LMFDB - Database - hmf

Formats: - HTML - YAML - JSON - 2026-10-23T22:38:47.008338
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	19796
ideals	jsonb	['[1, 1, 1]', '[2, 2, -w^2 + 2]', '[2, 2, -w^3 + 2w^2 + 4w - 5]', '[4, 2, w^3 - 3w^2 - 2w + 6]',...
label	text	'4.4.19796.1'
narrow_class_no	smallint	2
primes	jsonb	['[2, 2, -w^2 + 2]', '[2, 2, -w^3 + 2w^2 + 4w - 5]', '[5, 5, -w^3 + 2w^2 + 3w - 1]', '[13, 13, w...
{'degree': 3, 'discriminant': 321, 'id': 7, 'ideals': ['[1, 1, 1]', '[3, 3, w + 1]', '[3, 3, w - 1]', '[7, 7, w^2 - 2]', '[8, 2, 2]', '[9, 3, -w^2 + 2*w + 2]', '[9, 3, w^2 - 4]', '[9, 9, w^2 - w - 2]', '[11, 11, -w^2 + w + 1]', '[21, 21, -w^2 + 2*w + 3]', '[21, 21, 2*w + 1]', '[23, 23, -w - 3]', '[24, 6, 2*w + 2]', '[24, 6, 2*w - 2]', '[27, 3, 3]', '[27, 9, -w^2 + 3*w + 1]', '[27, 9, -w^2 + 2*w + 5]', '[27, 27, w^2 + w - 3]', '[29, 29, -w^2 + 2*w + 4]', '[31, 31, 2*w - 3]', '[33, 33, -2*w^2 + w + 6]', '[33, 33, w - 4]', '[41, 41, -2*w^2 + 3*w + 6]', '[43, 43, w^2 - 3*w + 3]', '[47, 47, w^2 + w - 4]', '[49, 7, 2*w^2 - 3*w - 3]', '[49, 49, 2*w^2 - 2*w - 5]', '[53, 53, w^2 - 3*w - 2]', '[56, 14, 2*w^2 - 4]', '[59, 59, 2*w^2 - w - 5]', '[59, 59, w^2 - w - 7]', '[59, 59, -w^2 - w + 7]', '[63, 21, 2*w^2 - 3*w - 2]', '[63, 21, w^2 + w - 5]', '[63, 63, w + 4]', '[64, 4, 4]', '[67, 67, 2*w^2 - 3*w - 7]', '[69, 69, -w^2 - 2*w + 3]', '[69, 69, -w^2 - w + 6]', '[72, 6, -2*w^2 + 4*w + 4]', '[72, 6, 2*w^2 - 8]', '[72, 18, 2*w^2 - 2*w - 4]', '[73, 73, -w^2 + 4*w - 5]', '[77, 77, -w^2 - w - 2]', '[79, 79, w^2 - 8]', '[79, 79, w^2 - 5*w + 5]', '[79, 79, w^2 - 3*w - 3]', '[81, 9, 2*w^2 - w - 4]', '[81, 9, 3*w + 3]', '[81, 9, 3*w - 3]', '[81, 27, -2*w^2 + 3*w + 8]', '[81, 81, -w + 5]', '[83, 83, -3*w^2 + w + 9]', '[87, 87, 2*w^2 - 2*w - 3]', '[87, 87, 2*w + 5]', '[88, 22, -2*w^2 + 2*w + 2]', '[89, 89, 2*w^2 - w - 2]', '[93, 93, 2*w^2 + w - 6]', '[93, 93, 2*w^2 - w - 3]', '[97, 97, w^2 - 3*w - 6]', '[99, 33, w^2 - 2*w - 8]', '[99, 33, w^2 - 3*w - 4]', '[99, 99, -w^2 + 2*w - 3]', '[101, 101, 3*w - 4]', '[103, 103, 3*w - 5]', '[107, 107, -3*w^2 + 10]', '[107, 107, w^2 - 3*w - 5]', '[109, 109, w^2 + 2*w - 4]', '[121, 11, 3*w^2 - 2*w - 9]', '[121, 121, -2*w^2 + 4*w + 5]', '[123, 123, -w^2 + w + 8]', '[123, 123, 3*w^2 - 5*w - 4]', '[125, 5, -5]', '[127, 127, w^2 + w - 10]', '[129, 129, w + 5]', '[129, 129, -w^2 + 4*w + 2]', '[137, 137, 3*w^2 - 3*w - 8]', '[139, 139, -5*w^2 + 3*w + 18]', '[141, 141, w^2 - w + 3]', '[141, 141, 3*w^2 + w - 5]', '[147, 21, w^2 + 2*w - 5]', '[147, 21, 3*w^2 - w - 8]', '[147, 147, -2*w^2 + 5*w + 3]', '[147, 147, 2*w^2 + w - 7]', '[149, 149, 3*w^2 - 4*w - 6]', '[157, 157, w - 6]', '[159, 159, -3*w^2 + 5*w + 1]', '[159, 159, -w^2 - w - 3]', '[161, 161, w^2 - 9]', '[163, 163, -4*w^2 + 2*w + 13]', '[163, 163, -w^2 - 3]', '[163, 163, 2*w^2 - 4*w - 11]', '[168, 42, -2*w^2 + 4*w + 6]', '[168, 42, 4*w + 2]', '[177, 177, -w^2 + 4*w + 3]', '[177, 177, -w^2 - 2*w + 6]', '[177, 177, 3*w^2 + 2*w - 7]', '[177, 177, w^2 - 4*w - 8]', '[177, 177, -w^2 + 4*w - 6]', '[177, 177, -3*w^2 + 2*w + 8]', '[181, 181, 3*w^2 - 11]', '[184, 46, -2*w - 6]', '[189, 21, 3*w^2 - 6]', '[189, 63, w^2 + 3*w - 4]', '[189, 63, w^2 - 2*w + 4]', '[189, 189, w^2 + 2*w - 8]', '[192, 12, 4*w + 4]', '[192, 12, 4*w - 4]', '[193, 193, 3*w^2 - 3*w - 7]', '[193, 193, -3*w^2 + 3*w + 16]', '[193, 193, w^2 + 2*w - 7]', '[197, 197, 2*w^2 + w - 8]', '[201, 201, -3*w^2 + 4*w + 5]', '[201, 201, w^2 - 2*w - 9]', '[203, 203, 3*w^2 + w - 9]', '[207, 69, -w^2 + 3*w - 5]', '[207, 69, 2*w^2 - 4*w - 7]', '[207, 207, -3*w^2 + w + 7]', '[211, 211, 4*w^2 - 5*w - 10]', '[216, 6, 6]', '[216, 18, -2*w^2 + 6*w + 2]', '[216, 18, -2*w^2 + 4*w + 10]', '[216, 54, 2*w^2 + 2*w - 6]', '[217, 217, -w^2 + 4*w + 4]', '[219, 219, w^2 - w - 9]', '[219, 219, 2*w^2 - 5*w - 4]', '[227, 227, -w - 6]', '[229, 229, w^2 - 4*w - 7]', '[231, 231, -3*w^2 + 2*w + 7]', '[231, 231, -4*w + 5]', '[232, 58, -2*w^2 + 4*w + 8]', '[233, 233, 3*w^2 - 5]', '[237, 237, 2*w^2 - 4*w - 9]', '[237, 237, 3*w^2 - 4*w - 4]', '[237, 237, -w^2 - 2*w - 4]', '[237, 237, -4*w + 7]', '[237, 237, 2*w^2 + w - 9]', '[237, 237, -3*w^2 + 4*w + 2]', '[239, 239, 2*w^2 - 3*w - 13]', '[243, 9, -3*w^2 + 6*w + 6]', '[243, 9, 3*w^2 - 12]', '[243, 27, 3*w^2 - 3*w - 6]', '[243, 27, -w^2 + 5*w + 2]', '[243, 81, -w^2 + 6*w - 5]', '[243, 243, -w^2 + 4*w + 5]', '[248, 62, 4*w - 6]', '[249, 249, -w^2 + w - 4]', '[249, 249, w^2 - 4*w - 6]', '[251, 251, 3*w^2 - 4*w - 3]', '[253, 253, 3*w^2 - 4]', '[257, 257, 3*w^2 - w - 6]', '[257, 257, 3*w^2 - 5*w - 9]', '[257, 257, w^2 + 3*w - 5]', '[261, 87, 2*w^2 + 3*w - 5]', '[261, 87, -w^2 - w + 11]', '[261, 261, 2*w^2 + w - 10]', '[263, 263, 2*w^2 + w - 11]', '[264, 66, -4*w^2 + 2*w + 12]', '[264, 66, 2*w - 8]', '[267, 267, 3*w^2 + 5*w - 4]', '[267, 267, -w^2 + 7*w]', '[277, 277, 3*w^2 - 2*w - 6]', '[279, 93, w^2 + w + 4]', '[279, 93, -w^2 + 10]', '[279, 279, -3*w^2 + 7*w + 4]', '[281, 281, 3*w^2 - 3*w - 5]', '[281, 281, -w^2 - 4]', '[281, 281, 4*w^2 - 3*w - 12]', '[287, 287, 3*w^2 - 13]', '[291, 291, -3*w^2 + w + 5]', '[291, 291, -5*w + 4]', '[293, 293, 2*w^2 - 5*w - 5]', '[297, 33, -3*w^2 + 3*w + 3]', '[297, 99, -4*w^2 + 6*w + 7]', '[297, 99, -2*w^2 - 2*w + 7]', '[297, 297, 2*w^2 - 2*w - 13]', '[301, 301, 3*w^2 - 3*w - 4]', '[303, 303, 3*w^2 - 7*w + 4]', '[303, 303, 3*w^2 - w - 4]', '[307, 307, 3*w^2 - 2*w - 3]', '[309, 309, 3*w^2 - 2*w - 5]', '[309, 309, 3*w^2 - 8*w + 5]', '[317, 317, 3*w^2 - w - 18]', '[317, 317, -w^2 + 2*w - 5]', '[317, 317, -4*w^2 + 7*w + 4]', '[319, 319, -w^2 - 3*w + 6]', '[321, 321, -2*w - 7]', '[321, 321, -3*w^2 + 2*w + 4]', '[321, 321, -6*w^2 - 2*w + 13]', '[321, 321, -w^2 - 4*w - 6]', '[327, 327, 2*w^2 - 2*w + 3]', '[327, 327, 4*w^2 + 2*w - 5]', '[328, 82, -4*w^2 + 6*w + 12]', '[329, 329, 5*w + 6]', '[341, 341, -4*w^2 + 9]', '[343, 7, 7]', '[343, 343, -w^2 + 2*w + 10]', '[344, 86, 2*w^2 - 6*w + 6]', '[349, 349, -w^2 + 3*w - 6]', '[353, 353, 3*w^2 - 6*w - 7]', '[353, 353, w^2 - w - 10]', '[353, 353, -5*w - 3]', '[363, 33, 4*w^2 + w - 12]', '[363, 33, -2*w^2 + 5*w + 6]', '[363, 363, w + 7]', '[363, 363, 4*w^2 - 7*w - 3]', '[367, 367, -4*w^2 - w + 7]', '[369, 123, -w^2 - 4*w + 17]', '[369, 123, 7*w^2 - 6*w - 25]', '[369, 369, 2*w^2 + 2*w - 15]', '[371, 371, -2*w^2 - 3*w + 6]', '[375, 15, -5*w - 5]', '[375, 15, -5*w + 5]', '[376, 94, 2*w^2 + 2*w - 8]', '[379, 379, 4*w^2 - 3*w - 11]', '[381, 381, 4*w^2 - 4*w - 21]', '[381, 381, 3*w^2 - 5*w - 11]', '[383, 383, 4*w^2 - w - 10]', '[387, 129, 4*w^2 - 6*w - 1]', '[387, 129, w^2 + 4*w - 5]', '[387, 387, 2*w^2 + 2*w + 3]', '[389, 389, w^2 - 5*w - 4]', '[389, 389, -5*w^2 + 7*w + 11]', '[389, 389, -7*w^2 + 4*w + 25]', '[392, 14, 4*w^2 - 6*w - 6]', '[392, 98, 4*w^2 - 4*w - 10]', '[397, 397, -w^2 + w - 5]', '[397, 397, 5*w^2 - 6*w - 22]', '[397, 397, -5*w^2 - w + 11]', '[401, 401, 2*w^2 - w - 14]', '[401, 401, 5*w^2 - 3*w - 16]', '[401, 401, w^2 + 3*w - 8]', '[409, 409, w^2 + 3*w - 9]', '[411, 411, -3*w^2 + 7*w + 5]', '[411, 411, 3*w^2 + w - 11]', '[413, 413, -5*w^2 + w + 14]', '[413, 413, 4*w + 9]', '[413, 413, 3*w^2 - 5*w - 12]', '[417, 417, 3*w^2 - 5*w - 13]', '[417, 417, w - 8]', '[423, 141, -2*w^2 + 3*w + 14]', '[423, 141, 4*w^2 - 5*w - 8]', '[423, 423, -2*w^2 + 5*w + 7]', '[424, 106, 2*w^2 - 6*w - 4]', '[431, 431, 2*w - 9]', '[433, 433, w^2 - 3*w - 11]', '[439, 439, w^2 - 11]', '[439, 439, 5*w - 6]', '[439, 439, 3*w^2 + 2*w - 9]', '[441, 21, 2*w^2 - 3*w + 4]', '[441, 21, -w^2 + 5*w + 5]', '[441, 63, 4*w^2 + w - 6]', '[441, 147, w^2 + 5]', '[441, 147, -w^2 + 5*w + 8]', '[441, 441, -w^2 - w + 12]', '[443, 443, -6*w^2 + 3*w + 20]', '[443, 443, -w^2 - w - 5]', '[443, 443, 2*w^2 - 5*w - 11]', '[447, 447, -4*w^2 + 10*w + 3]', '[447, 447, 2*w^2 + 2*w - 9]', '[448, 28, 4*w^2 - 8]', '[451, 451, -5*w + 9]', '[461, 461, 3*w^2 - 4*w - 18]', '[463, 463, 3*w^2 - 6*w - 17]', '[463, 463, -4*w^2 - 3*w + 9]', '[463, 463, 3*w^2 - 6*w - 8]', '[467, 467, 2*w^2 - 5*w - 8]', '[469, 469, -4*w^2 + 15]', '[471, 471, w^2 - 5*w - 6]', '[471, 471, w^2 - 7*w + 6]', '[472, 118, 4*w^2 - 2*w - 10]', '[472, 118, 2*w^2 - 2*w - 14]', '[472, 118, -2*w^2 - 2*w + 14]', '[473, 473, w^2 - 5*w - 7]', '[477, 159, -4*w^2 + 3*w + 10]', '[477, 159, -2*w^2 + 7*w - 8]', '[477, 477, -5*w + 7]', '[483, 483, -5*w + 8]', '[483, 483, 2*w^2 - 5*w - 10]', '[487, 487, 2*w^2 + 3*w - 7]', '[489, 489, -2*w^2 - 7*w - 2]', '[489, 489, -4*w^2 + w + 9]', '[489, 489, -w^2 + 2*w - 6]', '[489, 489, -7*w + 4]', '[489, 489, 2*w^2 - 5*w - 9]', '[489, 489, -7*w - 13]', '[499, 499, 5*w^2 - 8*w - 8]', '[503, 503, 3*w^2 + w - 12]', '[504, 42, 4*w^2 - 6*w - 4]', '[504, 42, 2*w^2 + 2*w - 10]', '[504, 126, 2*w + 8]', '[509, 509, w^2 - 6*w - 11]', '[511, 511, -4*w^2 + 5*w + 7]', '[512, 8, 8]', '[517, 517, w^2 - 6*w - 3]', '[523, 523, 3*w^2 - 9*w - 2]', '[529, 23, -w^2 + 4*w - 8]', '[529, 529, 5*w^2 - 5*w - 14]', '[531, 177, -4*w^2 + 6*w + 19]', '[531, 177, 2*w^2 + 2*w - 13]', '[531, 177, -7*w^2 + 3*w + 28]', '[531, 177, 5*w^2 - 7*w - 16]', '[531, 177, -7*w^2 + 11*w + 14]', '[531, 177, 5*w^2 - 3*w - 26]', '[531, 531, -w^2 + w + 11]', '[531, 531, 5*w^2 - 8*w - 13]', '[531, 531, -5*w^2 + 4*w + 15]', '[536, 134, 4*w^2 - 6*w - 14]', '[539, 77, -4*w^2 - w + 13]', '[539, 539, -w^2 + 3*w - 7]', '[541, 541, 2*w^2 + 2*w - 11]', '[543, 543, w + 8]', '[543, 543, -2*w^2 + 7*w + 3]', '[552, 138, -2*w^2 - 4*w + 6]', '[552, 138, -2*w^2 - 2*w + 12]', '[553, 553, -5*w^2 + 3*w + 15]', '[553, 553, -3*w^2 - 3*w + 8]', '[553, 553, -3*w^2 + 7*w + 6]', '[567, 63, -3*w^2 + 6*w + 9]', '[567, 63, 6*w + 3]', '[567, 63, 5*w^2 - 7*w - 10]', '[567, 189, 2*w^2 - 6*w + 7]', '[567, 567, 4*w^2 - 2*w - 9]', '[569, 569, 4*w^2 - 3*w - 9]', '[576, 12, -4*w^2 + 8*w + 8]', '[576, 12, 4*w^2 - 16]', '[576, 36, 4*w^2 - 4*w - 8]', '[579, 579, -3*w^2 + 8*w + 4]', '[579, 579, 4*w^2 - 5*w - 6]', '[579, 579, 3*w^2 + w - 13]', '[579, 579, 4*w^2 - w - 8]', '[579, 579, 3*w^2 + 2*w - 10]', '[579, 579, 2*w^2 - 5*w + 6]', '[581, 581, -w^2 - 4*w + 7]', '[583, 583, -w^2 + 8*w - 5]', '[584, 146, -2*w^2 + 8*w - 10]', '[587, 587, -w^2 - 4*w + 13]', '[591, 591, w^2 - w + 6]', '[591, 591, 5*w^2 + w - 10]', '[599, 599, 3*w - 11]', '[601, 601, -3*w^2 + 10*w - 9]', '[603, 201, -8*w^2 + 6*w + 29]', '[603, 201, 2*w^2 + 2*w - 19]', '[603, 603, -3*w^2 - w + 17]', '[607, 607, 4*w^2 - 6*w - 15]', '[609, 609, -2*w^2 + w + 15]', '[609, 609, w^2 + 2*w + 6]', '[613, 613, w - 9]', '[616, 154, -2*w^2 - 2*w - 4]', '[619, 619, 5*w^2 - 2*w - 14]', '[621, 69, -3*w - 9]', '[621, 207, -4*w^2 + 5*w + 5]', '[621, 207, w^2 - 6*w - 4]', '[621, 621, 4*w^2 - 7*w - 11]', '[623, 623, 3*w^2 + 4*w + 3]', '[631, 631, 4*w^2 - 5*w - 4]', '[632, 158, 2*w^2 - 16]', '[632, 158, 2*w^2 - 10*w + 10]', '[632, 158, 2*w^2 - 6*w - 6]', '[633, 633, 7*w^2 - 4*w - 24]', '[633, 633, 3*w^2 + w - 14]', '[647, 647, 4*w^2 - 4*w - 7]', '[647, 647, w^2 - 12]', '[647, 647, 4*w^2 - w - 7]', '[648, 18, 4*w^2 - 2*w - 8]', '[648, 18, 6*w + 6]', '[648, 18, 6*w - 6]', '[648, 54, -4*w^2 + 6*w + 16]', '[648, 162, -2*w + 10]', '[649, 649, -4*w^2 + 9*w + 6]', '[649, 649, -w^2 - 6]', '[649, 649, 4*w^2 - 3*w - 8]', '[651, 651, 3*w^2 + w - 16]', '[651, 651, 5*w^2 - 8*w - 7]', '[653, 653, 4*w^2 - 6*w - 17]', '[657, 219, -5*w^2 + 9*w + 2]', '[657, 219, -w^2 - 4*w + 8]', '[657, 657, -w^2 - w - 6]', '[659, 659, 3*w^2 - 6*w - 10]', '[659, 659, 3*w^2 + w - 15]', '[659, 659, 4*w^2 - 17]', '[661, 661, 2*w^2 - 3*w - 15]', '[661, 661, -5*w^2 + 5*w + 26]', '[661, 661, 5*w^2 - 12*w - 4]', '[664, 166, -6*w^2 + 2*w + 18]', '[667, 667, 2*w^2 - 6*w - 13]', '[673, 673, w^2 + w - 13]', '[677, 677, w^2 - 3*w - 12]', '[679, 679, -2*w^2 + 3*w - 5]', '[681, 681, -w^2 - 5*w + 6]', '[681, 681, -w^2 - 7*w - 6]', '[683, 683, 5*w^2 - 4*w - 14]', '[687, 687, -4*w^2 + w + 6]', '[687, 687, -2*w^2 - 7*w - 8]', '[693, 231, 2*w^2 - 7*w - 4]', '[693, 231, -4*w^2 - 3*w + 10]', '[693, 693, -4*w^2 + w + 5]', '[696, 174, 4*w^2 - 4*w - 6]', '[696, 174, 4*w + 10]', '[699, 699, 7*w + 2]', '[699, 699, 6*w^2 + 7*w - 8]', '[704, 44, -4*w^2 + 4*w + 4]', '[707, 707, -w^2 + 6*w + 5]', '[709, 709, 4*w^2 - 2*w - 7]', '[711, 237, 7*w^2 - 11*w - 17]', '[711, 237, -7*w^2 + 3*w + 31]', '[711, 237, w^2 - 2*w + 7]', '[711, 237, -4*w^2 + 12*w + 1]', '[711, 237, -5*w^2 + 3*w + 14]', '[711, 237, -w^2 + 5*w - 10]', '[711, 711, -w^2 - 4*w + 9]', '[711, 711, -6*w^2 + 7*w + 16]', '[711, 711, 2*w^2 + 4*w - 7]', '[712, 178, 4*w^2 - 2*w - 4]', '[713, 713, -2*w^2 - 3*w + 9]', '[717, 717, w^2 - 8*w - 15]', '[717, 717, -3*w^2 - 2*w + 11]', '[721, 721, -2*w^2 + 6*w + 7]', '[729, 9, 9]', '[729, 27, w^2 + 4*w - 11]', '[729, 27, -3*w^2 + 9*w + 3]', '[729, 27, -3*w^2 + 6*w + 15]', '[729, 81, 3*w^2 + 3*w - 9]', '[729, 243, 4*w^2 - 3*w - 4]', '[729, 729, 5*w^2 - 7*w - 9]', '[733, 733, 3*w^2 - 6*w - 11]', '[737, 737, w^2 + 4*w - 10]', '[739, 739, -2*w - 9]', '[743, 743, 6*w - 7]', '[744, 186, 4*w^2 + 2*w - 12]', '[744, 186, 4*w^2 - 2*w - 6]', '[747, 249, -2*w^2 - 6*w - 7]', '[747, 249, -4*w^2 + 2*w + 5]', '[747, 747, 3*w^2 - 4*w - 19]', '[749, 749, w^2 - 9*w - 17]', '[749, 749, -5*w^2 - 3*w + 12]', '[751, 751, w^2 - 6*w - 9]', '[753, 753, -4*w^2 + 13*w]', '[753, 753, 2*w^2 + 5*w - 6]', '[757, 757, 4*w^2 - 3*w - 5]', '[759, 759, -w^2 + w + 12]', '[759, 759, -3*w^2 + 8*w + 5]', '[761, 761, -7*w^2 + 8*w + 31]', '[763, 763, w^2 + 7*w + 5]', '[769, 769, w^2 - 6*w - 6]', '[771, 771, 5*w^2 + 5*w - 9]', '[771, 771, -5*w^2 + 8*w + 6]', '[771, 771, 3*w^2 - 4*w + 4]', '[771, 771, -w^2 + 7*w + 3]', '[771, 771, w^2 - 2*w - 12]', '[771, 771, 5*w^2 + 2*w - 6]', '[773, 773, -w - 9]', '[773, 773, w^2 - 4*w - 13]', '[773, 773, 5*w^2 - 18]', '[776, 194, 2*w^2 - 6*w - 12]', '[783, 87, -3*w^2 + 6*w + 12]', '[783, 261, w^2 + 7*w + 4]', '[783, 261, w^2 - 3*w + 8]', '[783, 783, 5*w^2 - w - 12]', '[787, 787, 3*w^2 - 6*w - 14]', '[789, 789, w^2 - 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w - 14]', '[401, 401, 5*w^2 - 3*w - 16]', '[401, 401, w^2 + 3*w - 8]', '[409, 409, w^2 + 3*w - 9]', '[431, 431, 2*w - 9]', '[433, 433, w^2 - 3*w - 11]', '[439, 439, w^2 - 11]', '[439, 439, 5*w - 6]', '[439, 439, 3*w^2 + 2*w - 9]', '[443, 443, -6*w^2 + 3*w + 20]', '[443, 443, -w^2 - w - 5]', '[443, 443, 2*w^2 - 5*w - 11]', '[461, 461, 3*w^2 - 4*w - 18]', '[463, 463, 3*w^2 - 6*w - 17]', '[463, 463, -4*w^2 - 3*w + 9]', '[463, 463, 3*w^2 - 6*w - 8]', '[467, 467, 2*w^2 - 5*w - 8]', '[487, 487, 2*w^2 + 3*w - 7]', '[499, 499, 5*w^2 - 8*w - 8]', '[503, 503, 3*w^2 + w - 12]', '[509, 509, w^2 - 6*w - 11]', '[523, 523, 3*w^2 - 9*w - 2]', '[529, 23, -w^2 + 4*w - 8]', '[541, 541, 2*w^2 + 2*w - 11]', '[569, 569, 4*w^2 - 3*w - 9]', '[587, 587, -w^2 - 4*w + 13]', '[599, 599, 3*w - 11]', '[601, 601, -3*w^2 + 10*w - 9]', '[607, 607, 4*w^2 - 6*w - 15]', '[613, 613, w - 9]', '[619, 619, 5*w^2 - 2*w - 14]', '[631, 631, 4*w^2 - 5*w - 4]', '[647, 647, 4*w^2 - 4*w - 7]', '[647, 647, w^2 - 12]', '[647, 647, 4*w^2 - w - 7]', '[653, 653, 4*w^2 - 6*w - 17]', '[659, 659, 3*w^2 - 6*w - 10]', '[659, 659, 3*w^2 + w - 15]', '[659, 659, 4*w^2 - 17]', '[661, 661, 2*w^2 - 3*w - 15]', '[661, 661, -5*w^2 + 5*w + 26]', '[661, 661, 5*w^2 - 12*w - 4]', '[673, 673, w^2 + w - 13]', '[677, 677, w^2 - 3*w - 12]', '[683, 683, 5*w^2 - 4*w - 14]', '[709, 709, 4*w^2 - 2*w - 7]', '[733, 733, 3*w^2 - 6*w - 11]', '[739, 739, -2*w - 9]', '[743, 743, 6*w - 7]', '[751, 751, w^2 - 6*w - 9]', '[757, 757, 4*w^2 - 3*w - 5]', '[761, 761, -7*w^2 + 8*w + 31]', '[769, 769, w^2 - 6*w - 6]', '[773, 773, -w - 9]', '[773, 773, w^2 - 4*w - 13]', '[773, 773, 5*w^2 - 18]', '[787, 787, 3*w^2 - 6*w - 14]', '[797, 797, w^2 - 6*w - 8]', '[811, 811, 2*w^2 + 3*w - 10]', '[811, 811, -2*w^2 - 3*w + 16]', '[811, 811, -6*w^2 + 11*w + 6]', '[823, 823, w^2 + 5*w - 7]', '[829, 829, -5*w^2 - 2*w + 14]', '[839, 839, 2*w^2 - 6*w - 9]', '[841, 29, 2*w^2 - 7*w - 5]', '[853, 853, 5*w^2 - 28]', '[857, 857, 7*w^2 - 9*w - 23]', '[877, 877, -8*w^2 + 3*w + 31]', '[881, 881, 6*w^2 - 9*w - 11]', '[907, 907, 4*w^2 - 7*w - 13]', '[911, 911, 2*w^2 + 3*w - 15]', '[911, 911, -w^2 - 7]', '[911, 911, 3*w^2 + 3*w - 10]', '[919, 919, w^2 - 7*w - 4]', '[941, 941, 6*w^2 - 11*w - 12]', '[947, 947, 5*w^2 - w - 11]', '[947, 947, 3*w^2 - 8*w - 6]', '[947, 947, 2*w^2 + 3*w - 12]', '[953, 953, -5*w^2 - 4*w + 11]', '[953, 953, 4*w^2 - w - 25]', '[953, 953, 6*w^2 - 7*w - 15]', '[961, 31, 4*w^2 + 2*w - 13]', '[977, 977, -2*w^2 + 3*w - 6]', '[991, 991, 5*w^2 - 5*w - 11]']}
Overview	Random
Universe	Knowledge
Classical	Maass
Hilbert	Bianchi
Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps
Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Table hmf_fields

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.
