Database - hmf_fields

Formats: - HTML - YAML - JSON - 2026-10-23T22:39:24.752973

Query: /api/hmf_fields/?_offset=0

Table hmf_fields

Information on base fields for Hilbert modular forms

Column	Type	Example
degree	smallint	2
discriminant	bigint	284
ideals	jsonb	['[1, 1, 1]', '[2, 2, -7*w + 59]', '[4, 2, 2]', '[5, 5, -2*w - 17]', '[5, 5, 2*w - 17]', '[7, 7, -w ...
label	text	'2.2.284.1'
narrow_class_no	smallint	2
primes	jsonb	['[2, 2, -7*w + 59]', '[5, 5, -2*w - 17]', '[5, 5, 2*w - 17]', '[7, 7, -w - 8]', '[7, 7, w - 8]', '[...

{'degree': 3, 'discriminant': 1556, 'id': 47, 'ideals': ['[1, 1, 1]', '[2, 2, w - 1]', '[3, 3, w - 2]', '[4, 2, -w^2 + 9]', '[6, 6, w^2 + w - 6]', '[8, 2, 2]', '[9, 3, w^2 + w - 7]', '[9, 9, -w^2 + 10]', '[11, 11, w]', '[11, 11, -2*w + 3]', '[11, 11, -w^2 + 3*w - 1]', '[12, 6, w^2 - 7]', '[16, 4, 2*w - 2]', '[17, 17, w + 2]', '[17, 17, -2*w + 5]', '[17, 17, -w^2 - w + 5]', '[18, 6, w^2 + w - 4]', '[18, 18, w + 1]', '[22, 22, -w^2 + 3*w]', '[22, 22, -2*w^2 - w + 17]', '[22, 22, -w^2 - w + 8]', '[23, 23, w - 4]', '[24, 6, 2*w - 4]', '[27, 3, 3]', '[27, 27, w^2 + w - 9]', '[29, 29, w^2 - 6]', '[31, 31, w^2 - w - 1]', '[32, 4, -2*w^2 + 18]', '[33, 33, -w - 4]', '[33, 33, w^2 - 2*w]', '[33, 33, -w^2 - 2*w + 2]', '[34, 34, -w^2 + w + 6]', '[34, 34, -2*w^2 - w + 15]', '[34, 34, -w^2 + w + 4]', '[36, 6, w^2 - 2*w - 1]', '[36, 18, -w^2 + 2*w + 3]', '[37, 37, -w^2 - 2*w + 6]', '[43, 43, w^2 - 3*w + 3]', '[44, 22, -w^2 + 11]', '[44, 22, -w^2 + 5]', '[44, 22, -w^2 + 3]', '[46, 46, w^2 - 5*w + 4]', '[47, 47, 3*w^2 - 28]', '[48, 12, 2*w^2 + 2*w - 12]', '[51, 51, w^2 - 4]', '[51, 51, -2*w + 1]', '[51, 51, -w^2 - 3*w + 1]', '[53, 53, w^2 - w - 3]', '[54, 6, 3*w - 3]', '[54, 54, w^2 - w - 2]', '[58, 58, 3*w - 5]', '[61, 61, -5*w + 6]', '[62, 62, 3*w^2 + w - 24]', '[64, 4, 4]', '[66, 66, w^2 + w - 12]', '[66, 66, 2*w^2 + 3*w - 11]', '[66, 66, w - 5]', '[68, 34, w^2 - 4*w + 5]', '[68, 34, -w^2 - 2*w + 7]', '[68, 34, -3*w^2 - 2*w + 23]', '[69, 69, w^2 - 6*w + 8]', '[71, 71, w^2 - w - 7]', '[72, 6, 2*w^2 + 2*w - 14]', '[72, 18, -2*w^2 + 20]', '[74, 74, -2*w^2 - w + 5]', '[81, 9, w^2 - 2*w + 2]', '[81, 9, 3*w - 6]', '[81, 81, -2*w + 7]', '[83, 83, -2*w^2 - w + 14]', '[86, 86, w^2 + 3*w - 2]', '[87, 87, -w^2 + 3*w + 1]', '[88, 22, 2*w]', '[88, 22, -4*w + 6]', '[88, 22, -2*w^2 + 6*w - 2]', '[89, 89, w^2 + 3*w - 3]', '[92, 46, 3*w^2 - 25]', '[93, 93, 2*w + 5]', '[94, 94, -w - 5]', '[96, 12, 2*w^2 - 14]', '[99, 33, 2*w^2 + 2*w - 11]', '[99, 33, -w^2 - w + 1]', '[99, 33, w^2 - 2*w - 4]', '[99, 99, -w^2 - 3*w + 7]', '[99, 99, -w^2 - 2*w + 8]', '[99, 99, -w^2 + w + 11]', '[101, 101, 2*w + 7]', '[102, 102, 5*w - 7]', '[102, 102, -2*w^2 - 5*w + 3]', '[102, 102, w^2 - w - 8]', '[103, 103, -w^2 - 2*w + 12]', '[106, 106, -w^2 + 7*w - 8]', '[107, 107, w^2 - 12]', '[108, 6, -3*w^2 + 27]', '[108, 54, 3*w^2 + 4*w - 17]', '[109, 109, 4*w^2 + 2*w - 31]', '[111, 111, -w^2 + w - 1]', '[116, 58, 5*w^2 + 2*w - 43]', '[121, 11, -4*w^2 - 5*w + 22]', '[121, 11, -4*w^2 - 2*w + 33]', '[121, 11, -w^2 + w + 9]', '[121, 121, 2*w + 1]', '[121, 121, w^2]', '[121, 121, -3*w^2 + 26]', '[122, 122, w^2 - w - 10]', '[124, 62, w^2 + 2*w - 9]', '[125, 5, -5]', '[128, 8, 4*w - 4]', '[129, 129, 2*w^2 + 2*w - 15]', '[131, 131, -3*w + 2]', '[132, 66, w^2 - 4*w + 1]', '[132, 66, w^2 + 2*w - 11]', '[132, 66, w^2 - 6*w + 5]', '[136, 34, 2*w + 4]', '[136, 34, -4*w + 10]', '[136, 34, -2*w^2 - 2*w + 10]', '[137, 137, w^2 + 2*w - 10]', '[137, 137, 5*w^2 + w - 41]', '[137, 137, w - 6]', '[138, 138, -2*w^2 - w + 13]', '[139, 139, -w^2 - 3*w - 1]', '[141, 141, -3*w^2 - w + 23]', '[142, 142, -w^2 + 3*w - 4]', '[144, 12, 2*w^2 + 2*w - 8]', '[144, 36, 2*w + 2]', '[148, 74, -3*w^2 - 2*w + 21]', '[149, 149, 3*w^2 + 2*w - 24]', '[151, 151, -2*w - 3]', '[153, 51, 2*w^2 - 4*w + 1]', '[153, 51, w^2 + w - 13]', '[153, 51, -w^2 - 4*w - 2]', '[153, 153, -w^2 + 5*w - 3]', '[153, 153, -2*w^2 - 2*w + 9]', '[153, 153, -4*w^2 - 3*w + 28]', '[157, 157, w^2 + 4*w - 8]', '[157, 157, -6*w + 7]', '[157, 157, 4*w - 7]', '[159, 159, -2*w^2 + 8*w - 5]', '[162, 18, 3*w^2 + 3*w - 18]', '[162, 18, 2*w^2 + 5*w - 5]', '[162, 162, -2*w^2 + w + 21]', '[163, 163, -2*w^2 + 13]', '[166, 166, -w^2 - 3*w + 8]', '[167, 167, 4*w^2 + w - 32]', '[172, 86, -w^2 + 2*w + 5]', '[174, 174, -w^2 + w + 14]', '[176, 44, -2*w^2 + 6*w]', '[176, 44, -4*w^2 - 2*w + 34]', '[176, 44, -2*w^2 - 2*w + 16]', '[178, 178, 3*w^2 + 3*w - 8]', '[183, 183, -3*w^2 - 4*w + 14]', '[184, 46, 2*w - 8]', '[186, 186, -2*w^2 + w + 15]', '[187, 187, w + 6]', '[187, 187, -3*w + 10]', '[187, 187, -2*w^2 - w + 6]', '[187, 187, -2*w^2 - 4*w + 11]', '[187, 187, w^2 + 2*w]', '[187, 187, -2*w^2 + 21]', '[187, 187, w^2 - 4*w + 6]', '[187, 187, -4*w + 9]', '[187, 187, -2*w^2 + 5*w]', '[188, 94, -w^2 - 4*w + 5]', '[191, 191, -5*w^2 - 3*w + 39]', '[192, 12, 4*w - 8]', '[193, 193, 5*w^2 + 2*w - 40]', '[193, 193, 2*w^2 + w - 12]', '[193, 193, -3*w - 10]', '[197, 197, 2*w^2 + 2*w - 19]', '[198, 66, 2*w^2 - w - 11]', '[198, 66, -w^2 + 5*w - 8]', '[198, 66, 2*w^2 - w - 23]', '[198, 198, -2*w^2 + w + 3]', '[198, 198, w^2 + w]', '[198, 198, w^2 - 7*w + 10]', '[199, 199, -2*w^2 + 3*w + 6]', '[202, 202, 2*w^2 + 5*w - 7]', '[204, 102, 3*w^2 + 2*w - 25]', '[204, 102, w^2 - 13]', '[204, 102, -w^2 + 2*w - 3]', '[206, 206, -2*w^2 + 5*w - 1]', '[207, 69, -2*w^2 - 2*w + 17]', '[207, 207, 3*w^2 + w - 29]', '[212, 106, 3*w^2 + 2*w - 27]', '[213, 213, -2*w^2 + 4*w + 3]', '[214, 214, -3*w + 1]', '[216, 6, 6]', '[216, 54, 2*w^2 + 2*w - 18]', '[218, 218, 2*w^2 + 3*w - 13]', '[222, 222, -3*w^2 - 7*w + 8]', '[227, 227, 3*w^2 + 2*w - 26]', '[229, 229, w^2 + 3*w - 9]', '[232, 58, 2*w^2 - 12]', '[233, 233, -5*w + 8]', '[241, 241, -3*w - 8]', '[242, 22, -3*w^2 - w + 22]', '[242, 22, -2*w^2 - w + 11]', '[242, 22, w^2 - w + 2]', '[242, 242, -2*w^2 + 5*w + 3]', '[242, 242, -6*w^2 - w + 55]', '[242, 242, -w + 7]', '[243, 9, 3*w^2 + 3*w - 21]', '[243, 27, -3*w^2 + 30]', '[243, 243, 5*w^2 + 7*w - 25]', '[244, 122, -w^2 - 1]', '[248, 62, 2*w^2 - 2*w - 2]', '[249, 249, w^2 - 2*w - 6]', '[250, 10, -5*w + 5]', '[251, 251, 4*w^2 - 39]', '[253, 253, w^2 - 4*w]', '[253, 253, -2*w^2 + 11*w - 12]', '[253, 253, 6*w^2 - 22*w + 15]', '[256, 8, -4*w^2 + 36]', '[257, 257, 2*w^2 - w - 16]', '[258, 258, 2*w^2 + w - 7]', '[261, 87, -2*w^2 + w + 20]', '[261, 261, 6*w^2 + 2*w - 49]', '[262, 262, 7*w^2 + w - 62]', '[263, 263, -4*w + 3]', '[264, 66, -2*w - 8]', '[264, 66, 2*w^2 - 4*w]', '[264, 66, -2*w^2 - 4*w + 4]', '[267, 267, 2*w^2 - 5]', '[271, 271, 3*w^2 + 2*w - 20]', '[272, 68, -2*w^2 + 2*w + 12]', '[272, 68, -4*w^2 - 2*w + 30]', '[272, 68, -2*w^2 + 2*w + 8]', '[274, 274, w^2 - 7*w + 6]', '[274, 274, 2*w^2 - 3*w - 1]', '[274, 274, w^2 + 3*w - 14]', '[276, 138, -3*w^2 + 2*w + 17]', '[278, 278, -3*w^2 - 7*w + 12]', '[279, 93, w^2 + 4*w - 4]', '[279, 279, 2*w^2 + w - 10]', '[281, 281, 8*w^2 + 3*w - 70]', '[282, 282, -w^2 - 3*w + 10]', '[284, 142, 7*w^2 + 2*w - 63]', '[288, 12, 2*w^2 - 4*w - 2]', '[288, 36, -2*w^2 + 4*w + 6]', '[289, 17, -2*w^2 + w + 10]', '[289, 17, -w^2 + 3*w + 3]', '[289, 17, -4*w^2 - 6*w + 21]', '[289, 289, w^2 + 4*w + 4]', '[289, 289, -w^2 + 2*w + 14]', '[289, 289, -4*w^2 + 35]', '[293, 293, -w^2 + 8*w - 10]', '[293, 293, 2*w^2 + w - 8]', '[293, 293, 8*w^2 + w - 72]', '[296, 74, -2*w^2 - 4*w + 12]', '[297, 33, 3*w]', '[297, 33, -6*w + 9]', '[297, 33, -3*w^2 + 9*w - 3]', '[297, 297, -w^2 + 3*w - 5]', '[297, 297, -2*w^2 + 4*w - 3]', '[297, 297, 2*w^2 - 11]', '[298, 298, 2*w^2 + w - 9]', '[302, 302, -2*w^2 - w + 3]', '[303, 303, 2*w^2 + 3*w - 14]', '[306, 102, 4*w^2 + w - 31]', '[306, 102, w^2 - 5*w + 2]', '[306, 102, 2*w^2 - w - 17]', '[306, 306, w^2 + 3*w + 2]', '[306, 306, -2*w^2 + 3*w + 5]', '[306, 306, -3*w^2 - 5*w + 16]', '[307, 307, 2*w^2 - 4*w - 1]', '[309, 309, -w^2 + 7*w - 13]', '[314, 314, 6*w^2 + 3*w - 49]', '[314, 314, 2*w^2 - w - 19]', '[314, 314, 4*w^2 + 5*w - 21]', '[317, 317, -5*w + 12]', '[318, 318, w + 7]', '[319, 319, w^2 - 6*w + 4]', '[319, 319, w^2 + 3*w - 11]', '[319, 319, -2*w^2 + 11*w - 16]', '[321, 321, -w^2 - 3*w + 13]', '[324, 18, -w^2 + 2*w + 7]', '[324, 18, 3*w^2 - 21]', '[324, 162, w^2 + 2*w + 1]', '[326, 326, -5*w + 9]', '[327, 327, -2*w^2 + w + 18]', '[331, 331, 5*w^2 + 3*w - 37]', '[331, 331, 2*w^2 - w - 4]', '[331, 331, 2*w - 9]', '[332, 166, w^2 - 8*w + 13]', '[333, 111, -2*w^2 - 5*w + 2]', '[333, 333, -4*w^2 - 4*w + 27]', '[334, 334, w^2 + 3*w - 12]', '[337, 337, 7*w - 10]', '[337, 337, -w^2 - w - 1]', '[337, 337, -12*w^2 - 4*w + 103]', '[341, 341, w^2 - 14]', '[341, 341, 4*w^2 + w - 38]', '[341, 341, 3*w^2 - 8*w]', '[343, 7, -7]', '[344, 86, 2*w^2 - 6*w + 6]', '[348, 174, -3*w^2 - 2*w + 31]', '[349, 349, 11*w^2 + 3*w - 93]', '[352, 44, -2*w^2 + 22]', '[352, 44, -2*w^2 + 10]', '[352, 44, -2*w^2 + 6]', '[353, 353, w^2 + 6*w - 8]', '[353, 353, -w^2 + w + 15]', '[353, 353, 3*w^2 - w - 23]', '[356, 178, -w^2 + 2*w + 17]', '[359, 359, 5*w^2 - 46]', '[359, 359, 10*w^2 + 3*w - 84]', '[359, 359, 3*w^2 + w - 21]', '[363, 33, -w^2 - 4*w]', '[363, 33, 2*w^2 + w - 22]', '[363, 33, 2*w^2 - 2*w - 7]', '[363, 363, 2*w^2 - 3*w - 2]', '[363, 363, 5*w^2 + 5*w - 33]', '[363, 363, 2*w^2 + 5*w - 12]', '[366, 366, -2*w^2 + w + 9]', '[367, 367, 2*w^2 - 2*w - 3]', '[368, 92, 2*w^2 - 10*w + 8]', '[372, 186, w^2 - 4*w + 7]', '[373, 373, -2*w^2 + 3*w + 4]', '[373, 373, 7*w^2 + 3*w - 59]', '[373, 373, w^2 + 2*w - 16]', '[374, 374, -3*w^2 + w + 30]', '[374, 374, -3*w + 11]', '[374, 374, 3*w + 1]', '[374, 374, 3*w + 7]', '[374, 374, w^2 + 5*w - 6]', '[374, 374, -7*w^2 - 3*w + 56]', '[374, 374, -5*w + 11]', '[374, 374, -4*w^2 - 3*w + 27]', '[374, 374, -3*w^2 - 3*w + 22]', '[375, 15, -5*w + 10]', '[376, 94, 6*w^2 - 56]', '[379, 379, -w^2 + 2*w - 4]', '[382, 382, -3*w^2 - 3*w + 16]', '[384, 24, 4*w^2 + 4*w - 24]', '[386, 386, 2*w^2 + 3*w - 15]', '[386, 386, w^2 + 5*w - 10]', '[386, 386, -3*w^2 - 7*w + 10]', '[387, 129, w^2 + 4*w - 10]', '[387, 387, -w + 8]', '[389, 389, w^2 + 4*w - 2]', '[389, 389, 14*w^2 + 4*w - 119]', '[391, 391, w^2 - 2*w - 8]', '[391, 391, 2*w^2 - 9]', '[391, 391, -2*w^2 + 13*w - 20]', '[393, 393, -5*w^2 - 4*w + 34]', '[394, 394, 2*w^2 - 3*w - 3]', '[396, 66, -w^2 + 8*w - 11]', '[396, 66, w^2 - 2*w - 13]', '[396, 66, -w^2 - 4*w + 1]', '[396, 198, -3*w^2 - 2*w + 19]', '[396, 198, -5*w^2 - 2*w + 39]', '[396, 198, w^2 - 6*w + 11]', '[397, 397, 2*w^2 - 7]', '[398, 398, -5*w^2 - 3*w + 40]', '[401, 401, -2*w^2 + 3*w - 2]', '[404, 202, -w^2 + 4*w + 1]', '[407, 407, -3*w^2 - 3*w + 11]', '[407, 407, 3*w^2 - 4]', '[407, 407, -2*w^2 + 9*w - 6]', '[408, 102, 2*w^2 - 8]', '[408, 102, -4*w + 2]', '[408, 102, -2*w^2 - 6*w + 2]', '[411, 411, w^2 - 5*w + 9]', '[411, 411, -4*w^2 + 2*w + 27]', '[411, 411, w^2 - 8*w + 12]', '[412, 206, -9*w^2 - 2*w + 75]', '[414, 138, -2*w^2 + w + 5]', '[414, 414, w^2 - 3*w - 4]', '[417, 417, -2*w^2 - 4*w + 13]', '[421, 421, -w^2 + w - 3]', '[423, 141, -2*w^2 + w + 8]', '[423, 423, 2*w^2 - 2*w - 13]', '[424, 106, 2*w^2 - 2*w - 6]', '[426, 426, -4*w^2 - 3*w + 31]', '[428, 214, 11*w^2 + 2*w - 97]', '[432, 12, 6*w - 6]', '[432, 108, 2*w^2 - 2*w - 4]', '[436, 218, 3*w^2 + 2*w - 9]', '[439, 439, -3*w - 2]', '[444, 222, w^2 - 2*w - 9]', '[447, 447, -w^2 - w + 15]', '[449, 449, 2*w^2 - 2*w - 5]', '[453, 453, -2*w^2 + w + 6]', '[454, 454, 2*w^2 - w - 7]', '[458, 458, 3*w^2 - 3*w - 2]', '[459, 51, 3*w + 6]', '[459, 51, -6*w + 15]', '[459, 51, -3*w^2 - 3*w + 15]', '[459, 459, -5*w + 4]', '[459, 459, 4*w^2 + 2*w - 29]', '[459, 459, w^2 - 2*w - 12]', '[461, 461, 2*w^2 + 3*w - 16]', '[464, 116, 6*w - 10]', '[466, 466, -7*w^2 - 3*w + 60]', '[467, 467, -2*w^2 + 7*w - 8]', '[467, 467, 2*w^2 + 4*w - 3]', '[467, 467, 5*w^2 + w - 47]', '[471, 471, -4*w^2 - 5*w + 20]', '[471, 471, w^2 + 5*w + 7]', '[471, 471, -2*w^2 + w + 24]', '[473, 473, -2*w^2 + 12*w - 11]', '[473, 473, -3*w^2 + 20]', '[473, 473, -3*w^2 - 5*w + 17]', '[477, 159, -w^2 + 2*w + 10]', '[477, 477, 4*w^2 + w - 30]', '[479, 479, 2*w + 9]', '[482, 482, -3*w^2 - 5*w + 8]', '[484, 22, -w^2 - 4*w + 11]', '[484, 22, -w^2 - 6*w + 11]', '[484, 22, 3*w^2 + 8*w - 5]', '[484, 242, -3*w^2 + 31]', '[484, 242, -w^2 + 2*w + 11]', '[484, 242, -w^2 + 8*w - 7]', '[486, 18, 3*w^2 + 3*w - 12]', '[486, 54, 3*w + 3]', '[486, 486, 3*w^2 + w - 20]', '[487, 487, 6*w^2 + 3*w - 50]', '[488, 122, -10*w + 12]', '[489, 489, 2*w^2 - 5*w - 4]', '[493, 493, -w - 8]', '[493, 493, 3*w^2 + 3*w - 23]', '[493, 493, 3*w^2 - 6*w - 8]', '[496, 124, 6*w^2 + 2*w - 48]', '[498, 498, -2*w^2 + 5*w - 5]', '[499, 499, 7*w^2 - w - 69]', '[500, 10, 5*w^2 - 45]', '[501, 501, -3*w^2 + 2*w + 20]', '[502, 502, -3*w - 5]', '[506, 506, 6*w^2 - 21*w + 11]', '[506, 506, 5*w^2 + 3*w - 46]', '[506, 506, 2*w^2 + 3*w - 21]', '[509, 509, 2*w^2 - 3*w - 10]', '[509, 509, -3*w - 4]', '[509, 509, -w^2 - 2*w - 2]', '[512, 8, 8]', '[514, 514, -w^2 + 3*w - 6]', '[516, 258, 3*w^2 - 8*w + 1]', '[517, 517, 3*w^2 - w - 33]', '[517, 517, 3*w^2 + 3*w - 13]', '[517, 517, 3*w^2 + 2*w - 18]', '[521, 521, -4*w^2 + 29]', '[522, 174, w^2 + w + 2]', '[522, 522, 2*w^2 + 3*w - 17]', '[523, 523, 5*w^2 + w - 39]', '[524, 262, w^2 - 15]', '[526, 526, 8*w^2 + w - 71]', '[527, 527, 3*w^2 - w - 29]', '[527, 527, 2*w^2 - 4*w - 7]', '[527, 527, 3*w^2 - 2*w - 16]', '[528, 132, 2*w^2 + 2*w - 24]', '[528, 132, 4*w^2 + 6*w - 22]', '[528, 132, 2*w - 10]', '[529, 23, 8*w^2 + w - 68]', '[529, 529, -8*w + 9]', '[534, 534, 8*w^2 + 13*w - 37]', '[541, 541, -6*w^2 - 3*w + 46]', '[542, 542, 2*w^2 + 5*w - 13]', '[544, 68, 2*w^2 - 8*w + 10]', '[544, 68, -2*w^2 - 4*w + 14]', '[544, 68, -6*w^2 - 4*w + 46]', '[547, 547, w^2 - 3*w - 5]', '[548, 274, 7*w^2 + 2*w - 57]', '[548, 274, 3*w^2 - 8*w + 3]', '[548, 274, 5*w^2 - 43]', '[549, 183, -4*w^2 - 4*w + 13]', '[549, 549, -w^2 - 5*w + 5]', '[552, 138, 2*w^2 - 12*w + 16]', '[556, 278, w^2 - 6*w + 3]', '[557, 557, w^2 - 7*w + 5]', '[557, 557, 4*w - 1]', '[557, 557, 8*w^2 + w - 74]', '[558, 186, -2*w^2 + 7*w - 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