 175, 235, 246, 283, 304, 347]; jap1[419] = [61, 183, 225, 278, 295, 300, 404]; jap1[421] = [99, 124, 138, 153, 199, 233, 318, 385, 401, 407]; jap1[431] = [95, 119, 155, 233, 246]; jap1[433] = [9, 14, 44, 114, 219, 225, 361, 407]; jap1[439] = [25, 30, 36, 118, 139, 180, 209, 250, 254, 258, 303, 319, 337, 351, 374, 419]; jap1[443] = [164, 185, 206, 263, 271, 319, 339, 426]; jap1[449] = [30, 61, 186, 201, 263, 280, 289, 314]; jap1[457] = [26, 63, 132, 168, 189, 250, 270, 290, 323, 381, 415, 451]; jap1[461] = [109, 240, 321, 350, 455, 459]; jap1[463] = [14, 122, 164, 165, 188, 192, 263, 312, 332, 371, 375, 378, 404, 457]; jap1[467] = [233, 266, 309, 339, 401]; jap1[479] = [125, 298, 375, 388, 413, 452]; jap1[487] = [48, 57, 87, 261, 288, 297, 322, 383]; jap1[491] = [27, 249, 294, 304, 408, 445]; jap1[499] = [30, 60, 170, 214, 257, 262, 301, 387]; jap1[503] = [214, 235, 252, 271, 311, 313, 318]; jap1[509] = [108, 120, 157, 158, 217, 274, 390, 471]; jap1[521] = [60, 96, 114, 190, 266, 320, 331]; jap1[523] = [7, 32, 103, 166, 223, 230, 300, 302, 320, 417, 455, 478]; jap1[541] = [24, 259, 348, 408, 424, 472, 517, 536]; jap1[547] = [0, 57, 131, 141, 208, 227, 230, 258, 320, 355, 393, 440, 500, 543]; jap1[557] = [38, 83, 247, 298, 544, 551]; jap1[563] = [5, 52, 220, 286, 308, 448, 537]; jap1[569] = [19, 25, 100, 288, 349, 364, 385, 458, 520, 527]; jap1[571] = [40, 93, 135, 153, 475, 528]; jap1[577] = [30, 61, 148, 149, 310, 323, 387, 504]; jap1[587] = [152, 177, 346, 494, 563]; jap1[593] = [14, 70, 81, 90, 101, 143, 207, 236, 253, 348, 451, 465, 557]; jap1[599] = [5, 66, 199, 233, 253, 495, 540, 590]; jap1[601] = [117, 286, 359, 393, 432, 474, 489, 517]; jap1[607] = [13, 79, 245, 266, 334, 361, 364, 380, 444, 487, 508, 509, 546, 591]; jap1[613] = [60, 146, 166, 218, 342, 355, 434, 543]; jap1[617] = [35, 151, 173, 191, 224, 319, 561]; jap1[619] = [36, 39, 66, 78, 120, 169, 230, 250, 276, 306, 312, 368, 384, 421, 551]; jap1[631] = [0, 3, 4, 18, 208, 274, 318, 405, 547, 550, 582]; jap1[641] = [238, 266, 320, 373, 381, 563]; jap1[643] = [14, 34, 78, 92, 101, 138, 177, 242, 264, 266, 278, 291, 358, 397]; jap1[647] = [82, 205, 271, 301, 397, 497, 517, 608]; jap1[653] = [58, 68, 143, 172, 192, 518, 553, 639]; jap1[659] = [43, 132, 198, 209, 219, 307, 339, 404, 419, 558, 590, 627]; jap1[661] = [18, 45, 131, 181, 219, 363, 439, 479, 565, 583]; jap1[673] = [21, 32, 46, 57, 60, 141, 167, 214, 244, 287, 309, 329, 389, 394, 400, 419, 432, 436, 530, 538, 587, 615, 617, 641]; jap1[677] = [13, 57, 66, 383, 443, 524, 552]; jap1[683] = [37, 87, 311, 356, 391, 404, 417, 438, 523, 626, 676]; jap1[691] = [2, 65, 81, 239, 286, 291, 305, 328, 344, 459, 609, 645, 657, 675, 679]; jap1[701] = [3, 25, 123, 210, 420, 466, 497, 663, 687]; jap1[709] = [33, 70, 133, 197, 223, 251, 373, 374, 405, 439, 476, 490, 581, 634, 638, 653, 684, 707]; jap1[719] = [28, 71, 181, 208, 477, 522, 613, 628, 644, 651, 703, 705]; jap1[727] = [110, 158, 195, 329, 335, 429, 483, 496, 505, 518, 537, 654]; jap1[733] = [21, 24, 42, 118, 154, 179, 226, 271, 279, 341, 350, 450, 663, 721]; jap1[739] = [24, 68, 73, 79, 88, 240, 247, 287, 317, 405, 518, 670]; jap1[743] = [19, 34, 37, 117, 213, 278, 286, 347, 436, 480, 611]; jap1[751] = [92, 300, 313, 374, 473, 537, 565, 582]; jap1[757] = [69, 139, 162, 174, 223, 276, 324, 367, 404, 406, 481, 715]; jap1[761] = [210, 286, 300, 304, 370, 373, 514, 530, 598, 601, 611, 669]; jap1[769] = [108, 140, 172, 184, 292, 476, 494, 509, 570, 621, 671, 716, 760, 766]; jap1[773] = [29, 37, 96, 125, 284, 513, 524, 575, 580, 656]; jap1[787] = [37, 56, 140, 290, 302, 336, 448, 514, 547, 644]; jap1[797] = [76, 123, 200, 208, 389, 744, 747]; jap1[809] = [205, 207, 456, 503, 618, 757]; jap1[811] = [46, 273, 400, 449, 527, 638, 667, 724]; jap1[821] = [50, 114, 217, 243, 473, 546, 762, 776, 792]; jap1[823] = [14, 77, 112, 236, 250, 252, 634, 734, 813, 814]; jap1[827] = [54, 114, 242, 247, 324, 351, 363, 532, 616]; jap1[829] = [6, 134, 138, 162, 273, 278, 315, 601]; jap1[839] = [6, 68, 161, 285, 333, 365, 627, 734]; jap1[853] = [19, 113, 203, 254, 276, 293, 340, 395, 459, 463, 498, 598, 676, 685, 792]; jap1[857] = [35, 71, 406, 436, 532, 556]; jap1[859] = [134, 159, 191, 256, 296, 299, 410, 435, 476, 487, 518, 531, 570, 614, 837, 855]; jap1[863] = [88, 116, 164, 228, 306, 392, 410, 427, 638, 697, 719, 770]; jap1[877] = [52, 71, 263, 264, 438, 485, 697, 815]; jap1[881] = [75, 177, 373, 413, 522, 630]; jap1[883] = [40, 153, 181, 203, 241, 251, 276, 298, 333, 345, 409, 454, 473, 599, 623, 642]; jap1[887] = [143, 208, 279, 294, 481, 751, 771, 812, 878]; jap1[907] = [108, 249, 351, 382, 404, 457, 557, 753, 831, 840]; jap1[911] = [154, 230, 281, 356, 506, 542, 691, 770, 865]; jap1[919] = [0, 56, 63, 177, 191, 228, 354, 372, 378, 470, 488, 552, 594, 637, 736, 740, 873]; jap1[929] = [15, 204, 262, 310, 447, 472, 542, 684, 699, 800, 848, 880, 890, 894]; jap1[937] = [86, 121, 154, 483, 500, 563, 630, 674, 730, 778, 829, 888]; jap1[941] = [37, 71, 517, 609, 793, 868]; jap1[947] = [92, 253, 598, 601, 610, 651, 713, 900]; jap1[953] = [75, 89, 231, 317, 323, 328, 346, 593, 703, 910]; jap1[967] = [48, 83, 108, 116, 152, 218, 350, 421, 490, 671, 770, 890, 907, 922]; jap1[971] = [49, 97, 174, 243, 376, 515, 589, 728]; jap1[977] = [135, 202, 507, 690, 814, 890, 895]; jap1[983] = [20, 118, 140, 176, 195, 236, 394, 470, 498, 800, 820]; jap1[991] = [56, 140, 236, 418, 441, 531, 634, 933]; jap1[997] = [41, 62, 91, 288, 409, 455, 484, 560, 624, 645, 648, 682, 819, 930, 987];