Database - hmf_fields

Formats: - HTML - YAML - JSON - 2026-10-23T22:39:28.652808

Query: /api/hmf_fields/?_offset=0

Table hmf_fields

Information on base fields for Hilbert modular forms

Column	Type	Example
degree	smallint	4
discriminant	bigint	3600
ideals	jsonb	['[1, 1, 1]', '[4, 2, -2/7*w^3 + 3/7*w^2 + 19/7*w - 17/7]', '[9, 3, -2/7*w^3 + 3/7*w^2 + 19/7*w - 10...
label	text	'4.4.3600.1'
narrow_class_no	smallint	2
primes	jsonb	['[4, 2, -2/7*w^3 + 3/7*w^2 + 19/7*w - 17/7]', '[9, 3, -2/7*w^3 + 3/7*w^2 + 19/7*w - 10/7]', '[11, 1...

{'degree': 3, 'discriminant': 1825, 'id': 54, 'ideals': ['[1, 1, 1]', '[5, 5, -w + 2]', '[7, 7, w]', '[8, 2, 2]', '[11, 11, w + 2]', '[13, 13, w + 1]', '[17, 17, -w^2 - w + 4]', '[23, 23, -w^2 + 6]', '[23, 23, -w^2 - w + 3]', '[23, 23, -w + 4]', '[25, 5, -w^2 - w + 6]', '[27, 3, 3]', '[29, 29, -w^2 - 2*w + 4]', '[31, 31, w^2 - 10]', '[35, 35, w^2 - w - 7]', '[40, 10, -2*w + 4]', '[41, 41, w + 4]', '[41, 41, w^2 - 5]', '[41, 41, -2*w - 5]', '[43, 43, w^2 - w - 4]', '[47, 47, w^2 - w - 9]', '[49, 7, w^2 - w - 8]', '[49, 49, w^2 + w - 7]', '[53, 53, 2*w^2 + w - 12]', '[55, 55, -w^2 + 4]', '[56, 14, 2*w]', '[59, 59, w^2 - 3]', '[61, 61, w^2 + w - 10]', '[61, 61, w^2 - w - 3]', '[61, 61, w^2 - 2*w - 4]', '[64, 4, 4]', '[65, 65, -w^2 + w + 2]', '[67, 67, w^2 + w - 8]', '[67, 67, w^2 + 2*w - 5]', '[67, 67, w - 5]', '[73, 73, w^2 + w - 9]', '[73, 73, -2*w^2 + w + 13]', '[77, 77, w^2 + 2*w]', '[83, 83, 3*w - 4]', '[85, 85, 2*w + 1]', '[88, 22, 2*w + 4]', '[91, 91, w^2 + w]', '[101, 101, -2*w^2 - 2*w + 11]', '[103, 103, -w - 5]', '[104, 26, 2*w + 2]', '[107, 107, -2*w - 3]', '[113, 113, w^2 + 2*w - 6]', '[115, 115, 2*w^2 - 13]', '[115, 115, w^2 + 3*w - 5]', '[115, 115, -w^2 + 2*w + 5]', '[119, 119, 3*w - 7]', '[121, 11, -3*w^2 - 2*w + 17]', '[121, 121, -3*w + 5]', '[125, 5, 5]', '[131, 131, -2*w^2 - w + 11]', '[135, 15, -3*w + 6]', '[136, 34, -2*w^2 - 2*w + 8]', '[139, 139, w - 6]', '[143, 143, w^2 + w - 13]', '[145, 145, 2*w^2 + w - 15]', '[151, 151, 2*w^2 - w - 12]', '[155, 155, -w^2 - 2*w + 13]', '[157, 157, w^2 - 2*w - 12]', '[161, 161, -w^2 + 4*w]', '[161, 161, -2*w - 7]', '[161, 161, -w^2 - 2*w + 7]', '[163, 163, -2*w^2 - w + 18]', '[167, 167, w^2 - 12]', '[169, 13, w^2 - 2*w - 6]', '[169, 169, w^2 + 2*w + 1]', '[175, 35, -2*w^2 - 2*w + 7]', '[179, 179, 2*w^2 + w - 16]', '[184, 46, -2*w^2 + 12]', '[184, 46, -2*w^2 - 2*w + 6]', '[184, 46, -2*w + 8]', '[187, 187, 2*w^2 + w - 17]', '[189, 21, 3*w]', '[191, 191, 2*w^2 - 2*w - 13]', '[193, 193, -w^2 - w - 1]', '[197, 197, -w - 6]', '[199, 199, w^2 + 3*w - 6]', '[200, 10, -2*w^2 - 2*w + 12]', '[203, 203, -3*w - 7]', '[205, 205, w^2 - 3*w - 3]', '[205, 205, 2*w^2 + w - 10]', '[205, 205, -w^2 - 2*w + 8]', '[215, 215, 2*w^2 - 6*w - 1]', '[216, 6, 6]', '[217, 217, -w^2 + 2*w + 7]', '[221, 221, w^2 + 2*w - 12]', '[229, 229, w^2 - 2*w - 11]', '[232, 58, -2*w^2 - 4*w + 8]', '[233, 233, -3*w^2 - w + 27]', '[235, 235, 2*w^2 - w - 11]', '[239, 239, w^2 + 2*w - 9]', '[241, 241, w^2 - w - 13]', '[245, 35, 2*w^2 - 2*w - 9]', '[245, 245, w - 7]', '[248, 62, 2*w^2 - 20]', '[253, 253, -2*w^2 - 3*w + 2]', '[253, 253, -w^2 + 2*w + 8]', '[253, 253, w^2 + 2*w - 11]', '[257, 257, -3*w - 1]', '[257, 257, 2*w^2 - 11]', '[257, 257, w^2 + 2*w - 10]', '[263, 263, 2*w^2 - 3*w - 10]', '[265, 265, w^2 - 2*w - 10]', '[269, 269, w^2 + 4*w - 1]', '[269, 269, -2*w^2 - 3*w + 10]', '[269, 269, 2*w^2 + w - 9]', '[271, 271, w^2 - 2*w - 9]', '[275, 55, -w^2 + 4*w + 1]', '[277, 277, -2*w^2 + 4*w + 3]', '[280, 70, 2*w^2 - 2*w - 14]', '[281, 281, -w^2 - 2]', '[287, 287, -2*w^2 - 5*w]', '[287, 287, w^2 + 4*w]', '[287, 287, w^2 + 3*w - 7]', '[289, 17, 2*w^2 - 3*w - 6]', '[289, 289, w^2 - 13]', '[295, 295, w^2 - 5*w + 1]', '[297, 33, 3*w + 6]', '[299, 299, -w^2 + 3*w + 4]', '[299, 299, 4*w - 9]', '[299, 299, -2*w^2 - 2*w + 13]', '[301, 301, 4*w - 7]', '[305, 305, 2*w^2 - 7*w + 1]', '[305, 305, 4*w - 13]', '[305, 305, 3*w^2 - 8*w - 1]', '[307, 307, w^2 + 2*w - 16]', '[313, 313, -3*w - 2]', '[317, 317, 3*w^2 - 20]', '[317, 317, -3*w^2 - w + 26]', '[317, 317, 2*w^2 + w - 8]', '[319, 319, 2*w^2 - w - 10]', '[320, 20, -4*w + 8]', '[325, 65, 3*w^2 - 2*w - 18]', '[328, 82, 2*w + 8]', '[328, 82, 2*w^2 - 10]', '[328, 82, -4*w - 10]', '[329, 329, -w - 7]', '[331, 331, w^2 + 5*w + 5]', '[335, 335, 2*w - 9]', '[335, 335, -w^2 + w - 3]', '[335, 335, -w^2 + 7*w - 10]', '[337, 337, -w^2 - w - 2]', '[341, 341, -3*w^2 + 2*w + 27]', '[343, 7, 7]', '[343, 343, 2*w^2 + w - 7]', '[344, 86, 2*w^2 - 2*w - 8]', '[349, 349, -3*w - 5]', '[349, 349, 3*w^2 + w - 25]', '[349, 349, 2*w^2 - 2*w - 15]', '[351, 39, 3*w + 3]', '[365, 365, 3*w - 11]', '[365, 365, -3*w^2 + 5*w + 12]', '[371, 371, 3*w^2 + 4*w - 14]', '[373, 373, w^2 + 3*w - 8]', '[373, 373, 2*w^2 + 4*w - 9]', '[373, 373, 2*w^2 + w - 22]', '[376, 94, 2*w^2 - 2*w - 18]', '[377, 377, 2*w^2 - 3*w - 5]', '[379, 379, w^2 + 5*w - 3]', '[385, 385, -w^2 - 4*w + 7]', '[391, 391, -2*w^2 + 9]', '[391, 391, 3*w + 10]', '[391, 391, w - 8]', '[392, 14, 2*w^2 - 2*w - 16]', '[392, 98, 2*w^2 + 2*w - 14]', '[397, 397, 2*w^2 + 3*w - 11]', '[397, 397, w^2 - 3*w - 5]', '[397, 397, 2*w^2 - w - 9]', '[403, 403, -2*w^2 + 2*w + 17]', '[409, 409, w^2 - 4*w - 2]', '[413, 413, w^2 + 5*w - 7]', '[415, 415, -3*w^2 + 10*w - 8]', '[421, 421, 2*w^2 - 3*w - 11]', '[424, 106, 4*w^2 + 2*w - 24]', '[425, 85, -2*w^2 + 3*w + 2]', '[427, 427, 5*w - 7]', '[427, 427, -w^2 + 4*w - 7]', '[427, 427, 2*w^2 - 2*w - 7]', '[431, 431, 2*w^2 + 2*w - 1]', '[433, 433, 2*w^2 - 3*w - 4]', '[440, 110, -2*w^2 + 8]', '[443, 443, 2*w^2 - 5]', '[448, 28, 4*w]', '[449, 449, 3*w^2 - w - 19]', '[451, 451, 3*w^2 + 3*w - 17]', '[451, 451, w^2 + 3*w - 9]', '[451, 451, -2*w^2 + 3*w + 3]', '[455, 455, w^2 - 14]', '[459, 51, -3*w^2 - 3*w + 12]', '[463, 463, 2*w^2 - w - 8]', '[463, 463, 3*w^2 - 19]', '[463, 463, -w^2 - 3]', '[467, 467, 4*w^2 + 2*w - 27]', '[469, 469, 3*w^2 + 3*w - 7]', '[469, 469, w^2 - 5*w]', '[469, 469, 2*w^2 - 7]', '[472, 118, 2*w^2 - 6]', '[473, 473, 2*w^2 + 2*w - 15]', '[479, 479, 2*w^2 - 2*w - 3]', '[479, 479, 3*w^2 + 2*w - 15]', '[479, 479, w^2 + w - 15]', '[487, 487, 2*w^2 - w - 4]', '[487, 487, 5*w^2 + 2*w - 32]', '[487, 487, -4*w^2 - 3*w + 24]', '[488, 122, 2*w^2 + 2*w - 20]', '[488, 122, 2*w^2 - 2*w - 6]', '[488, 122, 2*w^2 - 4*w - 8]', '[491, 491, -w^2 - 2*w - 3]', '[493, 493, w^2 - 3*w - 6]', '[505, 505, w + 8]', '[511, 511, -w^2 - 3*w + 14]', '[511, 511, 2*w^2 - w - 7]', '[512, 8, 8]', '[515, 515, w^2 + 3*w - 10]', '[517, 517, 2*w^2 - 3*w - 25]', '[520, 130, -2*w^2 + 2*w + 4]', '[521, 521, 2*w^2 - 2*w - 5]', '[527, 527, -4*w^2 - w + 26]', '[529, 23, -3*w^2 + 2*w + 17]', '[529, 23, w^2 + 3*w + 4]', '[529, 23, -2*w^2 + w + 5]', '[529, 529, -w^2 + 3*w - 6]', '[529, 529, -w^2 - w - 3]', '[529, 529, w^2 + 4*w - 8]', '[533, 533, -3*w^2 + 29]', '[533, 533, 3*w^2 - 3*w - 19]', '[533, 533, 2*w^2 + 3*w - 12]', '[535, 535, 2*w^2 - w - 6]', '[536, 134, 2*w^2 + 2*w - 16]', '[536, 134, 2*w^2 + 4*w - 10]', '[536, 134, 2*w - 10]', '[539, 77, 2*w^2 - 2*w - 23]', '[539, 539, 2*w^2 - 7*w]', '[541, 541, -w^2 + w - 4]', '[547, 547, 3*w^2 + w - 17]', '[547, 547, 4*w + 9]', '[547, 547, -2*w - 9]', '[557, 557, w^2 - 4*w - 3]', '[557, 557, 3*w^2 - 4*w - 12]', '[557, 557, 2*w^2 + 2*w - 19]', '[559, 559, w^2 + 3*w - 11]', '[563, 563, w^2 + 3*w - 13]', '[565, 565, -w^2 + 2*w - 5]', '[569, 569, w^2 + 2*w - 17]', '[571, 571, -4*w - 1]', '[575, 115, 3*w^2 + 3*w - 8]', '[575, 115, 2*w^2 - 3*w - 12]', '[575, 115, -2*w^2 - 2*w + 17]', '[577, 577, w^2 + 3*w - 12]', '[581, 581, 3*w^2 - 4*w]', '[583, 583, 7*w^2 + 6*w - 38]', '[584, 146, 2*w^2 + 2*w - 18]', '[584, 146, -4*w^2 + 2*w + 26]', '[595, 595, 3*w^2 + 2*w - 21]', '[599, 599, 5*w - 11]', '[601, 601, 5*w - 9]', '[605, 55, -w^2 + 3*w + 13]', '[605, 605, -3*w^2 - 4*w + 15]', '[611, 611, w^2 - 2*w - 16]', '[613, 613, 3*w^2 + 3*w - 10]', '[616, 154, 2*w^2 + 4*w]', '[617, 617, 3*w^2 - w - 18]', '[621, 69, -3*w^2 + 18]', '[621, 69, -3*w^2 - 3*w + 9]', '[621, 69, -3*w + 12]', '[625, 25, -5*w + 10]', '[631, 631, 2*w^2 - w - 22]', '[637, 91, w^2 - w - 15]', '[637, 637, 3*w^2 + 2*w - 14]', '[643, 643, w^2 + 5*w - 1]', '[647, 647, 2*w^2 + w - 23]', '[649, 649, 3*w^2 + 5*w - 13]', '[655, 655, -w^2 + 3*w + 8]', '[664, 166, 6*w - 8]', '[667, 667, -w^2 - 4*w + 9]', '[667, 667, w^2 - 5*w - 1]', '[667, 667, w^2 + 5*w + 3]', '[671, 671, 4*w^2 - 27]', '[671, 671, 2*w^2 + 3*w - 13]', '[671, 671, w^2 - 15]', '[675, 15, -3*w^2 - 3*w + 18]', '[677, 677, 5*w^2 + 3*w - 29]', '[680, 170, 4*w + 2]', '[683, 683, 3*w^2 + 2*w - 29]', '[689, 689, 5*w^2 + 5*w - 26]', '[691, 691, w^2 - 3*w - 12]', '[695, 695, -w^2 + 8*w - 12]', '[697, 697, -w^2 + 6*w - 1]', '[697, 697, -w^2 - 4*w - 6]', '[697, 697, -w^2 - 4]', '[701, 701, 2*w^2 - 4*w - 9]', '[704, 44, 4*w + 8]', '[707, 707, -4*w^2 - 5*w + 14]', '[709, 709, w^2 - 3*w - 9]', '[713, 713, -3*w^2 - w + 16]', '[713, 713, -7*w^2 + w + 53]', '[713, 713, -3*w^2 - 2*w + 33]', '[715, 715, -2*w^2 - 4*w + 11]', '[719, 719, 2*w^2 - 3*w - 13]', '[721, 721, -w^2 - 5*w]', '[725, 145, w^2 + w - 16]', '[728, 182, 2*w^2 + 2*w]', '[729, 9, 9]', '[731, 731, -w - 9]', '[733, 733, -w^2 - 2*w - 4]', '[733, 733, 2*w^2 - 5*w - 6]', '[733, 733, w^2 - 3*w - 11]', '[737, 737, 5*w^2 + 7*w - 17]', '[737, 737, 4*w^2 + 2*w - 23]', '[737, 737, w^2 - 3*w - 10]', '[739, 739, 3*w^2 + 2*w - 22]', '[739, 739, -w^2 + 4*w + 17]', '[739, 739, 3*w^2 - 5*w - 13]', '[743, 743, 3*w^2 + w - 31]', '[749, 749, -2*w^2 - 3*w]', '[751, 751, 3*w^2 - 3*w - 20]', '[755, 755, 3*w^2 - 6*w - 10]', '[761, 761, 4*w + 13]', '[767, 767, 2*w^2 + 5*w - 10]', '[769, 769, -4*w - 3]', '[773, 773, 3*w^2 + 2*w - 13]', '[775, 155, -6*w^2 - w + 46]', '[783, 87, -3*w^2 - 6*w + 12]', '[785, 785, 3*w^2 - 17]', '[791, 791, 3*w^2 + 2*w - 7]', '[793, 793, 3*w^2 - w - 17]', '[793, 793, 2*w - 11]', '[793, 793, w^2 + 4*w - 10]', '[799, 799, 5*w^2 + 4*w - 29]', '[803, 803, -5*w^2 - w + 40]', '[803, 803, 4*w^2 + w - 25]', '[805, 805, 4*w + 7]', '[805, 805, w^2 - 3*w + 7]', '[805, 805, 2*w^2 + 3*w - 14]', '[808, 202, -4*w^2 - 4*w + 22]', '[815, 815, -w^2 - 4*w + 22]', '[823, 823, 3*w^2 - 4*w - 11]', '[824, 206, -2*w - 10]', '[827, 827, -5*w^2 - 4*w + 26]', '[827, 827, 3*w^2 - 7*w - 1]', '[827, 827, w - 10]', '[829, 829, w^2 - 6*w + 12]', '[832, 52, 4*w + 4]', '[833, 119, 4*w^2 + 3*w - 25]', '[833, 833, -4*w^2 + 3*w + 28]', '[835, 835, w^2 + 4*w - 17]', '[837, 93, 3*w^2 - 30]', '[841, 29, 2*w^2 + 3*w - 23]', '[841, 841, -w^2 + 2*w - 6]', '[845, 65, 3*w^2 - 6*w - 5]', '[845, 845, -w^2 - 5*w + 9]', '[847, 77, -5*w^2 - 7*w + 21]', '[847, 847, 2*w^2 - 3*w - 14]', '[856, 214, -4*w - 6]', '[857, 857, 3*w^2 + 2*w - 23]', '[857, 857, 4*w^2 + 3*w - 20]', '[857, 857, 4*w^2 - 3*w - 23]', '[859, 859, -3*w^2 - 4*w + 16]', '[863, 863, -4*w - 5]', '[871, 871, w^2 - 4*w - 5]', '[871, 871, 3*w^2 + w - 15]', '[871, 871, 4*w^2 + 5*w - 12]', '[875, 35, 5*w]', '[881, 881, 3*w^2 + 2*w - 12]', '[883, 883, w^2 - 5*w - 2]', '[887, 887, 4*w^2 - 2*w - 25]', '[895, 895, w^2 + 2*w - 18]', '[899, 899, -3*w^2 - 3*w + 19]', '[901, 901, -2*w^2 - 10*w - 13]', '[904, 226, 2*w^2 + 4*w - 12]', '[907, 907, -5*w^2 - 5*w + 23]', '[913, 913, 3*w^2 + 2*w - 8]', '[917, 917, -3*w^2 - 5*w + 14]', '[919, 919, w^2 - w - 16]', '[920, 230, 4*w^2 - 26]', '[920, 230, 2*w^2 + 6*w - 10]', '[920, 230, -2*w^2 + 4*w + 10]', '[929, 929, 2*w^2 + 3*w - 15]', '[935, 935, w^2 + 3*w - 20]', '[943, 943, 2*w^2 - w - 23]', '[943, 943, 3*w^2 - 2*w - 15]', '[943, 943, 4*w^2 + 8*w - 5]', '[943, 943, 3*w^2 - 3*w - 13]', '[943, 943, 2*w^2 - 3*w - 20]', '[943, 943, -2*w^2 - 7*w + 4]', '[943, 943, -2*w^2 - 4*w - 1]', '[943, 943, -w^2 + 16]', '[943, 943, -3*w^2 - 2*w + 24]', '[945, 105, 3*w^2 - 3*w - 21]', '[949, 949, 3*w^2 - 16]', '[949, 949, -3*w^2 - 2*w + 27]', '[952, 238, 6*w - 14]', '[953, 953, 2*w^2 - 3*w - 15]', '[953, 953, -w^2 + 7*w - 2]', '[953, 953, w^2 - 2*w - 17]', '[955, 955, 4*w^2 - 7*w - 12]', '[961, 31, 4*w^2 + 2*w - 29]', '[961, 961, w^2 + 4*w - 16]', '[965, 965, 7*w - 9]', '[968, 22, -6*w^2 - 4*w + 34]', '[968, 242, -6*w + 10]', '[971, 971, 3*w^2 - w - 16]', '[973, 973, w^2 - 6*w]', '[977, 977, 3*w^2 + 2*w - 9]', '[983, 983, 3*w^2 - 4*w - 17]', '[985, 985, w^2 + 4*w - 12]', '[989, 989, 2*w^2 + w - 24]', '[989, 989, 4*w^2 - 8*w - 9]', '[989, 989, -w^2 - 5]', '[991, 991, -2*w^2 + 3*w - 4]', '[995, 995, -2*w^2 + 4*w - 5]', '[1000, 10, 10]', '[1001, 1001, 2*w^2 - 5*w - 7]', '[1003, 1003, -3*w^2 - 6*w + 2]', '[1009, 1009, -3*w^2 + 6*w + 4]', '[1013, 1013, -w - 10]', '[1013, 1013, 2*w^2 + 3*w - 22]', '[1013, 1013, 2*w^2 + 5*w - 11]', '[1015, 1015, 3*w^2 + w - 14]', '[1025, 205, w^2 - 4*w + 9]', '[1025, 205, w^2 - 4*w - 16]', '[1025, 205, w^2 - 4*w - 6]', '[1031, 1031, 5*w^2 + w - 33]', '[1031, 1031, w^2 + w - 17]', '[1031, 1031, 2*w^2 - 3*w - 16]', '[1033, 1033, w^2 + 4*w - 15]', '[1037, 1037, -w^2 - 2*w - 5]', '[1037, 1037, 2*w^2 + 3*w - 16]', '[1037, 1037, 2*w^2 - 3*w - 19]', '[1039, 1039, w^2 + 4*w - 13]', '[1048, 262, -4*w^2 - 2*w + 22]', '[1049, 1049, 2*w^2 - 3*w - 26]', '[1049, 1049, 6*w - 13]', '[1049, 1049, w^2 + 5*w - 10]', '[1051, 1051, 6*w - 11]', '[1057, 1057, w^2 + 4*w - 14]', '[1061, 1061, 3*w^2 - 4*w - 10]', '[1069, 1069, -5*w - 1]', '[1075, 215, 2*w^2 - 3*w - 17]', '[1079, 1079, 3*w^2 - w - 4]', '[1080, 30, -6*w + 12]', '[1081, 1081, 7*w^2 + w - 54]', '[1081, 1081, 4*w^2 + 5*w - 20]', '[1081, 1081, 4*w^2 - 3*w - 29]', '[1085, 1085, 9*w^2 - 3*w - 70]', '[1088, 68, -4*w^2 - 4*w + 16]', '[1091, 1091, 6*w^2 + 2*w - 39]', '[1091, 1091, 3*w^2 + 6*w - 13]', '[1091, 1091, 4*w^2 + w - 24]', '[1097, 1097, 2*w^2 + 4*w - 13]', '[1097, 1097, 5*w^2 + 2*w - 36]', '[1097, 1097, 4*w^2 + 2*w - 37]', '[1099, 1099, -w^2 - 4*w - 7]', '[1105, 1105, 2*w^2 + 3*w + 1]', '[1107, 123, 3*w + 12]', '[1107, 123, 3*w^2 - 15]', '[1107, 123, -6*w - 15]', '[1109, 1109, 3*w^2 - 3*w - 22]', '[1111, 1111, -w^2 + 5*w + 3]', '[1112, 278, 2*w - 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