Database - hmf_fields

Formats: - HTML - YAML - JSON - 2026-10-23T22:38:47.003852

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	472
ideals	jsonb	['[1, 1, 1]', '[2, 2, -51*w + 554]', '[3, 3, -w + 11]', '[3, 3, w + 11]', '[4, 2, 2]', '[6, 6, -7*w ...
label	text	'2.2.472.1'
narrow_class_no	smallint	2
primes	jsonb	['[2, 2, -51*w + 554]', '[3, 3, -w + 11]', '[3, 3, w + 11]', '[13, 13, 29*w + 315]', '[13, 13, 29*w ...

{'degree': 3, 'discriminant': 1384, 'id': 39, 'ideals': ['[1, 1, 1]', '[2, 2, w - 2]', '[2, 2, w^2 + 2*w - 5]', '[4, 2, -w^2 + 8]', '[4, 2, w^2 + w - 8]', '[4, 4, -w + 1]', '[7, 7, w^2 + w - 7]', '[8, 2, 2]', '[8, 4, -w^2 - 2*w + 6]', '[8, 4, -w^2 - w + 10]', '[8, 8, -w - 3]', '[11, 11, -w^2 - w + 11]', '[11, 11, 2*w^2 + 2*w - 15]', '[11, 11, w^2 + w - 9]', '[13, 13, 2*w - 5]', '[14, 14, w]', '[14, 14, -w^2 + 7]', '[16, 4, 2*w - 4]', '[16, 4, w^2 - 10]', '[16, 4, 2*w^2 + 4*w - 10]', '[16, 8, -w^2 - w + 6]', '[16, 16, -w^2 + 9]', '[17, 17, -w^2 - w + 5]', '[22, 22, w + 1]', '[22, 22, w + 2]', '[22, 22, 2*w^2 + 3*w - 11]', '[22, 22, -2*w^2 - 3*w + 10]', '[22, 22, -2*w^2 - w + 17]', '[22, 22, -w + 4]', '[26, 26, -w - 4]', '[26, 26, w^2 - 3]', '[27, 3, -3]', '[28, 14, 3*w^2 + 2*w - 28]', '[28, 14, w^2 - 3*w]', '[28, 28, -w^2 - 2*w + 7]', '[29, 29, w^2 + w - 3]', '[32, 4, -2*w^2 + 16]', '[32, 4, 2*w^2 + 2*w - 16]', '[32, 8, -w^2 + 6]', '[32, 8, -2*w + 2]', '[32, 16, w^2 - w - 4]', '[32, 32, w^2 + 2*w - 3]', '[34, 34, 2*w^2 + w - 20]', '[34, 34, w^2 - 2*w - 1]', '[37, 37, -2*w^2 + 15]', '[43, 43, 3*w^2 + w - 27]', '[44, 22, w^2 - w - 2]', '[44, 22, w^2 - 12]', '[44, 22, w^2 - 4]', '[44, 22, w^2 - w - 6]', '[44, 22, w^2 + 3*w - 6]', '[44, 22, -3*w^2 - 4*w + 20]', '[44, 44, -w^2 + 5]', '[44, 44, w^2 - 2*w - 3]', '[44, 44, -2*w^2 - 3*w + 13]', '[49, 7, -w^2 + w + 3]', '[49, 49, 2*w + 7]', '[52, 26, -w^2 - 2*w + 8]', '[52, 26, -w^2 - w + 12]', '[52, 52, 3*w^2 + 4*w - 19]', '[54, 6, -3*w + 6]', '[54, 6, -3*w^2 - 6*w + 15]', '[56, 14, 2*w^2 + 2*w - 14]', '[56, 28, -w^2 - 2*w + 14]', '[56, 28, 3*w^2 + w - 28]', '[56, 56, 3*w - 7]', '[58, 58, 5*w - 8]', '[58, 58, 8*w^2 + 15*w - 41]', '[64, 4, 4]', '[64, 8, w^2 - 4*w + 2]', '[64, 8, -2*w^2 - 4*w + 12]', '[64, 8, -2*w^2 - 2*w + 20]', '[64, 16, -2*w - 6]', '[64, 32, w^2 + 3*w - 8]', '[64, 64, w - 5]', '[67, 67, 2*w^2 + 2*w - 17]', '[68, 34, -w^2 - 2*w + 12]', '[68, 34, -w^2 - 3*w + 2]', '[68, 68, 3*w^2 + 2*w - 25]', '[71, 71, 2*w - 1]', '[74, 74, w^2 + 2*w - 9]', '[74, 74, -2*w^2 - 3*w + 8]', '[77, 77, -2*w^2 + 21]', '[77, 77, 2*w - 7]', '[77, 77, 4*w^2 + 2*w - 35]', '[79, 79, 3*w^2 + w - 25]', '[83, 83, w^2 + 3*w - 5]', '[86, 86, -w - 5]', '[86, 86, 4*w^2 + 7*w - 22]', '[88, 22, -2*w^2 - 2*w + 22]', '[88, 22, 4*w^2 + 4*w - 30]', '[88, 22, 2*w^2 + 2*w - 18]', '[88, 44, 3*w^2 + 3*w - 22]', '[88, 44, -3*w^2 - 2*w + 30]', '[88, 44, w^2 - 5*w + 4]', '[88, 44, -w^2 - 2*w + 10]', '[88, 44, -w^2 - w + 2]', '[88, 44, -w^2 - 2*w + 2]', '[88, 88, w^2 + 2*w - 11]', '[88, 88, -3*w^2 - 6*w + 17]', '[88, 88, -w^2 + 1]', '[89, 89, -4*w^2 - 4*w + 31]', '[89, 89, -2*w^2 + 17]', '[89, 89, 2*w^2 + 2*w - 19]', '[91, 91, -w^2 + w + 7]', '[97, 97, 2*w^2 + 2*w - 13]', '[98, 14, 4*w^2 + 3*w - 40]', '[98, 14, -4*w^2 - 3*w + 33]', '[98, 98, 2*w^2 + 3*w - 14]', '[98, 98, 2*w^2 + w - 21]', '[101, 101, 2*w^2 + 2*w - 9]', '[101, 101, 3*w^2 + 3*w - 31]', '[101, 101, w^2 + 3*w - 3]', '[103, 103, -w^2 + 3*w + 1]', '[104, 26, 4*w - 10]', '[104, 52, -w^2 + 2*w - 2]', '[104, 52, w^2 + 3*w - 4]', '[104, 104, -2*w^2 - w + 15]', '[108, 6, 3*w^2 - 24]', '[108, 6, -3*w^2 - 3*w + 24]', '[108, 12, 3*w - 3]', '[109, 109, -w^2 + w + 15]', '[112, 28, 2*w]', '[112, 28, -3*w^2 - 4*w + 14]', '[112, 28, -2*w^2 + 14]', '[112, 56, -w^2 - 3*w]', '[112, 112, 4*w^2 + 3*w - 35]', '[116, 58, -w^2 + 2*w + 4]', '[116, 58, 3*w^2 + 5*w - 18]', '[116, 116, -w^2 - 6*w + 11]', '[119, 119, -2*w^2 - 4*w + 7]', '[121, 11, w^2 + 3*w - 9]', '[121, 11, 3*w^2 + 5*w - 13]', '[121, 11, 2*w^2 - 6*w + 3]', '[121, 121, 4*w - 5]', '[121, 121, w^2 - w - 13]', '[121, 121, w^2 + w - 13]', '[125, 5, -5]', '[127, 127, -w^2 - 3*w + 15]', '[128, 8, 4*w - 8]', '[128, 8, 2*w^2 - 20]', '[128, 8, 4*w^2 + 8*w - 20]', '[128, 16, 3*w^2 + 4*w - 18]', '[128, 16, -2*w^2 - 2*w + 12]', '[128, 32, -2*w^2 + 18]', '[128, 64, w^2 - 7*w + 10]', '[128, 128, -2*w^2 - 5*w + 11]', '[134, 134, -2*w^2 - 3*w + 23]', '[134, 134, -w + 6]', '[136, 34, -2*w^2 - 2*w + 10]', '[136, 68, -w^2 + 6*w - 10]', '[136, 68, -w^2 + w + 8]', '[136, 136, -4*w^2 - w + 33]', '[137, 137, -2*w - 5]', '[137, 137, -2*w^2 - 4*w + 13]', '[137, 137, -2*w^2 + 2*w + 9]', '[139, 139, -4*w + 9]', '[142, 142, 5*w^2 + 8*w - 23]', '[142, 142, 2*w^2 - 5*w + 2]', '[143, 143, -2*w^2 - 2*w + 11]', '[143, 143, -w^2 - 3*w + 17]', '[143, 143, -2*w^2 + 19]', '[148, 74, w^2 - 3*w + 4]', '[148, 74, -3*w^2 - 2*w + 24]', '[148, 148, 5*w^2 + 8*w - 25]', '[149, 149, -2*w - 1]', '[154, 154, 4*w^2 + w - 35]', '[154, 154, -w^2 - 4*w + 7]', '[154, 154, -2*w^2 + w + 14]', '[154, 154, 2*w^2 + w - 14]', '[154, 154, 4*w^2 + 5*w - 28]', '[154, 154, 3*w^2 + 4*w - 21]', '[157, 157, -2*w^2 + 23]', '[158, 158, -4*w^2 - 7*w + 18]', '[158, 158, 2*w^2 + 3*w - 15]', '[163, 163, -w^2 + w - 1]', '[166, 166, 12*w^2 + 21*w - 59]', '[166, 166, 2*w^2 - w - 4]', '[169, 13, 5*w^2 + w - 41]', '[169, 169, 3*w^2 + w - 31]', '[172, 86, -3*w^2 + 32]', '[172, 86, -w^2 - 3*w + 10]', '[172, 172, -8*w^2 - 15*w + 39]', '[173, 173, -5*w^2 - 9*w + 23]', '[173, 173, w^2 - w - 9]', '[176, 44, 2*w + 2]', '[176, 44, -w^2 + 4*w - 6]', '[176, 44, 2*w + 4]', '[176, 44, -5*w^2 - 8*w + 26]', '[176, 44, 4*w^2 + 6*w - 22]', '[176, 44, -4*w^2 - 6*w + 20]', '[176, 44, -4*w^2 - 2*w + 34]', '[176, 44, -w^2 - 4*w + 10]', '[176, 44, -2*w + 8]', '[176, 88, w^2 - w - 12]', '[176, 88, -3*w^2 - w + 24]', '[176, 88, w^2 - 5*w + 8]', '[176, 176, 3*w^2 + 4*w - 15]', '[176, 176, 5*w - 9]', '[176, 176, -w^2 - 4*w - 3]', '[178, 178, -w - 6]', '[178, 178, 2*w^2 - 3*w - 6]', '[178, 178, -3*w + 10]', '[178, 178, 4*w^2 + 3*w - 37]', '[178, 178, w^2 + 2*w - 1]', '[178, 178, 3*w^2 + 4*w - 17]', '[179, 179, w^2 + w - 1]', '[182, 182, 2*w^2 - 5*w]', '[182, 182, 2*w^2 + 3*w - 7]', '[187, 187, -2*w^2 + 13]', '[187, 187, -2*w - 3]', '[187, 187, -6*w^2 - 2*w + 53]', '[189, 21, -3*w^2 - 3*w + 21]', '[191, 191, 3*w^2 + 3*w - 25]', '[193, 193, -5*w^2 - 3*w + 43]', '[194, 194, 3*w - 2]', '[194, 194, -2*w^2 + w + 11]', '[196, 14, 3*w^2 + 4*w - 16]', '[196, 14, w^2 - w - 10]', '[196, 28, 5*w^2 + 2*w - 43]', '[196, 98, w^2]', '[196, 98, -w^2 - 3*w + 14]', '[196, 196, -2*w^2 - 5*w + 7]', '[197, 197, 2*w^2 - 4*w - 3]', '[199, 199, w^2 - w - 11]', '[202, 202, 13*w^2 + 24*w - 67]', '[202, 202, -2*w^2 - 5*w + 10]', '[202, 202, 14*w^2 + 25*w - 69]', '[202, 202, 7*w - 10]', '[202, 202, 2*w^2 + w - 13]', '[202, 202, 2*w^2 + w - 8]', '[203, 203, 4*w^2 + 6*w - 21]', '[206, 206, -4*w^2 - w + 39]', '[206, 206, 6*w^2 + 5*w - 60]', '[208, 52, -2*w - 8]', '[208, 52, -3*w^2 + 22]', '[208, 52, 2*w^2 - 6]', '[208, 104, w^2 - 3*w - 2]', '[208, 208, -4*w^2 - 7*w + 23]', '[211, 211, -w^2 - 3*w + 11]', '[216, 6, 6]', '[216, 12, 3*w^2 + 6*w - 18]', '[216, 12, 3*w^2 + 3*w - 30]', '[216, 24, 3*w + 9]', '[218, 218, 2*w^2 + 3*w - 16]', '[218, 218, 3*w^2 + 2*w - 31]', '[221, 221, w^2 - 5*w + 3]', '[223, 223, 3*w^2 + 5*w - 19]', '[224, 28, 6*w^2 + 4*w - 56]', '[224, 28, 2*w^2 - 6*w]', '[224, 56, w^2 - 14]', '[224, 56, -2*w^2 - 4*w + 14]', '[224, 112, -w^2 - w + 14]', '[224, 224, -5*w^2 - 4*w + 49]', '[227, 227, 2*w^2 + 2*w - 23]', '[229, 229, w^2 + 3*w - 13]', '[232, 58, 2*w^2 + 2*w - 6]', '[232, 116, -7*w^2 - 14*w + 38]', '[232, 116, -w^2 - 3*w + 12]', '[232, 232, -5*w^2 - 10*w + 23]', '[238, 238, -2*w^2 - 5*w + 14]', '[238, 238, -w + 7]', '[239, 239, -9*w^2 - 15*w + 43]', '[241, 241, -5*w^2 - 5*w + 39]', '[242, 22, -4*w^2 - w + 36]', '[242, 22, 4*w^2 + 3*w - 32]', '[242, 22, -2*w^2 - 5*w + 8]', '[242, 22, w^2 - 8*w + 13]', '[242, 22, 3*w^2 + 2*w - 23]', '[242, 22, -w^2 + 2*w - 3]', '[242, 242, w^2 + 4*w + 1]', '[242, 242, -3*w^2 + 25]', '[242, 242, -5*w + 12]', '[242, 242, 2*w^2 + 3*w - 22]', '[242, 242, -2*w^2 - w + 12]', '[242, 242, -2*w^2 - 5*w + 9]', '[250, 10, -5*w + 10]', '[250, 10, -5*w^2 - 10*w + 25]', '[251, 251, 2*w^2 - 2*w - 3]', '[254, 254, -2*w^2 + 11*w - 16]', '[254, 254, -2*w^2 - w + 9]', '[256, 8, -4*w^2 + 32]', '[256, 8, 4*w^2 + 4*w - 32]', '[256, 16, -2*w^2 + 12]', '[256, 16, w^2 + 4*w - 6]', '[256, 16, -4*w + 4]', '[256, 32, 2*w^2 - 2*w - 8]', '[256, 64, 2*w^2 + 4*w - 6]', '[256, 128, -3*w^2 - 3*w + 26]', '[256, 256, -w^2 + 6*w - 5]', '[259, 259, -5*w^2 - 3*w + 49]', '[268, 134, 3*w^2 + 7*w - 16]', '[268, 134, -w^2 + 8*w - 12]', '[268, 268, -2*w^2 - w + 11]', '[269, 269, -4*w^2 - 4*w + 29]', '[271, 271, 6*w^2 - 47]', '[272, 68, 4*w^2 + 2*w - 40]', '[272, 68, 3*w^2 + 4*w - 22]', '[272, 68, 2*w^2 - 4*w - 2]', '[272, 136, 3*w^2 + 5*w - 12]', '[272, 272, -2*w^2 - 3*w + 17]', '[274, 274, -2*w^2 + w + 15]', '[274, 274, -2*w^2 + w + 2]', '[274, 274, 4*w^2 + 5*w - 16]', '[274, 274, -2*w^2 - w + 10]', '[274, 274, -15*w^2 - 26*w + 75]', '[274, 274, -w^2 - 4*w + 11]', '[277, 277, -2*w^2 + 2*w + 29]', '[277, 277, 4*w^2 + 8*w - 23]', '[277, 277, 7*w^2 + 5*w - 61]', '[278, 278, 6*w^2 + w - 50]', '[278, 278, -5*w^2 - 4*w + 43]', '[281, 281, -6*w^2 - 4*w + 51]', '[283, 283, 4*w^2 + 4*w - 43]', '[283, 283, 3*w^2 + 3*w - 29]', '[283, 283, -2*w^2 + 4*w + 1]', '[284, 142, 3*w^2 + 3*w - 20]', '[284, 142, -w^2 - 4*w + 20]', '[284, 284, -2*w^2 + 3*w - 1]', '[286, 286, -5*w + 6]', '[286, 286, 3*w - 1]', '[286, 286, 2*w^2 - w - 10]', '[286, 286, 2*w^2 - 3*w - 5]', '[286, 286, -4*w^2 - 5*w + 18]', '[286, 286, 3*w^2 + 6*w - 11]', '[289, 17, 3*w^2 + w - 23]', '[289, 289, 4*w^2 + 6*w - 17]', '[296, 74, 4*w^2 - 30]', '[296, 148, -w^2 + w + 16]', '[296, 148, w^2 - 2*w - 6]', '[296, 296, -2*w^2 + w + 5]', '[297, 33, 3*w^2 + 3*w - 33]', '[297, 33, -6*w^2 - 6*w + 45]', '[297, 33, -3*w^2 - 3*w + 27]', '[298, 298, -7*w^2 - 12*w + 33]', '[298, 298, -2*w^2 + 3*w + 2]', '[301, 301, -10*w^2 - 6*w + 91]', '[307, 307, 7*w^2 + 5*w - 69]', '[307, 307, -6*w^2 - 2*w + 51]', '[307, 307, -8*w + 13]', '[308, 154, -w^2 + 4*w]', '[308, 154, 5*w^2 + 9*w - 28]', '[308, 154, -3*w^2 - 3*w + 28]', '[308, 154, w^2 + 2*w]', '[308, 154, w^2 + w]', '[308, 154, -5*w^2 - 10*w + 28]', '[308, 308, -w - 7]', '[308, 308, -2*w^2 + 9*w - 7]', '[308, 308, -2*w^2 - 3*w + 21]', '[313, 313, 2*w^2 - 11]', '[313, 313, -5*w^2 - 5*w + 37]', '[313, 313, w^2 - 3*w + 5]', '[314, 314, 2*w^2 + 3*w - 18]', '[314, 314, 4*w^2 + 3*w - 41]', '[316, 158, -5*w^2 - 4*w + 40]', '[316, 158, w^2 - w + 2]', '[316, 316, 10*w^2 + 17*w - 51]', '[317, 317, -7*w^2 - 5*w + 59]', '[319, 319, 7*w^2 + 11*w - 39]', '[319, 319, -2*w + 9]', '[319, 319, 2*w^2 + 4*w - 15]', '[326, 326, 2*w^2 - 13*w + 16]', '[326, 326, -6*w^2 - 13*w + 33]', '[331, 331, -6*w + 11]', '[332, 166, 5*w^2 + 7*w - 30]', '[332, 166, -w^2 - 2*w + 16]', '[332, 332, -3*w^2 - 2*w + 9]', '[337, 337, -4*w + 13]', '[337, 337, 6*w^2 + 4*w - 59]', '[337, 337, w^2 - 3*w - 3]', '[338, 26, -2*w^2 - 3*w + 6]', '[338, 26, 2*w^2 + 3*w - 19]', '[338, 338, -5*w^2 - 4*w + 51]', '[338, 338, -2*w^2 - 3*w + 20]', '[343, 7, 7]', '[343, 343, -2*w^2 + 2*w + 7]', '[344, 86, 6*w^2 + 2*w - 54]', '[344, 172, -7*w^2 - 7*w + 54]', '[344, 172, 3*w^2 + 2*w - 22]', '[344, 344, w^2 + 4*w - 5]', '[346, 346, w^2 + 1]', '[346, 346, -4*w^2 - 7*w + 17]', '[346, 346, -6*w^2 - 5*w + 48]', '[346, 346, -2*w^2 + 3*w + 4]', '[347, 347, 8*w^2 + 14*w - 43]', '[351, 39, -6*w + 15]', '[352, 44, 2*w^2 - 2*w - 4]', '[352, 44, 2*w^2 - 24]', '[352, 44, 2*w^2 - 8]', '[352, 44, 2*w^2 - 2*w - 12]', '[352, 44, 2*w^2 + 6*w - 12]', '[352, 44, -6*w^2 - 8*w + 40]', '[352, 88, 3*w^2 - 34]', '[352, 88, -2*w^2 + 10]', '[352, 88, 2*w^2 - 4*w - 6]', '[352, 88, 5*w^2 + 8*w - 30]', '[352, 88, -4*w^2 - 6*w + 26]', '[352, 88, 3*w^2 - 26]', '[352, 176, -3*w^2 - w + 32]', '[352, 176, -3*w^2 + w + 22]', '[352, 176, -3*w^2 - 5*w + 20]', '[352, 352, -2*w^2 + 3*w + 3]', '[352, 352, -2*w^2 - w + 23]', '[352, 352, 4*w^2 + 5*w - 29]', '[353, 353, 5*w^2 + w - 43]', '[356, 178, -w^2 - 4*w + 12]', '[356, 178, -9*w^2 - 17*w + 44]', '[356, 178, -11*w^2 - 8*w + 108]', '[356, 178, 9*w^2 + 5*w - 80]', '[356, 178, 11*w^2 + 4*w - 96]', '[356, 178, -7*w^2 - 3*w + 68]', '[356, 356, 4*w^2 + 5*w - 25]', '[356, 356, 3*w - 11]', '[356, 356, -2*w^2 + w + 9]', '[358, 358, 10*w^2 + 19*w - 51]', '[358, 358, 7*w - 12]', '[364, 182, 5*w^2 + 3*w - 42]', '[364, 182, -w^2 - 4*w]', '[364, 364, -w^2 + 4*w - 7]', '[367, 367, 2*w^2 - 9]', '[367, 367, 3*w^2 + 3*w - 19]', '[367, 367, w^2 + w - 15]', '[374, 374, 2*w^2 - 7*w + 2]', '[374, 374, -2*w^2 + 3*w + 9]', '[374, 374, -4*w^2 - 7*w + 24]', '[374, 374, -3*w^2 - 6*w + 19]', '[374, 374, -2*w^2 + w + 6]', '[374, 374, -w^2 + 15]', '[377, 377, -w^2 + 9*w - 13]', '[378, 42, -3*w]', '[378, 42, 3*w^2 - 21]', '[379, 379, 7*w^2 + 5*w - 67]', '[382, 382, 8*w^2 + 13*w - 43]', '[382, 382, -w + 8]', '[383, 383, -3*w^2 - 7*w + 15]', '[383, 383, -6*w^2 - 2*w + 57]', '[383, 383, w^2 - 5*w + 9]', '[386, 386, 7*w^2 + 2*w - 59]', '[386, 386, 2*w^2 - w - 16]', '[388, 194, 7*w^2 + 11*w - 32]', '[388, 194, 3*w^2 - 8*w + 4]', '[388, 388, -2*w^2 - 5*w + 15]', '[389, 389, -2*w^2 - 4*w + 25]', '[392, 14, -2*w^2 + 2*w + 6]', '[392, 28, -5*w^2 - 2*w + 50]', '[392, 28, -5*w^2 - 9*w + 22]', '[392, 56, 3*w^2 + 4*w - 23]', '[392, 98, 4*w + 14]', '[392, 196, 5*w^2 + 2*w - 42]', '[392, 196, -3*w^2 - 3*w + 14]', '[392, 392, -w^2 + 2*w + 7]', '[394, 394, -3*w - 8]', '[394, 394, 7*w^2 + 4*w - 61]', '[397, 397, 2*w^2 - 2*w - 5]', '[398, 398, -2*w^2 + w + 8]', '[398, 398, -6*w^2 - 11*w + 27]', '[404, 202, 3*w^2 + 7*w - 12]', '[404, 202, w^2 + 4*w - 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