Database - hmf_fields (Information on base fields for Hilbert modular forms)

Formats: - HTML - YAML - JSON - 2026-03-15T15:48:11.394916

Query: /api/hmf_fields/?_offset=0

Column	Type
degree	smallint
discriminant	bigint
ideals	jsonb
label	text
narrow_class_no	smallint
primes	jsonb

{'degree': 3, 'discriminant': 1489, 'id': 43, 'ideals': ['[1, 1, 1]', '[7, 7, w]', '[8, 2, 2]', '[13, 13, w^2 - 3*w - 5]', '[17, 17, w - 1]', '[19, 19, -w^2 + 2*w + 6]', '[19, 19, -w^2 + 2*w + 10]', '[19, 19, -w + 3]', '[23, 23, w - 2]', '[27, 3, 3]', '[29, 29, w^2 - 2*w - 5]', '[31, 31, w^2 - 3*w - 6]', '[31, 31, w^2 - w - 8]', '[31, 31, w^2 - 2*w - 4]', '[41, 41, w^2 - w - 5]', '[43, 43, w^2 - 3*w - 10]', '[47, 47, -w - 4]', '[47, 47, w^2 - w - 9]', '[47, 47, -2*w^2 + 3*w + 17]', '[49, 7, w^2 - w - 10]', '[49, 49, -w^2 + 3*w + 7]', '[53, 53, w^2 - w - 4]', '[56, 14, 2*w]', '[59, 59, -w^2 + 2*w + 11]', '[61, 61, w^2 - 3*w - 1]', '[61, 61, w^2 - 3*w - 8]', '[61, 61, w^2 - 3*w - 9]', '[64, 4, 4]', '[71, 71, 2*w^2 - 5*w - 13]', '[73, 73, 2*w^2 - 5*w - 10]', '[89, 89, w^2 - 4*w - 6]', '[91, 91, 2*w^2 - 3*w - 14]', '[97, 97, 2*w - 1]', '[101, 101, 2*w^2 - 5*w - 9]', '[103, 103, 2*w^2 - 4*w - 13]', '[104, 26, 2*w^2 - 6*w - 10]', '[107, 107, -w - 5]', '[109, 109, 2*w^2 - 5*w - 8]', '[113, 113, w^2 - 5*w - 6]', '[119, 119, -2*w^2 + 5*w + 14]', '[125, 5, -5]', '[127, 127, -w^2 + 2*w + 12]', '[133, 133, -w^2 + 3*w]', '[133, 133, w^2 - 7]', '[133, 133, w^2 - 4*w - 7]', '[136, 34, 2*w - 2]', '[151, 151, 2*w - 9]', '[152, 38, -2*w^2 + 4*w + 12]', '[152, 38, -2*w^2 + 4*w + 20]', '[152, 38, -2*w + 6]', '[157, 157, 2*w^2 - 3*w - 13]', '[157, 157, 3*w^2 - 7*w - 18]', '[157, 157, 2*w^2 - 5*w - 15]', '[161, 161, w^2 - 2*w]', '[167, 167, 2*w - 3]', '[169, 13, -w^2 + 4*w - 2]', '[169, 169, w^2 - 4*w - 8]', '[173, 173, 2*w^2 - 6*w - 11]', '[179, 179, 3*w^2 - 8*w - 17]', '[179, 179, 2*w^2 - 5*w - 16]', '[179, 179, 2*w^2 - 5*w - 17]', '[181, 181, 2*w - 5]', '[184, 46, 2*w - 4]', '[189, 21, 3*w]', '[191, 191, w^2 - 4*w - 9]', '[193, 193, w^2 - 4*w - 10]', '[193, 193, w^2 + w - 5]', '[193, 193, w^2 - 8]', '[197, 197, 2*w^2 - 4*w - 11]', '[199, 199, -w - 6]', '[203, 203, -w^2 + 5*w + 7]', '[211, 211, -3*w^2 + 5*w + 22]', '[216, 6, 6]', '[217, 217, -2*w^2 + 4*w + 7]', '[217, 217, 2*w + 7]', '[217, 217, -w^2 + 6*w + 7]', '[221, 221, -3*w^2 + 8*w + 12]', '[223, 223, 2*w^2 - 3*w - 12]', '[227, 227, 4*w^2 - 9*w - 26]', '[229, 229, w^2 - 2*w - 13]', '[232, 58, 2*w^2 - 4*w - 10]', '[241, 241, -w^2 + 3*w - 1]', '[247, 247, -w^2 + 9]', '[247, 247, -2*w^2 + 2*w + 11]', '[247, 247, -w^2 + w - 1]', '[248, 62, 2*w^2 - 6*w - 12]', '[248, 62, 2*w^2 - 2*w - 16]', '[248, 62, 2*w^2 - 4*w - 8]', '[251, 251, 2*w^2 - 4*w - 9]', '[257, 257, 3*w^2 - 7*w - 27]', '[263, 263, w^2 - 6*w - 4]', '[277, 277, w^2 - 5*w - 1]', '[281, 281, 3*w - 1]', '[283, 283, 2*w^2 - 3*w - 11]', '[283, 283, w^2 - 5*w - 8]', '[283, 283, w^2 - 13]', '[287, 287, 5*w + 7]', '[289, 17, w^2 - 10]', '[289, 289, w^2 - 2*w + 1]', '[293, 293, 2*w^2 - w - 9]', '[293, 293, -4*w - 1]', '[293, 293, 2*w^2 - 6*w - 3]', '[299, 299, w^2 + w - 6]', '[301, 301, -2*w^2 + 7]', '[307, 307, 2*w^2 - 4*w - 3]', '[313, 313, w^2 - 12]', '[313, 313, 3*w^2 - 7*w - 23]', '[313, 313, w^2 - 11]', '[323, 323, -w^2 + 4*w - 3]', '[323, 323, 2*w^2 - 6*w - 13]', '[323, 323, 2*w^2 - 2*w - 17]', '[328, 82, 2*w^2 - 2*w - 10]', '[329, 329, w + 7]', '[329, 329, w^2 - 3*w - 14]', '[329, 329, -w^2 - 4*w]', '[331, 331, 2*w^2 - 3*w - 10]', '[331, 331, 3*w^2 - 7*w - 26]', '[331, 331, -2*w^2 + 8*w + 5]', '[343, 7, 7]', '[343, 343, 2*w^2 - 3*w - 7]', '[344, 86, 2*w^2 - 6*w - 20]', '[347, 347, w^2 - 5*w - 9]', '[351, 39, 3*w^2 - 9*w - 15]', '[353, 353, -w^2 - w - 3]', '[359, 359, 3*w^2 - 7*w - 16]', '[361, 19, -2*w^2 + 3*w + 9]', '[361, 19, 2*w^2 - 5*w - 3]', '[361, 19, -w^2 - 2*w + 4]', '[361, 361, -w^2 + w + 15]', '[361, 361, 3*w^2 - 7*w - 25]', '[361, 361, w - 8]', '[367, 367, 2*w^2 - 3*w - 8]', '[371, 371, 6*w + 7]', '[373, 373, 2*w^2 - 7*w - 11]', '[373, 373, 3*w - 2]', '[373, 373, -4*w^2 + 7*w + 30]', '[376, 94, -2*w - 8]', '[376, 94, 2*w^2 - 2*w - 18]', '[376, 94, -4*w^2 + 6*w + 34]', '[377, 377, 2*w^2 - 8*w - 3]', '[383, 383, 2*w^2 - 7*w - 1]', '[389, 389, w^2 - 5*w - 10]', '[389, 389, 2*w^2 - 2*w - 9]', '[389, 389, -3*w^2 + 7*w + 10]', '[391, 391, w^2 - 3*w + 2]', '[392, 14, 2*w^2 - 2*w - 20]', '[392, 98, -2*w^2 + 6*w + 14]', '[401, 401, 2*w^2 - w - 5]', '[403, 403, 3*w^2 - 11*w - 8]', '[403, 403, -3*w^2 + 6*w + 19]', '[403, 403, 3*w^2 - 10*w - 5]', '[413, 413, w^2 + w - 7]', '[419, 419, 3*w^2 - 3*w - 22]', '[421, 421, -w^2 + w - 2]', '[424, 106, 2*w^2 - 2*w - 8]', '[427, 427, -2*w^2 + w + 7]', '[427, 427, -2*w^2 + 2*w + 7]', '[427, 427, -2*w^2 + 9*w + 7]', '[437, 437, 3*w^2 - 8*w - 19]', '[437, 437, 3*w^2 - 4*w - 27]', '[437, 437, -2*w^2 + 6*w + 19]', '[439, 439, 3*w^2 - 7*w - 15]', '[448, 28, 4*w]', '[449, 449, 2*w^2 - 6*w - 15]', '[457, 457, 3*w^2 - 5*w - 20]', '[459, 51, 3*w - 3]', '[461, 461, -w^2 + 2*w - 2]', '[472, 118, -2*w^2 + 4*w + 22]', '[479, 479, 4*w^2 - 6*w - 29]', '[487, 487, 2*w^2 - 3*w - 23]', '[488, 122, 2*w^2 - 6*w - 2]', '[488, 122, 2*w^2 - 6*w - 16]', '[488, 122, 2*w^2 - 6*w - 18]', '[493, 493, -2*w^2 + 7*w + 12]', '[497, 497, -3*w^2 + 7*w + 14]', '[503, 503, -w - 8]', '[503, 503, 2*w^2 - 6*w - 17]', '[503, 503, -3*w^2 + 9*w + 16]', '[511, 511, -3*w^2 + 10*w + 14]', '[512, 8, 8]', '[513, 57, -3*w^2 + 6*w + 18]', '[513, 57, -3*w^2 + 6*w + 30]', '[513, 57, -3*w + 9]', '[523, 523, 4*w^2 - 9*w - 31]', '[523, 523, 3*w^2 - 7*w - 12]', '[523, 523, w^2 + 2*w - 5]', '[527, 527, -w^2 + 3*w + 15]', '[527, 527, -3*w^2 + 7*w + 13]', '[527, 527, -2*w^2 + 8*w + 11]', '[529, 23, w^2 + w - 8]', '[529, 529, w^2 - 4*w + 4]', '[533, 533, -3*w + 4]', '[551, 551, 4*w^2 - 7*w - 29]', '[551, 551, 4*w^2 - 11*w - 22]', '[551, 551, w - 9]', '[559, 559, -w^2 + 2*w + 15]', '[563, 563, 3*w^2 - 8*w - 20]', '[563, 563, 3*w^2 - 4*w - 19]', '[563, 563, w^2 - 6*w - 2]', '[568, 142, 4*w^2 - 10*w - 26]', '[569, 569, w^2 - w - 16]', '[571, 571, w^2 + 3*w - 3]', '[584, 146, 4*w^2 - 10*w - 20]', '[587, 587, -2*w - 9]', '[589, 589, 4*w^2 - 9*w - 32]', '[589, 589, -w^2 + 3*w - 3]', '[589, 589, 5*w^2 - 13*w - 25]', '[589, 589, 4*w^2 - 9*w - 34]', '[589, 589, 3*w^2 - 5*w - 19]', '[589, 589, 3*w - 8]', '[589, 589, 8*w^2 - 13*w - 66]', '[589, 589, 4*w^2 - 12*w - 19]', '[589, 589, 3*w^2 - 5*w - 31]', '[593, 593, 2*w^2 - 7*w - 22]', '[599, 599, 5*w^2 - 12*w - 33]', '[611, 611, -4*w^2 + 9*w + 24]', '[611, 611, -2*w^2 + 7*w + 13]', '[611, 611, 5*w^2 - 10*w - 36]', '[613, 613, 4*w^2 - 9*w - 33]', '[617, 617, 3*w^2 - 6*w - 17]', '[619, 619, 5*w^2 - 13*w - 29]', '[621, 69, 3*w - 6]', '[623, 623, -3*w^2 + 4*w + 7]', '[631, 631, -5*w - 1]', '[637, 91, -5*w^2 + 12*w + 29]', '[637, 637, -w^2 + 6*w + 14]', '[641, 641, w^2 + w - 9]', '[647, 647, -w^2 + w - 3]', '[661, 661, w^2 - 6*w - 11]', '[667, 667, -3*w^2 + 9*w + 17]', '[673, 673, 4*w^2 - 5*w - 27]', '[679, 679, 2*w^2 - w]', '[683, 683, -w^2 + 2*w - 3]', '[689, 689, w^2 - 6*w - 1]', '[691, 691, w^2 - 6*w - 13]', '[697, 697, -w^2 + 6*w + 12]', '[701, 701, w^2 + 2*w - 6]', '[707, 707, -3*w^2 + 11*w + 14]', '[709, 709, -3*w^2 + 6*w + 16]', '[712, 178, 2*w^2 - 8*w - 12]', '[713, 713, -2*w^2 + 4*w + 23]', '[713, 713, -4*w^2 + 10*w + 19]', '[713, 713, -3*w^2 + 10*w + 15]', '[719, 719, 3*w^2 - 5*w - 18]', '[721, 721, -2*w^2 + 7*w + 14]', '[727, 727, -w - 9]', '[728, 182, 4*w^2 - 6*w - 28]', '[729, 9, 9]', '[731, 731, -3*w^2 + 3*w + 17]', '[733, 733, 3*w^2 - 4*w - 18]', '[743, 743, 2*w^2 - w - 16]', '[743, 743, 2*w^2 - 6*w - 1]', '[743, 743, w^2 + w - 10]', '[749, 749, -w^2 - 5*w]', '[751, 751, 2*w^2 - 3*w - 24]', '[763, 763, -3*w^2 + 12*w + 14]', '[767, 767, 4*w^2 - 10*w - 27]', '[776, 194, 4*w - 2]', '[779, 779, w^2 - 3*w - 16]', '[779, 779, 3*w^2 - 8*w - 22]', '[779, 779, 5*w^2 - 7*w - 36]', '[783, 87, 3*w^2 - 6*w - 15]', '[787, 787, 3*w^2 - 6*w - 5]', '[791, 791, -4*w^2 + 4*w + 7]', '[793, 793, 8*w^2 - 25*w - 30]', '[793, 793, w^2 - 4*w + 5]', '[793, 793, -w + 10]', '[797, 797, 4*w^2 - 9*w - 23]', '[799, 799, -w^2 + 2*w + 16]', '[799, 799, 3*w^2 - 6*w - 31]', '[799, 799, -w^2 - 3*w + 4]', '[808, 202, 4*w^2 - 10*w - 18]', '[809, 809, w^2 + w - 16]', '[811, 811, 4*w^2 - 8*w - 39]', '[817, 817, 4*w^2 - 5*w - 32]', '[817, 817, 8*w^2 - 17*w - 72]', '[817, 817, 5*w^2 - 9*w - 37]', '[821, 821, -5*w^2 + 13*w + 24]', '[824, 206, 4*w^2 - 8*w - 26]', '[829, 829, 5*w^2 - 8*w - 37]', '[829, 829, 3*w^2 - 8*w - 27]', '[829, 829, w^2 + w - 11]', '[832, 52, 4*w^2 - 12*w - 20]', '[833, 119, -w^2 + w + 17]', '[833, 833, 3*w^2 - 6*w - 14]', '[837, 93, 3*w^2 - 9*w - 18]', '[837, 93, 3*w^2 - 3*w - 24]', '[837, 93, 3*w^2 - 6*w - 12]', '[839, 839, 3*w^2 - 2*w - 15]', '[841, 29, 3*w^2 - 5*w - 17]', '[841, 841, -w^2 + 3*w - 4]', '[853, 853, 3*w^2 - 6*w - 13]', '[856, 214, -2*w - 10]', '[857, 857, 4*w^2 - 13*w - 18]', '[857, 857, 3*w^2 - 8*w - 23]', '[857, 857, w^2 - 4*w - 17]', '[859, 859, 5*w^2 - 11*w - 32]', '[863, 863, 3*w^2 - 9*w - 31]', '[863, 863, 4*w^2 - 10*w - 17]', '[863, 863, -w^2 + 6*w - 1]', '[872, 218, 4*w^2 - 10*w - 16]', '[875, 35, -5*w]', '[877, 877, 2*w^2 - 7*w - 20]', '[883, 883, 2*w^2 - w - 17]', '[889, 889, w^2 + 2*w - 7]', '[893, 893, -7*w^2 + 12*w + 65]', '[893, 893, 3*w^2 - 4*w - 34]', '[893, 893, 3*w^2 - 8*w - 33]', '[893, 893, 3*w^2 - 4*w - 17]', '[893, 893, -16*w^2 + 28*w + 135]', '[893, 893, 9*w^2 - 15*w - 76]', '[893, 893, -8*w^2 + 16*w + 67]', '[893, 893, 5*w^2 - 11*w - 40]', '[893, 893, w^2 + w - 12]', '[899, 899, -w^2 + 6*w - 2]', '[899, 899, 3*w^2 - 8*w - 26]', '[899, 899, 6*w^2 - 14*w - 41]', '[901, 901, -w^2 + 7*w + 11]', '[904, 226, 2*w^2 - 10*w - 12]', '[907, 907, 3*w^2 - 8*w - 24]', '[923, 923, 3*w^2 - 12*w + 2]', '[929, 929, w^2 + w - 13]', '[931, 133, 6*w^2 - 13*w - 46]', '[931, 133, 10*w^2 - 17*w - 86]', '[931, 133, 3*w^2 - 3*w - 37]', '[931, 931, -5*w^2 + 12*w + 28]', '[931, 931, -5*w^2 + 11*w + 42]', '[931, 931, -w^2 - w + 14]', '[937, 937, 4*w - 3]', '[941, 941, 5*w^2 - 11*w - 41]', '[941, 941, 2*w^2 - 7*w - 19]', '[941, 941, 2*w^2 - 5*w - 24]', '[943, 943, -2*w^2 + 7*w + 17]', '[949, 949, 6*w^2 - 21*w - 13]', '[952, 238, -4*w^2 + 10*w + 28]', '[961, 31, 4*w^2 - 7*w - 27]', '[961, 31, 2*w^2 - 7*w - 18]', '[961, 31, 2*w^2 - 9*w - 4]', '[961, 961, -w^2 + 2*w - 4]', '[961, 961, w^2 - 7*w - 16]', '[961, 961, 5*w^2 - 13*w - 30]', '[967, 967, 2*w^2 - w - 24]', '[971, 971, 4*w^2 - 9*w - 22]', '[983, 983, 6*w^2 - 15*w - 37]', '[989, 989, -4*w^2 + 6*w + 27]', '[997, 997, 4*w^2 - 10*w - 37]', '[1000, 10, -10]', '[1003, 1003, 2*w^2 - w - 18]', '[1007, 1007, -w - 10]', '[1007, 1007, 3*w^2 - 9*w - 19]', '[1007, 1007, 4*w^2 - 5*w - 26]', '[1013, 1013, 4*w^2 - 7*w - 40]', '[1013, 1013, 3*w^2 - 3*w - 25]', '[1013, 1013, 5*w^2 - 13*w - 23]', '[1016, 254, -2*w^2 + 4*w + 24]', '[1021, 1021, 4*w^2 - 8*w - 25]', '[1031, 1031, 4*w^2 - 11*w - 24]', '[1037, 1037, -3*w^2 + 4*w + 16]', '[1037, 1037, -3*w^2 + 5*w + 15]', '[1037, 1037, -3*w^2 + 12*w + 8]', '[1051, 1051, w^2 + 3*w - 5]', '[1057, 1057, 2*w^2 - 9*w]', '[1061, 1061, -3*w^2 + 10*w + 3]', '[1063, 1063, 2*w^2 - 9*w - 3]', '[1064, 266, -2*w^2 + 6*w]', '[1064, 266, 2*w^2 - 14]', '[1064, 266, 2*w^2 - 8*w - 14]', '[1069, 1069, 3*w^2 - 5*w - 11]', '[1081, 1081, 5*w^2 - 9*w - 48]', '[1081, 1081, -2*w^2 + 3*w + 25]', '[1081, 1081, -w^2 - 2*w + 8]', '[1088, 68, 4*w - 4]', '[1091, 1091, w^2 - 3*w - 17]', '[1093, 1093, 2*w^2 - w - 23]', '[1093, 1093, 5*w^2 - 9*w - 36]', '[1093, 1093, w - 11]', '[1097, 1097, w^2 - 2*w - 17]', '[1097, 1097, w^2 - 7*w - 2]', '[1097, 1097, 2*w^2 - w - 19]', '[1099, 1099, -4*w^2 + 12*w + 21]', '[1099, 1099, -w^2 + 7*w + 14]', '[1099, 1099, -3*w^2 + 5*w + 14]', '[1107, 123, 3*w^2 - 3*w - 15]', '[1117, 1117, 3*w^2 - w - 12]', '[1117, 1117, 4*w^2 - 10*w - 29]', '[1117, 1117, 2*w^2 - 9*w - 2]', '[1121, 1121, -6*w^2 + 11*w + 45]', '[1121, 1121, -4*w^2 + 5*w + 40]', '[1121, 1121, -10*w^2 + 19*w + 89]', '[1127, 161, -2*w^2 + 2*w + 27]', '[1127, 1127, 4*w^2 - 9*w - 21]', '[1129, 1129, -w^2 - 5]', '[1129, 1129, 3*w^2 - 5*w - 13]', '[1129, 1129, 5*w - 1]', '[1153, 1153, -w^2 + 3*w - 5]', '[1157, 1157, 5*w^2 - 15*w - 12]', '[1159, 1159, 2*w^2 - w - 20]', '[1159, 1159, -w^2 + w + 18]', '[1159, 1159, 3*w^2 - 3*w - 26]', '[1159, 1159, 6*w^2 - 13*w - 52]', '[1159, 1159, 5*w^2 - 18*w - 10]', '[1159, 1159, 7*w^2 - 15*w - 62]', '[1159, 1159, 5*w^2 - 11*w - 31]', '[1159, 1159, 5*w^2 - 10*w - 34]', '[1159, 1159, -5*w^2 + 13*w + 22]', '[1161, 129, 3*w^2 - 9*w - 30]', '[1163, 1163, 5*w^2 - 13*w - 18]', '[1163, 1163, 2*w^2 - w - 22]', '[1163, 1163, 2*w^2 - 8*w - 23]', '[1169, 1169, 2*w^2 - 3*w]', '[1171, 1171, 3*w^2 - 9*w - 20]', '[1181, 1181, 4*w^2 - 7*w - 26]', '[1183, 91, 3*w^2 - 12*w - 7]', '[1183, 1183, -2*w^2 + w + 21]', '[1187, 1187, 3*w^2 - 9*w - 4]', '[1189, 1189, -2*w - 11]', '[1207, 1207, -5*w^2 + 12*w + 27]', '[1208, 302, 4*w - 18]', '[1211, 1211, -4*w^2 + 9*w + 14]', '[1213, 1213, -5*w^2 + 14*w + 27]', '[1216, 76, -4*w^2 + 8*w + 24]', '[1216, 76, -4*w^2 + 8*w + 40]', '[1216, 76, -4*w + 12]', '[1217, 1217, 4*w^2 - 5*w - 34]', '[1219, 1219, -2*w^2 + 8*w + 15]', '[1223, 1223, 4*w - 5]', '[1229, 1229, 3*w^2 - 3*w - 31]', '[1231, 1231, w^2 - 4*w - 18]', '[1237, 1237, 3*w^2 - 2*w - 13]', '[1241, 1241, -5*w^2 + 15*w + 24]', '[1247, 1247, -6*w^2 + 15*w + 32]', '[1253, 1253, -3*w^2 + 4*w + 14]', '[1253, 1253, -5*w^2 + 13*w + 21]', '[1253, 1253, -3*w^2 + 3*w + 14]', '[1256, 314, 4*w^2 - 6*w - 26]', '[1256, 314, 6*w^2 - 14*w - 36]', '[1256, 314, 4*w^2 - 10*w - 30]', '[1259, 1259, 4*w^2 - 9*w - 20]', '[1261, 1261, -5*w^2 + 13*w + 19]', '[1267, 1267, 2*w^2 - 5*w]', '[1269, 141, -3*w - 12]', '[1269, 141, 3*w^2 - 3*w - 27]', '[1269, 141, -6*w^2 + 9*w + 51]', '[1271, 1271, 6*w^2 - 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