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Rational point on Y^2=DX^4 (1 <= D <= 1000), X=xp/zp Y=yp/zp^2 from rational point on y^2=x^3-4Dx (1 <= D <= 1000) (using Cremona's mwrank.exe) X=2x/y Y=(X*x^2)/2-1 ignoring "-". D | xp, yp, zp ----+----------------------------------- 3 | 1, 2, 1 5 | 2, 9, 1 8 | 1, 3, 1 9 | 2, 5, 3 13 | 2, 17, 3 14 | 2, 15, 1 14 | 6, 137, 5 15 | 1, 4, 1 18 | 2, 17, 1 19 | 1, 10, 3 20 | 1, 3, 2 21 | 2, 31, 5 24 | 1, 5, 1 28 | 2, 23, 3 29 | 2, 33, 5 31 | 3, 56, 5 33 | 1, 17, 4 33 | 2, 23, 1 34 | 2, 25, 3 34 | 28, 4577, 15 35 | 1, 6, 1 37 | 30, 23449, 151 39 | 2, 55, 7 39 | 4, 103, 5 40 | 1, 11, 3 46 | 6, 671, 25 46 | 10, 809, 21 47 | 5, 336, 17 48 | 1, 2, 2 49 | 3, 65, 4 51 | 1, 26, 5 53 | 2, 57, 7 55 | 2, 31, 3 55 | 4, 119, 3 56 | 2, 39, 5 60 | 2, 31, 1 61 | 90, 64369, 109 63 | 1, 8, 1 63 | 2, 29, 9 65 | 4, 129, 1 65 | 3, 209, 14 66 | 2, 41, 5 66 | 10, 889, 19 67 | 15, 3026, 49 68 | 1, 9, 4 68 | 3, 49, 8 69 | 4, 215, 13 73 | 4, 137, 3 73 | 3, 77, 2 77 | 40, 15639, 83 79 | 3, 80, 1 80 | 1, 9, 1 83 | 3, 82, 1 84 | 1, 5, 2 85 | 2, 89, 9 88 | 1, 13, 3 89 | 4, 153, 5 89 | 7, 1245, 34 90 | 2, 13, 3 92 | 90, 119351, 301 93 | 2, 127, 11 94 | 4, 175, 9 94 | 14, 2777, 45 95 | 2, 39, 1 98 | 2, 9, 7 99 | 1, 50, 7 99 | 2, 47, 5 100 | 2, 41, 3 101 | 1450, 72997881, 8359 104 | 1, 27, 5 105 | 1, 19, 4 105 | 2, 41, 1 109 | 10, 68129, 261 111 | 2, 49, 5 113 | 4, 177, 7 113 | 5, 369, 16 114 | 2, 65, 7 114 | 10, 1081, 13 115 | 1, 14, 3 120 | 1, 11, 1 121 | 70, 4901, 33 124 | 4, 287, 15 125 | 2, 129, 11 126 | 10, 1129, 11 127 | 175, 347776, 207 128 | 1, 3, 2 129 | 1, 65, 8 129 | 2, 175, 13 131 | 3, 106, 5 133 | 2, 47, 3 136 | 10, 1169, 9 138 | 2, 47, 1 138 | 14, 2953, 43 141 | 8, 3119, 55 143 | 1, 12, 1 144 | 1, 5, 3 145 | 4, 209, 9 145 | 6, 521, 17 148 | 1, 19, 6 149 | 70, 102729, 289 150 | 2, 11, 5 150 | 2, 49, 1 152 | 15, 2789, 17 153 | 1, 13, 2 154 | 2, 95, 9 154 | 10, 1241, 3 155 | 4, 351, 17 155 | 6, 479, 13 156 | 10, 1249, 1 157 | 15810, 8494718929, 88861 158 | 4, 207, 7 158 | 18, 7193, 77 159 | 1, 28, 5 163 | 1, 82, 9 164 | 2, 57, 5 165 | 2, 71, 7 168 | 1, 13, 1 171 | 2, 77, 15 173 | 2, 177, 13 175 | 1, 16, 3 178 | 2, 97, 9 178 | 44, 26033, 57 179 | 3, 130, 7 180 | 1, 7, 2 181 | 659230, 9220300757321, 2670111 183 | 2, 73, 7 183 | 8, 1207, 29 184 | 2, 55, 3 185 | 4, 249, 11 185 | 15, 3061, 8 188 | 24, 7903, 17 189 | 2, 55, 1 191 | 11, 7416, 85 195 | 1, 14, 1 196 | 12, 337, 35 197 | 85964410, 114288283364168169, 219078991 198 | 2, 19, 3 200 | 1, 51, 7 201 | 1, 101, 10 201 | 6, 511, 5 203 | 4, 1863, 43 203 | 6, 527, 11 205 | 44, 27761, 39 206 | 4, 231, 5 206 | 2070, 180306889, 13019 208 | 1, 17, 3 209 | 3, 8465, 92 209 | 2, 63, 5 211 | 33, 15866, 35 212 | 5, 16563, 182 213 | 4, 263, 11 216 | 1, 29, 5 219 | 2, 295, 17 219 | 44, 28657, 25 220 | 14, 3281, 39 221 | 60, 64769, 191 223 | 7, 1312, 33 224 | 1, 15, 1 224 | 3, 137, 5 225 | 1, 13, 6 226 | 12, 9281, 95 226 | 200, 622049, 399 227 | 3135, 175327346, 9689 228 | 1, 11, 4 229 | 2, 233, 15 232 | 55, 50891, 147 233 | 4, 297, 13 233 | 5, 429, 14 234 | 6, 833, 25 237 | 210, 910591, 779 238 | 4, 247, 3 238 | 22, 15593, 117 239 | 13, 14400, 119 240 | 1, 4, 2 242 | 330, 2176561, 1169 243 | 1, 2, 3 248 | 2, 63, 1 253 | 2, 103, 9 254 | 4, 255, 1 254 | 102, 165817, 35 255 | 1, 16, 1 258 | 2, 137, 11 258 | 14, 3433, 37 259 | 2, 65, 3 260 | 1, 33, 8 260 | 3, 73, 4 264 | 2, 65, 1 269 | 110, 226689, 331 271 | 19, 65296, 255 273 | 2, 367, 19 273 | 1, 23, 4 274 | 4, 265, 3 274 | 52, 46097, 105 275 | 1, 6, 5 276 | 2, 71, 5 277 | 16423210, 6364939035625529, 67173561 279 | 2, 35, 9 280 | 1, 19, 3 281 | 20, 175689, 419 281 | 329, 2777181, 1450 284 | 6, 1367, 35 285 | 12, 2431, 1 287 | 5, 456, 13 288 | 1, 17, 1 289 | 1, 145, 12 289 | 56, 3425, 153 291 | 10, 2791, 47 292 | 20, 45881, 213 293 | 2, 297, 17 294 | 2, 73, 5 295 | 6, 641, 13 295 | 8, 1319, 27 296 | 65, 74811, 133 299 | 6, 1145, 31 299 | 6, 623, 5 301 | 56, 60839, 165 303 | 1, 52, 7 304 | 1, 10, 6 306 | 4, 281, 5 307 | 225, 1202426, 901 308 | 1, 9, 2 308 | 3, 79, 2 309 | 6, 655, 13 310 | 2, 71, 3 310 | 174, 807721, 779 312 | 5, 1901, 43 315 | 2, 71, 1 316 | 53200, 50319156959, 29679 317 | 7160774570, 9156486995910318703809, 95450823979 319 | 1, 20, 3 320 | 1, 3, 4 323 | 3, 202, 11 323 | 2, 87, 7 323 | 6, 647, 1 325 | 6, 649, 1 328 | 1, 83, 9 328 | 3, 203, 11 328 | 14, 3713, 33 333 | 2, 73, 1 333 | 4, 101, 9 334 | 12, 10535, 101 334 | 26, 29897, 165 335 | 3, 236, 13 336 | 1, 31, 5 337 | 2600, 160887089, 10119 337 | 5, 481, 12 339 | 1, 170, 13 340 | 3, 83, 2 341 | 90, 149671, 73 342 | 1260, 143296649, 11843 344 | 3, 3485, 59 345 | 3, 179, 8 345 | 2, 89, 7 348 | 4, 343, 13 349 | 6, 673, 5 351 | 2, 79, 5 353 | 4, 417, 17 353 | 7, 1377, 32 354 | 2, 185, 13 354 | 22, 16057, 115 355 | 6, 689, 11 356 | 40, 59721, 227 357 | 70, 92921, 89 360 | 1, 19, 1 360 | 2, 37, 9 361 | 850, 1646021, 5301 363 | 2, 13, 11 365 | 2, 369, 19 367 | 1275, 31146416, 703 369 | 1, 25, 4 371 | 2, 81, 5 373 | 6, 697, 7 376 | 112, 243919, 135 380 | 18, 8081, 71 381 | 1274, 2928604591, 54115 383 | 5, 504, 11 384 | 1, 5, 2 385 | 1, 41, 6 385 | 3, 311, 16 386 | 6, 15641, 125 386 | 60, 75329, 161 388 | 2, 113, 9 388 | 7, 1249, 48 389 | 130, 357369, 359 390 | 2, 79, 1 390 | 14, 3961, 29 393 | 1, 197, 14 393 | 6, 1103, 29 395 | 10, 3441, 53 395 | 66, 90559, 163 396 | 20, 8441, 53 397 | 5214689070, 678486823935140827489, 20208571931 398 | 8, 2247, 43 398 | 114, 259273, 37 399 | 2, 535, 23 399 | 1, 32, 5 399 | 8, 1423, 25 403 | 1, 22, 3 404 | 1, 51, 10 405 | 2, 9, 3 406 | 2, 239, 15 406 | 150, 522169, 509 408 | 1, 53, 7 410 | 2, 81, 1 410 | 708, 14242801, 3161 412 | 11050, 38207326871, 195261 413 | 6, 2327, 47 414 | 2, 95, 7 415 | 5, 1604, 39 418 | 4, 337, 9 418 | 14, 4073, 27 419 | 3, 250, 13 420 | 1, 13, 4 421 | 217190, 968049796169, 135009 423 | 4, 623, 23 424 | 3, 187, 5 425 | 4, 489, 19 425 | 1, 21, 2 429 | 4, 335, 7 431 | 1819, 83538576, 6895 434 | 2, 87, 5 434 | 216, 975857, 295 435 | 3, 194, 7 437 | 70, 103119, 109 438 | 2, 97, 7 438 | 52, 56593, 23 440 | 1, 21, 1 444 | 14, 4177, 25 445 | 2, 449, 21 445 | 6, 761, 7 445 | 52, 57041, 9 446 | 658, 39572871, 6205 446 | 30, 52409, 221 447 | 65, 89404, 61 448 | 1, 23, 3 450 | 6, 929, 23 451 | 1, 226, 15 453 | 6, 847, 19 456 | 2, 89, 5 461 | 240767770, 1264941190283659521, 475038539 463 | 5, 544, 9 464 | 1, 33, 5 466 | 2, 241, 15 466 | 496720, 386896743601169, 19668759 467 | 53295, 447639074506, 665891 468 | 1, 11, 2 468 | 2, 29, 3 469 | 12, 4855, 61 471 | 2, 631, 25 471 | 60, 78151, 43 472 | 1485, 49656269, 3613 473 | 3, 277, 14 473 | 2, 87, 1 475 | 6, 157, 5 475 | 2, 119, 9 476 | 30, 19639, 19 478 | 10, 5239, 69 478 | 994, 30002393, 4563 479 | 7, 1440, 31 483 | 1, 22, 1 485 | 962, 21348729, 2521 488 | 1, 123, 11 490 | 2, 89, 3 493 | 6, 817, 13 495 | 1, 28, 9 495 | 2, 89, 1 496 | 3, 56, 10 497 | 5, 561, 8 497 | 20, 8919, 13 498 | 4, 377, 11 498 | 26, 30553, 163 499 | 39, 34490, 77 501 | 4, 359, 5 505 | 4, 569, 21 505 | 6, 809, 1 508 | 8, 4223, 63 509 | 22814, 11938856913, 46435 510 | 2, 151, 11 510 | 14, 4441, 19 511 | 9, 3536, 55 513 | 1, 257, 16 513 | 2, 103, 7 514 | 24, 22865, 137 514 | 68, 116417, 225 515 | 1, 54, 7 517 | 19019850, 12665551473700151, 98138207 518 | 2, 303, 17 518 | 18, 8633, 67 520 | 3, 211, 7 522 | 70, 37333, 57 525 | 2, 19, 5 527 | 5, 576, 7 528 | 1, 17, 8 528 | 1, 23, 1 529 | 11, 7585, 84 531 | 1, 34, 5 531 | 20, 9401, 43 532 | 5, 2197, 66 533 | 2, 537, 23 536 | 21, 10229, 25 539 | 2, 15, 7 540 | 4, 391, 11 541 | 5510, 708441521, 7539 542 | 350, 3775671, 1573 542 | 390, 3668441, 979 543 | 2, 193, 13 544 | 1, 25, 3 544 | 14, 4577, 15 547 | 55, 4004626, 2001 548 | 2, 153, 11 549 | 2, 97, 5 549 | 4, 125, 3 552 | 40, 38951, 101 553 | 5, 589, 6 553 | 12, 5623, 67 557 | 21830, 652490767569, 807709 558 | 14, 4633, 13 559 | 2, 95, 3 560 | 1, 6, 2 563 | 3, 22802, 151 564 | 2, 95, 1 564 | 5, 383, 22 565 | 1118, 29812169, 1569 568 | 4, 583, 21 570 | 4, 479, 17 570 | 14, 4681, 11 572 | 4830, 577263311, 12169 573 | 4, 383, 1 574 | 6, 935, 19 574 | 34, 85817, 285 575 | 1, 24, 1 579 | 1, 290, 17 579 | 6, 1015, 23 579 | 14, 10183, 95 580 | 1, 73, 12 580 | 22, 16961, 111 581 | 66, 416671, 635 583 | 2, 97, 3 583 | 8, 1607, 21 584 | 18, 8897, 65 585 | 1, 29, 4 588 | 2, 97, 1 589 | 40, 38831, 9 591 | 55, 83524, 199 592 | 15, 23449, 151 593 | 4, 657, 23 593 | 5, 609, 4 594 | 2, 305, 17 594 | 14, 4777, 5 595 | 1, 26, 3 596 | 85, 88323, 98 597 | 22148490, 64100834007994111, 250938731 598 | 2, 127, 9 598 | 14, 4793, 3 600 | 1, 7, 5 601 | 120, 458569, 541 601 | 7, 1501, 30 603 | 4, 131, 3 604 | 946, 56911607, 7245 607 | 5, 616, 3 609 | 1, 103, 10 609 | 4, 535, 19 611 | 15, 15214, 119 613 | 6, 937, 17 616 | 4, 5639, 75 617 | 1600, 245209929, 15389 617 | 5, 621, 2 620 | 2, 111, 7 620 | 138, 480721, 281 621 | 176, 779111, 325 623 | 5, 624, 1 624 | 1, 55, 7 624 | 2, 103, 5 627 | 5, 626, 1 629 | 2, 633, 25 630 | 2, 43, 9 632 | 140, 509679, 361 633 | 5, 629, 2 633 | 2, 847, 29 636 | 4970, 645186271, 12961 640 | 1, 11, 6 643 | 5, 634, 3 644 | 1, 15, 4 644 | 9, 3361, 80 645 | 24, 15569, 73 646 | 6, 1529, 35 646 | 100, 431969, 591 648 | 1, 3, 3 649 | 1, 325, 18 649 | 2, 247, 15 650 | 2, 21, 5 650 | 12, 3689, 19 651 | 6, 1111, 25 651 | 10, 3151, 43 653 | 598, 19769697, 4187 655 | 10, 3649, 51 657 | 5, 641, 4 658 | 2, 103, 3 658 | 76, 172433, 297 659 | 3, 370, 17 660 | 1, 13, 2 661 | 37230, 43705643209, 159071 663 | 2, 103, 1 663 | 8, 1687, 19 664 | 1, 85, 9 665 | 1, 69, 8 665 | 3, 3851, 62 666 | 10, 5921, 73 668 | 522, 12412183, 3197 669 | 1066, 33953695, 4123 671 | 1, 36, 5 675 | 1, 26, 1 676 | 30, 106921, 323 677 | 42670, 51216327129, 139511 680 | 1, 171, 13 684 | 2, 35, 3 685 | 6, 1009, 19 687 | 650, 27333751, 4999 689 | 4, 753, 25 689 | 6, 1265, 29 690 | 2, 199, 13 690 | 22, 17401, 109 691 | 62941, 104460084226, 90585 695 | 14, 12561, 107 695 | 12, 5879, 67 696 | 5, 3779, 61 697 | 140, 589289, 531 697 | 15, 25661, 158 700 | 4, 431, 9 701 | 3533941190, 872471631054132766929, 28414544861 703 | 1, 28, 3 705 | 3, 239, 2 705 | 2, 161, 11 706 | 4, 481, 15 706 | 44976040, 53758132198551809, 32059521 707 | 1225, 39903366, 671 709 | 1222, 39768473, 855 710 | 24, 15991, 67 710 | 18, 9401, 61 711 | 2, 83, 15 712 | 5660, 6442727921, 79911 713 | 13, 14637, 118 713 | 12, 3847, 11 717 | 320, 7864320239, 88681 718 | 6, 1007, 17 718 | 38, 133193, 357 719 | 7, 1560, 29 722 | 2190, 10252170001, 101249 723 | 1, 362, 19 723 | 2, 967, 31 723 | 68, 129793, 193 724 | 3, 131, 10 725 | 12, 3881, 13 726 | 60, 106729, 211 728 | 1, 27, 1 729 | 2, 5, 9 731 | 2, 111, 5 731 | 840, 122299169, 10991 732 | 104390, 837875191201, 885601 733 | 2, 737, 27 734 | 8, 2415, 41 734 | 138, 517657, 205 735 | 1, 124, 11 735 | 1, 8, 7 736 | 3, 671, 25 736 | 5, 809, 21 738 | 2, 377, 19 739 | 3, 29930, 173 740 | 2, 201, 13 741 | 1222, 42857311, 3685 744 | 1, 37, 5 747 | 9240, 25679686889, 159917 749 | 8, 109575, 331 751 | 693, 48931376, 6865 752 | 5, 336, 34 753 | 5, 689, 8 753 | 14, 29063, 169 755 | 4, 471, 13 757 | 358091450, 5096238244666339049, 1917696399 759 | 2, 113, 5 759 | 16, 17143, 125 760 | 1, 29, 3 763 | 2, 137, 9 763 | 282, 19580527, 4411 764 | 252, 2138207, 1105 765 | 2, 121, 7 765 | 2, 37, 3 767 | 55, 113604, 277 768 | 1, 2, 4 770 | 2, 111, 1 770 | 18, 9641, 59 771 | 261, 2882906, 1475 773 | 442, 22411737, 4663 774 | 20, 11129, 11 776 | 60, 100289, 31 781 | 30, 29879, 127 783 | 1, 28, 1 784 | 3, 65, 8 787 | 5, 706, 9 788 | 1, 99, 14 789 | 8, 3335, 53 791 | 4, 7239, 85 791 | 60, 101249, 1 793 | 4, 857, 27 793 | 42, 50977, 107 796 | 10, 10199, 99 797 | 9689291268670, 44431893811418353355436425649, 210600981540301 798 | 2, 113, 1 798 | 22, 17833, 107 799 | 8, 1823, 15 801 | 1, 401, 20 803 | 3, 442, 19 804 | 1, 35, 8 805 | 24, 18161, 89 808 | 3, 283, 11 813 | 6, 1327, 29 815 | 3, 284, 11 816 | 1, 26, 10 818 | 48, 65897, 19 818 | 84, 246833, 377 819 | 2, 365, 33 819 | 1, 38, 5 820 | 1, 23, 6 820 | 26, 31841, 159 821 | 246790, 1753383752409, 412279 824 | 14, 76935, 277 825 | 1, 29, 2 825 | 2, 311, 17 828 | 4, 463, 7 828 | 6, 1097, 19 829 | 170, 852209, 429 831 | 126, 2679991, 1625 833 | 1, 33, 4 834 | 4, 545, 17 834 | 150, 660841, 347 835 | 1, 86, 9 837 | 2370, 4831176919, 69487 840 | 1, 29, 1 845 | 2, 849, 29 846 | 2, 119, 5 848 | 1, 57, 7 851 | 15, 582206, 763 852 | 10, 30071, 173 853 | 6, 1177, 23 855 | 8, 1879, 13 856 | 63, 706829, 835 858 | 2, 127, 7 858 | 34, 86953, 283 860 | 1848, 101782951, 4261 861 | 30, 1063289, 1031 862 | 18860, 23605182991, 145497 862 | 410, 4980761, 819 863 | 11, 7752, 83 866 | 594, 10591081, 1445 866 | 660, 13639969, 2159 867 | 5, 746, 11 868 | 2, 143, 9 869 | 4, 783, 25 870 | 2, 169, 11 870 | 328, 3716641, 1391 872 | 95, 266571, 77 873 | 1, 49, 12 876 | 2, 121, 5 876 | 1500, 248681809, 15479 878 | 14, 19647, 137 878 | 42, 197993, 437 879 | 3, 268, 5 880 | 1, 31, 3 880 | 2, 119, 3 881 | 200, 344141649, 18551 881 | 2669, 340577601, 16340 883 | 1, 442, 21 884 | 1, 15, 2 884 | 18, 10097, 55 885 | 2, 119, 1 888 | 3, 317, 13 890 | 2, 129, 7 890 | 148860, 701330477041, 483929 892 | 1379560, 94069325453951, 8657601 893 | 2, 207, 13 895 | 10, 12679, 111 896 | 1, 39, 5 898 | 2, 457, 21 898 | 248, 1843073, 63 899 | 1, 30, 1 900 | 2, 17, 15 901 | 6, 4361, 65 903 | 2, 313, 17 903 | 8, 1927, 11 904 | 1, 227, 15 904 | 3, 275, 7 904 | 22, 18257, 105 905 | 4, 969, 29 905 | 10, 3849, 49 910 | 2, 121, 3 910 | 68, 141761, 159 911 | 287, 2506536, 565 913 | 5, 769, 12 913 | 6, 3647, 59 914 | 24, 39065, 187 914 | 1488, 89780177, 7735 915 | 2, 121, 1 916 | 585, 5320547, 1562 917 | 30, 28111, 83 920 | 3, 3731, 61 921 | 21, 38501, 190 921 | 2, 1231, 35 924 | 4, 487, 5 925 | 182, 26428529, 5139 926 | 476, 11802351, 3095 926 | 150, 690649, 301 932 | 80, 211161, 283 933 | 16, 49463, 221 937 | 120, 668569, 709 937 | 315, 3175181, 962 938 | 2, 543, 23 938 | 18, 10313, 53 939 | 4, 505, 11 939 | 76, 190417, 265 941 | 37195785070, 76868662544190706581921, 253160835589 943 | 7, 1672, 27 943 | 4, 2647, 51 943 | 8, 1967, 9 945 | 1, 31, 2 945 | 2, 209, 13 947 | 3315, 3212247986, 56519 949 | 6, 1273, 25 952 | 10, 20119, 141 954 | 4, 181, 15 955 | 18, 33569, 179 955 | 14, 10559, 93 956 | 1560, 214186079, 14161 957 | 20, 22481, 137 958 | 6, 1127, 13 958 | 75110, 1331308861241, 1148829 959 | 12, 6143, 65 960 | 1, 31, 1 961 | 5727, 2056525601, 42280 963 | 1, 58, 7 963 | 6, 3023, 53 964 | 2, 257, 15 964 | 11, 7441, 120 965 | 2, 969, 31 969 | 1, 485, 22 969 | 2, 127, 5 973 | 30, 28759, 79 975 | 1, 8, 5 976 | 45, 64369, 109 978 | 6, 39617, 199 978 | 26, 32473, 157 979 | 10, 3479, 39 984 | 1, 125, 11 988 | 4, 503, 3 989 | 2, 135, 7 990 | 6, 1169, 17 991 | 27, 266216, 515 994 | 6, 1135, 1 994 | 92, 343457, 465 995 | 4, 519, 11 996 | 9, 9883, 140 997 | 21329624677741230, 14391049283467552993254253873806169, 29340760454551241 999 | 2, 175, 11 999 | 8, 2023, 5 1000 | 3, 331, 13