
// A data file accompanying Section 6 of the paper:
//
// "EVERYWHERE LOCAL SOLUBILITY FOR HYPERSURFACES IN PRODUCTS
// OF PROJECTIVE SPACES"
// TOM FISHER, WEI HO, AND JENNIFER PARK

///////////////////////////////////////////////////////
//                                                   //
//               Experiment with H = 1000            //
//                                                   //
///////////////////////////////////////////////////////

// We list data relating to 1000 randomly chosen (2,2)-forms
// with integer coefficients in [-H,H] where H = 1000.

// The data listed is as follows:
// forms - a list of (2,2)-forms, each specified by 9 coefficients.
// solution_data - a list of data relating to the existence
//    or otherwise of a solution. This might be either (i) a
//    list of places where local solubility fails (-1 indicates
//    the infinite place), (ii) a solution (4 coordinates), or
//    (iii) a binary quartic (5 coefficients) or quadric
//    intersection (20 coefficients) that proves insolubility via
//    the Cassels-Tate pairing
// rank_data - the upper bounds r2,r4,r8 for the Mordell-Weil rank
//    of the Jacobian obtained by 2-, 4- or 8-descent, followed by
//    a list of the x-coordinates of the known generators.
//    In this experiment we did not compute r8 (recorded as -1). 
// qilist - a list of quadric intersections (20 coefficients)
//    that we use as witnesses to the fact that certain 2-Selmer
//    group elements are in the image of the 4-Selmer group.
// ctp24data - a list of pairs of binary quartics (5 coefficients)
//    and quadric intersections (20 coefficients) together with
//    the output (0 or 1) of running CasselsTatePairing on them.

forms := [
[ -301, -719, -375, 723, 162, -263, 831, -983, -201 ],
[ 455, 607, -568, 633, -634, -397, -937, 703, 397 ],
[ -172, -916, 760, -665, 102, 699, -574, -862, -751 ],
[ 643, 281, 322, 304, -468, -324, 521, -338, -858 ],
[ -558, 637, 325, -663, 468, -95, -354, 813, 92 ],
[ 265, -144, 45, -614, -382, 197, -853, -324, 973 ],
[ -305, -8, -861, 725, 538, 250, -14, 132, 735 ],
[ 225, 698, -759, 259, -592, 508, 509, -612, -429 ],
[ -792, 554, 683, 572, -19, 193, 255, 91, -901 ],
[ -754, 437, -642, -360, -662, 239, 853, 566, 819 ],
[ -355, -203, 87, -655, -519, 278, -961, 86, -832 ],
[ -919, 333, -368, 759, 748, -662, 715, 993, -581 ],
[ -690, 982, -971, -293, -98, 62, -678, 962, 248 ],
[ -407, 18, 669, -671, 816, -362, 206, -443, 638 ],
[ 498, 106, -487, -933, 305, 235, -434, 680, 452 ],
[ -506, -559, -712, -252, -991, 120, 385, -229, -562 ],
[ 118, -55, -934, -217, -209, -97, 617, -629, -432 ],
[ 989, 341, 86, -229, -479, 591, -700, 877, 123 ],
[ 370, -412, 951, 173, -659, -678, -28, -811, -926 ],
[ 966, 316, 978, 791, -671, 340, 57, -721, -366 ],
[ -942, 319, -543, -203, 283, -500, 811, -547, -833 ],
[ 421, 250, -871, 547, 608, -979, -966, 421, 589 ],
[ 884, 572, -208, -121, 876, -219, -490, 883, -306 ],
[ 969, 391, -573, -60, -356, -517, 168, 264, -331 ],
[ 699, -603, -19, 276, 131, -44, 29, 685, -623 ],
[ 403, -884, -583, 706, -48, -586, -461, 447, -578 ],
[ 934, -464, 887, -34, -784, -676, 181, 727, 557 ],
[ 552, 488, 411, -47, -738, 216, -934, -533, -422 ],
[ -278, 89, -9, -366, 296, 264, -818, -764, 331 ],
[ -858, -673, -90, -501, 747, 690, -415, -212, -7 ],
[ 917, -24, -722, 108, -3, 90, -455, 528, -122 ],
[ -474, -930, -788, -70, 708, -478, 132, 333, -182 ],
[ 218, -331, 239, 463, -463, 796, 905, -689, 911 ],
[ 988, -628, -961, 688, 252, -404, -500, 515, -168 ],
[ 633, -562, 937, 665, 443, 707, 696, -937, -190 ],
[ 91, -945, 41, 576, 23, -200, 418, -22, -40 ],
[ -866, -144, 729, -800, -920, -672, -574, -768, 220 ],
[ 870, -28, -559, -75, 207, 582, -748, 953, -371 ],
[ 287, -151, -25, -150, 764, -528, 89, 865, -586 ],
[ 440, -173, -998, 17, 105, 146, -468, 854, -392 ],
[ -210, 107, 229, -441, -908, 611, 880, 414, 154 ],
[ -341, -978, 407, -514, -541, -572, -821, -377, -98 ],
[ 31, -280, -200, -941, 323, -916, 112, -803, -790 ],
[ -427, 877, 367, -283, 526, -4, -347, 350, -392 ],
[ -287, -618, 775, -406, 712, -541, 52, 39, 649 ],
[ -557, -868, 450, -956, -121, -374, 401, 78, 317 ],
[ 264, 132, -153, 479, -724, -859, 868, -645, -241 ],
[ -472, -162, 804, -793, 355, -503, -933, 868, 816 ],
[ 397, 313, -567, -631, 654, 106, -993, -861, 394 ],
[ -678, -691, -512, 186, -442, 732, -391, 984, -359 ],
[ -507, 162, -313, -250, 814, 458, -685, 851, -404 ],
[ -832, -731, 724, -593, 470, 60, -900, 818, -947 ],
[ 540, -373, -192, -529, 74, -454, -965, 151, -60 ],
[ -285, -894, -227, 130, -122, 891, 258, 753, 481 ],
[ -943, -368, -674, 553, 893, -199, 350, -291, -54 ],
[ -923, -789, -805, 362, 628, -466, -819, 699, -846 ],
[ -163, -533, -970, 546, -882, -69, -335, 575, -189 ],
[ 187, 928, 811, -577, -436, 663, -530, -328, -748 ],
[ -387, 316, 712, 228, -589, 55, -345, 286, 923 ],
[ 420, 248, 446, 359, 605, -82, -164, 735, -963 ],
[ -712, -757, -693, 858, 10, 663, 853, -111, -953 ],
[ 456, 572, -754, -166, 177, 826, -515, 87, 933 ],
[ 794, 666, 614, 668, -107, 589, -255, 538, 976 ],
[ -83, -77, -670, -603, 782, -815, 198, 74, 594 ],
[ -817, 690, -380, -652, -166, 920, 220, -720, -439 ],
[ -935, 314, 675, 263, 494, 371, 779, -202, 540 ],
[ 684, 571, -928, 706, 39, -407, 624, -922, -590 ],
[ -296, -523, 847, -330, -297, 940, 610, 393, -353 ],
[ 78, 73, -265, -37, -168, -145, 175, -749, -486 ],
[ 221, -321, -605, 974, 984, -680, 51, 846, -357 ],
[ -517, 558, -88, -533, 751, -800, -943, -655, 490 ],
[ 736, 449, -983, 641, 624, -672, 181, -248, -922 ],
[ 465, 522, 616, 84, -741, 31, 911, -550, -811 ],
[ -624, -874, 19, -826, 776, 745, 985, 965, 957 ],
[ -721, -430, -892, -370, 271, -832, 886, -539, -186 ],
[ -813, 94, 601, 302, -457, 83, 925, 345, 259 ],
[ -952, -405, 978, 738, -47, 377, 698, -159, -990 ],
[ -961, 410, -964, 812, -295, 405, -129, -228, -571 ],
[ 934, -371, -185, 900, 153, -326, 194, 514, 778 ],
[ 95, 97, 469, 901, -307, 6, -976, -843, -861 ],
[ -309, -537, -732, -140, 548, -306, -534, 490, -519 ],
[ 987, 819, 583, -28, -929, -358, 536, -438, 551 ],
[ 667, -650, -564, -246, 976, -586, -658, -830, 846 ],
[ 997, 843, -787, 903, 866, -303, -146, 174, 901 ],
[ -410, -993, 208, -947, -925, 926, -512, -533, 888 ],
[ 188, -950, -40, -116, 148, 581, 5, 406, -762 ],
[ 745, 785, -860, 207, -184, -47, 659, -145, -736 ],
[ 351, 18, -975, 58, 169, 59, 166, 571, 580 ],
[ -936, 581, -203, -496, -332, 224, -859, -466, 309 ],
[ 368, 149, 714, -598, -91, 601, 816, -166, 0 ],
[ -701, -725, 514, 229, -427, 135, -406, -677, -783 ],
[ -263, -943, 963, 519, -345, 598, 369, -501, 517 ],
[ 377, 442, 461, 842, 7, -441, 36, 65, -703 ],
[ -872, -721, 371, -347, -295, -437, 897, 793, 345 ],
[ -367, 68, -975, -385, 108, -773, 578, -106, -465 ],
[ 610, -854, -429, -48, -430, -271, -287, 873, -159 ],
[ -546, 188, -881, 966, 774, -103, 990, -151, 874 ],
[ -466, 942, -308, -617, 463, -543, 905, -432, 336 ],
[ -950, 489, 363, 283, 257, 316, -257, -176, -646 ],
[ -361, 658, 443, 43, 599, 0, -396, 480, 978 ],
[ 572, -784, 716, 304, 924, -521, -863, 457, -757 ],
[ -18, -358, 934, -634, 512, -7, -745, 638, -997 ],
[ -66, -327, 957, -191, -872, 139, 435, 536, 420 ],
[ 597, -458, -646, -127, -492, -960, -55, -537, 888 ],
[ 964, -255, -455, 755, 537, 810, -88, -571, 659 ],
[ -440, -762, -624, -850, 569, -222, 665, -499, 612 ],
[ 993, 178, -851, 55, -529, 391, 493, -32, 955 ],
[ -3, -621, 8, -376, 204, 678, 89, 826, -183 ],
[ 953, 791, -164, -632, -406, -134, -2, 506, -450 ],
[ 706, -548, 442, 918, 771, 58, -898, -96, 708 ],
[ 896, -796, -314, -73, -911, 777, 10, -566, 181 ],
[ 62, 731, -777, 840, -711, 216, 941, -193, 329 ],
[ -209, 647, 217, 641, 978, 328, -442, 545, -312 ],
[ 990, 630, 423, 67, 435, -1, -473, 666, -752 ],
[ -630, 935, -363, 866, -94, -349, -293, 920, 886 ],
[ 8, -955, 513, 24, -505, -570, 565, 257, -381 ],
[ 729, -79, -674, 470, -870, 983, -221, -685, 805 ],
[ -278, 910, -637, 947, 703, 92, 165, 250, 318 ],
[ 402, -70, -218, -990, -418, 883, 536, -128, -636 ],
[ -283, 877, 525, 160, 185, -215, 416, 189, -619 ],
[ 608, 388, 693, 893, 162, 2, -126, 417, -458 ],
[ 154, -873, -788, -270, 364, 492, -54, 21, 449 ],
[ 29, 904, -467, 213, -105, 605, -778, -252, 692 ],
[ 243, -487, 149, -703, -599, -41, 688, -696, -796 ],
[ 459, 589, 408, -745, -330, 279, -286, 479, -564 ],
[ -286, -542, -124, -97, -674, 432, -370, 458, -546 ],
[ -339, 458, -307, -394, -937, -673, -803, 794, -688 ],
[ -877, 511, 657, 878, -141, -453, -494, -958, 455 ],
[ -516, 446, 471, 784, 21, -394, -74, -436, -172 ],
[ -891, 60, -522, 278, 832, -461, -611, -709, -940 ],
[ -427, -47, -827, -981, 340, -403, 807, -276, -419 ],
[ 63, 338, -958, 787, 301, 53, -44, 351, 428 ],
[ 687, 706, -767, 135, -433, -106, -119, 601, -858 ],
[ -202, 518, -679, -433, -578, 122, 648, 294, -156 ],
[ 339, 925, 219, 988, 241, 151, -154, -607, 391 ],
[ 721, -646, 416, -258, 493, 630, -874, 194, 897 ],
[ 196, -74, 669, 596, 632, -541, -940, 912, 875 ],
[ 401, 131, 248, 625, -585, -198, 62, 555, -260 ],
[ -325, -567, -950, -943, -62, -674, -797, 240, -122 ],
[ -661, 870, 291, -159, -693, -435, 925, 824, -546 ],
[ 658, -9, -90, 578, 508, 241, -437, 556, 731 ],
[ 11, 972, -230, -441, 966, 990, 882, -336, -613 ],
[ 211, 98, 500, -616, -978, -308, 571, -150, 109 ],
[ -215, -1, -284, 96, 767, -736, 789, -419, -84 ],
[ 221, -949, -477, -466, 243, -312, -792, 398, 95 ],
[ 735, 684, -168, 654, 973, 536, -719, 372, -386 ],
[ 525, 308, -447, -973, -140, 223, 765, -554, 547 ],
[ -688, 837, -364, -850, 50, -331, 484, -645, -799 ],
[ 233, -57, -896, 2, 210, -348, 448, -705, -220 ],
[ -94, 204, -42, -895, -938, 760, -797, -615, -709 ],
[ 425, -825, 62, -926, -397, -395, 625, 39, -185 ],
[ 505, -94, -752, 974, -634, -27, 11, 848, 975 ],
[ -966, 635, 698, 61, 600, -568, -92, 520, -100 ],
[ 587, -22, 273, 450, 135, -855, 116, -8, 363 ],
[ -332, -531, -422, -69, -284, -7, -964, 158, -150 ],
[ -645, -569, 641, 442, -945, 132, -559, 253, -19 ],
[ 199, -628, 22, 306, 998, 272, 293, -827, -114 ],
[ -828, -506, 557, 535, 310, 463, -276, 861, -385 ],
[ -749, 889, -565, -724, 301, -886, -640, 743, -864 ],
[ -253, 670, -421, 43, 823, 725, 59, 708, -926 ],
[ 589, -941, -564, 762, 135, -892, -172, -252, 56 ],
[ -142, 507, -37, 125, 875, -54, -372, 634, -396 ],
[ 569, 302, 863, -44, -906, -955, -444, 507, 362 ],
[ 633, -249, -871, 764, 253, 781, 365, 304, 890 ],
[ -904, 823, 349, -888, -611, 178, 678, -28, 679 ],
[ 540, 649, -596, -919, 881, 847, 677, -131, 120 ],
[ 712, 364, 596, -549, 994, -739, -832, -563, -983 ],
[ 957, -599, 445, 169, 559, -971, -582, -956, -422 ],
[ 59, -164, -741, 233, -736, 600, -445, 578, -167 ],
[ -661, 31, -899, -33, 842, -959, -714, -317, 237 ],
[ -175, -807, 443, -799, 983, 385, -340, 528, -668 ],
[ 232, 356, 646, 959, -669, -167, -813, 284, -771 ],
[ 523, -993, -173, 800, -300, 94, 598, 452, 646 ],
[ -905, -721, 336, 467, -918, 858, -939, 939, -63 ],
[ -773, 716, 472, 621, -888, -491, 813, -993, -50 ],
[ -795, 36, 64, -575, 139, 214, -633, -517, 279 ],
[ 84, -513, 65, 90, -504, -170, -763, -913, 307 ],
[ 134, 287, -934, -449, 142, 375, -380, -883, -705 ],
[ 468, -349, -759, 88, 607, -597, -700, -345, 462 ],
[ 670, -98, -847, -394, 234, 363, -497, -646, -823 ],
[ -758, 634, -671, 443, 973, 719, 335, 646, 670 ],
[ -923, -273, 22, 6, -869, 678, -431, -528, -866 ],
[ -607, 576, 911, 635, 594, -983, -954, -475, 155 ],
[ -928, -277, -81, -302, -119, -558, 921, 451, 316 ],
[ -411, 259, 424, 289, -216, -387, -43, -758, 393 ],
[ -228, 801, -380, 766, 262, -750, 742, -423, -479 ],
[ 368, 195, 248, -5, 666, -235, -787, 18, 474 ],
[ -320, -282, -412, 708, -633, -684, 620, -389, -45 ],
[ 715, 903, 483, -845, -902, -496, -541, 723, 522 ],
[ 513, 216, 434, 376, -674, -774, -85, -620, -877 ],
[ -755, -481, -46, -70, 912, 928, -858, 646, 985 ],
[ -914, -984, -877, -171, -35, -433, 923, -100, -673 ],
[ 921, -883, -797, 299, 266, 793, -79, -700, 164 ],
[ -273, -639, -364, -789, 977, 369, -364, 982, 694 ],
[ -180, -845, -262, 963, 70, 730, -449, -414, -660 ],
[ -393, 675, 952, 308, 610, -58, -687, 151, -430 ],
[ -58, -514, -280, 551, 533, 820, 775, -740, -795 ],
[ -481, 669, 11, -920, -963, 393, -753, -47, 601 ],
[ -329, 607, -734, -739, 676, -484, -566, 584, 92 ],
[ -336, -839, -65, -445, -558, 439, -719, -311, 768 ],
[ 732, -191, 684, 655, -503, 438, 112, 766, 564 ],
[ -901, 724, -399, -495, -174, -252, 957, -301, 142 ],
[ -319, 697, 718, 607, -993, 687, 242, 808, -187 ],
[ 395, 332, -986, -888, -777, 232, 954, 379, -990 ],
[ 629, -935, 665, -804, 477, 549, -592, 893, 181 ],
[ 844, 401, 880, -983, -804, 207, -59, 142, 430 ],
[ 318, -947, -123, 493, 151, -460, -288, 260, 466 ],
[ -810, -313, -410, -560, -268, -243, 401, -640, -531 ],
[ -366, -177, 736, -79, 5, 120, -670, 428, -724 ],
[ 730, -810, 167, 949, 602, -755, 372, -963, -147 ],
[ -664, 229, 158, -549, -626, 28, 267, -549, 968 ],
[ 899, 103, 231, 63, -586, 866, -815, -947, -108 ],
[ -373, 507, 72, -265, 212, -404, 348, 212, -899 ],
[ -241, -936, 379, -196, 208, -43, 337, -808, -970 ],
[ 239, -840, -29, -808, -639, -131, -236, -459, 610 ],
[ -885, 864, 82, 75, -135, -597, 828, 300, -327 ],
[ 958, 329, 921, 371, 45, -386, -278, -599, -550 ],
[ -157, -306, 700, 165, -97, -505, -979, -804, -990 ],
[ -935, 860, 144, -536, 302, 318, -118, -955, 671 ],
[ 584, 910, 219, -768, 320, 518, 735, -12, 622 ],
[ 326, 663, -174, 397, 997, -454, -816, -923, 205 ],
[ -904, -177, 867, 762, -363, -442, 398, 300, -201 ],
[ -628, -864, 23, 674, 883, -453, 295, -913, 826 ],
[ -648, 107, 172, 727, 849, -900, 620, -897, -952 ],
[ 931, 54, 396, -39, 491, -46, -340, 988, 388 ],
[ -167, 146, 712, -973, -412, -140, -995, 189, 345 ],
[ 601, -522, -412, -179, -135, -144, -724, -705, 16 ],
[ 263, 684, 466, 80, 84, 873, 83, -426, -754 ],
[ -654, 597, -683, 825, -693, -848, 160, 974, 563 ],
[ 825, 814, 257, -541, -155, 774, 534, -183, -144 ],
[ 860, -282, -119, 666, 276, 194, 447, -916, -245 ],
[ 968, -544, 637, -763, -90, 938, 370, 945, 648 ],
[ 580, -907, -244, -276, 207, 220, -653, -45, -790 ],
[ 33, 631, 755, 268, -278, -942, -194, -552, -160 ],
[ -439, 865, 833, -760, -466, 205, 402, -695, 152 ],
[ -555, 518, 432, -36, -521, -195, -443, -180, -668 ],
[ -817, 130, 313, -4, -423, -392, 195, 308, -591 ],
[ 401, -343, 16, 839, 923, -937, -802, -493, -661 ],
[ 165, 441, -918, 544, -765, 504, 320, 888, -290 ],
[ 254, 937, 563, 893, -133, 397, 103, -886, 950 ],
[ -533, 754, 978, -187, 112, 114, 944, -557, -12 ],
[ 647, -691, -898, 276, -391, -566, -157, -613, 318 ],
[ 829, 131, 467, 800, 429, 353, -827, -202, 688 ],
[ -340, -720, -797, -789, 626, 939, -901, 588, -856 ],
[ 659, -925, -900, -383, 872, 587, 711, 312, 699 ],
[ -43, -957, 34, 857, -401, -328, 713, 962, 222 ],
[ -28, -435, -52, -632, 606, -156, 76, 301, -274 ],
[ -251, 307, -569, -500, 323, -523, 794, 440, -681 ],
[ -838, 690, -892, -84, -668, -495, 480, 680, 782 ],
[ 917, 533, -650, -440, -405, -529, 247, -889, 85 ],
[ 484, -725, -175, -965, -437, 865, 544, -18, -433 ],
[ -381, 307, -358, 759, 624, 661, 345, -662, -312 ],
[ 157, -885, 0, -779, -52, 658, -888, 530, -687 ],
[ 500, 713, 223, 409, 437, -667, 442, 989, 155 ],
[ 658, 805, 992, 810, -970, -256, 594, 77, -554 ],
[ -718, 52, -160, 800, -515, -262, 111, 424, -453 ],
[ 341, -337, -448, 198, -812, 620, 212, 296, -114 ],
[ 840, 311, 436, 864, -669, -475, 76, -446, -920 ],
[ -742, -247, -997, 55, -200, 323, 347, -641, 231 ],
[ -8, 20, 416, 377, 689, 953, 883, -566, -530 ],
[ -348, 425, -876, 427, 377, 945, 727, -147, 47 ],
[ -170, 56, -65, -49, -429, 828, -531, 250, 548 ],
[ 701, 466, -765, -769, 230, -77, -846, 329, -499 ],
[ -215, 204, 237, 613, 484, 490, 496, -957, 152 ],
[ -526, -993, 473, -766, -250, 774, -559, 739, 127 ],
[ 123, 78, 424, 307, 722, -58, -723, 397, -822 ],
[ 363, -849, -705, 713, -675, -643, 432, -512, -791 ],
[ -516, -12, -894, 518, -24, -500, -442, 342, 18 ],
[ -589, 11, -643, 940, 783, 568, 284, -14, 996 ],
[ 720, -89, -295, 445, -109, 939, -947, -638, -293 ],
[ -257, -83, -446, -625, -341, 297, -948, 890, 217 ],
[ 137, 395, 993, 689, 49, 441, -873, -471, 407 ],
[ -706, -65, 842, 195, 832, 714, -885, -476, -303 ],
[ 131, 812, -254, -303, 617, -955, 68, -595, -602 ],
[ -495, -74, -785, -420, -252, -169, 133, 769, -94 ],
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];

ctp24data := [];

