LMFDB - Hilbert modular form data

Formats: - HTML - YAML - JSON - 2024-05-01T07:01:48.877277

Column	Type
deg	smallint
dimension	integer
disc	bigint
field_bad_primes	integer[]
field_label	text
is_CM	text
is_base_change	text
label	text
label_nsuffix	smallint
label_suffix	text
level_bad_primes	integer[]
level_ideal	text
level_label	text
level_norm	integer
parallel_weight	smallint
short_label	text
weight	text

hmf_forms • Show schema

{'deg': 2, 'dimension': 2, 'disc': 220, 'field_bad_primes': [2, 5, 11], 'field_label': '2.2.220.1', 'is_CM': 'yes', 'is_base_change': 'no', 'label': '2.2.220.1-1.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-b', 'weight': '[2, 2]'}

Column	Type
AL_eigenvalues	jsonb
hecke_eigenvalues	jsonb
hecke_polynomial	text
label	text

hmf_hecke • Show schema

{'AL_eigenvalues': [], 'hecke_eigenvalues': [0, 'e', '-e', -3, 0, 0, 0, 0, 0, 0, 0, '-9*e', '9*e', '12*e', '-12*e', 14, '13*e', '-13*e', 0, 0, 0, 0, -9, -9, '4*e', '-4*e', 0, 0, 0, 0, 0, 0, '-16*e', '16*e', 0, 0, -25, -25, 0, 0, 0, 0, 0, 0, '-e', 'e', -5, -5, 0, 0, 0, 0, -30, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, '-37*e', '37*e', 0, 0, '39*e', '-39*e', -15, -15, -30, -30, 10, 10, 0, 0, 0, 0, '21*e', '-21*e', -39, -39, 0, 0, '31*e', '-31*e', '3*e', '-3*e', 0, 0, '43*e', '-43*e', 0, 0, -45, -45, 15, 15, 0, 0, 0, 0, '-48*e', '48*e', 0, 0, 0, 0, 45, 45, '-41*e', '41*e', '27*e', '-27*e', 0, 0, 13, 13, 0, 0, 0, 0, '-24*e', '24*e', 19, 19, '-53*e', '53*e', 0, 0, 0, 0, 0, 0, '49*e', '-49*e', 29, 29, 58, 0, 0, 0, 0, '36*e', '-36*e', 0, 0, 57, 57, '56*e', '-56*e', '8*e', '-8*e', 0, 0, 30, 30, 0, 0, '-57*e', '57*e', 0, 0, -37, '-51*e', '51*e', 0, 0], 'hecke_polynomial': 'x^2 + 1', 'label': '2.2.220.1-1.1-b'}

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

hmf_fields • Show schema

{'degree': 2, 'discriminant': 220, 'ideals': ['[1, 1, 1]', '[2, 2, w + 1]', '[3, 3, w + 1]', '[3, 3, w + 2]', '[4, 2, 2]', '[5, 5, -2*w + 15]', '[6, 6, -w - 7]', '[6, 6, -w + 7]', '[8, 4, 2*w + 2]', '[9, 3, 3]', '[9, 9, -w + 8]', '[9, 9, w + 8]', '[10, 10, w + 5]', '[11, 11, 3*w - 22]', '[12, 6, 2*w + 2]', '[12, 6, 2*w + 4]', '[13, 13, w + 4]', '[13, 13, w + 9]', '[15, 15, w + 5]', '[15, 15, w + 10]', '[16, 4, 4]', '[17, 17, w + 2]', '[17, 17, w + 15]', '[18, 6, 3*w + 3]', '[18, 18, w + 1]', '[18, 18, w + 17]', '[19, 19, -w - 6]', '[19, 19, w - 6]', '[20, 10, -4*w + 30]', '[22, 22, w + 11]', '[23, 23, w + 3]', '[23, 23, w + 20]', '[24, 12, -2*w - 14]', '[24, 12, -2*w + 14]', '[25, 5, 5]', '[26, 26, w + 9]', '[26, 26, w - 9]', '[27, 9, 3*w + 3]', '[27, 9, 3*w + 6]', '[27, 27, w + 1]', '[27, 27, w + 26]', '[30, 30, -w - 5]', '[30, 30, -w + 5]', '[32, 8, 4*w + 4]', '[33, 33, w + 11]', '[33, 33, w + 22]', '[34, 34, 3*w - 23]', '[34, 34, -3*w - 23]', '[36, 6, 6]', '[36, 18, -2*w + 16]', '[36, 18, 2*w + 16]', '[38, 38, w + 13]', '[38, 38, w + 25]', '[39, 39, w + 4]', '[39, 39, 4*w + 29]', '[39, 39, -4*w + 29]', '[39, 39, -w + 4]', '[40, 20, 2*w + 10]', '[44, 22, 6*w - 44]', '[45, 15, -6*w + 45]', '[45, 45, w + 10]', '[45, 45, -w + 10]', '[46, 46, -w - 3]', '[46, 46, w - 3]', '[47, 47, w + 14]', '[47, 47, w + 33]', '[48, 12, 4*w + 4]', '[48, 12, 4*w + 8]', '[49, 7, -7]', '[50, 10, 5*w + 5]', '[51, 51, w + 2]', '[51, 51, 2*w - 13]', '[51, 51, 2*w + 13]', '[51, 51, w - 2]', '[52, 26, 2*w + 8]', '[52, 26, 2*w + 18]', '[54, 18, -3*w - 21]', '[54, 18, -3*w + 21]', '[54, 54, -w - 1]', '[54, 54, -w + 1]', '[55, 55, w]', '[57, 57, w + 13]', '[57, 57, w + 25]', '[57, 57, w + 32]', '[57, 57, w + 44]', '[60, 30, 2*w + 10]', '[60, 30, 2*w + 20]', '[64, 8, 8]', '[65, 65, w + 30]', '[65, 65, w + 35]', '[66, 66, -w - 11]', '[66, 66, w - 11]', '[67, 67, w + 16]', '[67, 67, w + 51]', '[68, 34, 2*w + 4]', '[68, 34, 2*w + 30]', '[69, 69, 5*w - 38]', '[69, 69, -2*w + 17]', '[69, 69, -2*w - 17]', '[69, 69, 5*w + 38]', '[72, 12, 6*w + 6]', '[72, 36, 2*w + 2]', '[72, 36, 2*w + 34]', '[73, 73, w + 36]', '[73, 73, w + 37]', '[75, 15, 5*w + 5]', '[75, 15, 5*w + 10]', '[76, 38, -2*w - 12]', '[76, 38, 2*w - 12]', '[78, 78, w + 17]', '[78, 78, w + 35]', '[78, 78, w + 43]', '[78, 78, w + 61]', '[79, 79, 5*w + 36]', '[79, 79, 5*w - 36]', '[80, 20, -8*w + 60]', '[81, 9, 9]', '[81, 27, -3*w + 24]', '[81, 27, 3*w + 24]', '[81, 81, 4*w + 31]', '[81, 81, -4*w + 31]', '[85, 85, w + 15]', '[85, 85, w + 70]', '[88, 44, 2*w + 22]', '[89, 89, -w - 12]', '[89, 89, w - 12]', '[90, 30, 3*w + 15]', '[90, 90, w + 35]', '[90, 90, w + 55]', '[92, 46, 2*w + 6]', '[92, 46, 2*w + 40]', '[94, 94, 7*w - 51]', '[94, 94, 7*w + 51]', '[95, 95, -3*w + 20]', '[95, 95, 27*w - 200]', '[96, 24, -4*w - 28]', '[96, 24, -4*w + 28]', '[98, 14, 7*w + 7]', '[99, 33, 9*w - 66]', '[99, 99, 2*w - 11]', '[99, 99, 2*w + 11]', '[100, 10, 10]', '[102, 102, w + 19]', '[102, 102, w + 49]', '[102, 102, w + 53]', '[102, 102, w + 83]', '[103, 103, w + 40]', '[103, 103, w + 63]', '[104, 52, 2*w + 18]', '[104, 52, 2*w - 18]', '[108, 18, 6*w + 6]', '[108, 18, 6*w + 12]', '[108, 54, 2*w + 2]', '[108, 54, 2*w + 52]', '[110, 110, w + 55]', '[114, 114, -w - 13]', '[114, 114, 13*w + 97]', '[114, 114, 13*w - 97]', '[114, 114, -w + 13]', '[115, 115, w + 20]', '[115, 115, w + 95]', '[117, 39, 3*w + 12]', '[117, 39, 3*w + 27]', '[117, 117, w + 17]', '[117, 117, w + 35]', '[117, 117, w + 82]', '[117, 117, w + 100]', '[120, 60, -2*w - 10]', '[120, 60, -2*w + 10]', '[121, 11, 11]', '[125, 25, -10*w + 75]', '[128, 16, 8*w + 8]', '[130, 130, -3*w + 25]', '[130, 130, -3*w - 25]', '[131, 131, -6*w - 43]', '[131, 131, -6*w + 43]', '[132, 66, 2*w + 22]', '[132, 66, 2*w + 44]', '[134, 134, 3*w + 19]', '[134, 134, 3*w - 19]', '[135, 45, 3*w + 15]', '[135, 45, 3*w + 30]', '[135, 135, w + 55]', '[135, 135, w + 80]', '[136, 68, 6*w - 46]', '[136, 68, -6*w - 46]', '[138, 138, w + 43]', '[138, 138, w + 49]', '[138, 138, w + 89]', '[138, 138, w + 95]', '[139, 139, 2*w - 9]', '[139, 139, -2*w - 9]', '[141, 141, -w - 14]', '[141, 141, 2*w - 19]', '[141, 141, -2*w - 19]', '[141, 141, w - 14]', '[143, 143, w + 22]', '[143, 143, w + 121]', '[144, 12, 12]', '[144, 36, -4*w + 32]', '[144, 36, 4*w + 32]', '[146, 146, 5*w + 39]', '[146, 146, 5*w - 39]', '[147, 21, 7*w + 7]', '[147, 21, 7*w + 14]', '[150, 30, -5*w - 35]', '[150, 30, -5*w + 35]', '[151, 151, 4*w - 27]', '[151, 151, 4*w + 27]', '[152, 76, 2*w + 26]', '[152, 76, 2*w + 50]', '[153, 51, 3*w + 6]', '[153, 51, 3*w + 45]', '[153, 153, w + 19]', '[153, 153, w + 53]', '[153, 153, w + 100]', '[153, 153, w + 134]', '[156, 78, 2*w + 8]', '[156, 78, 8*w + 58]', '[156, 78, -8*w + 58]', '[156, 78, -2*w + 8]', '[158, 158, w + 23]', '[158, 158, w + 135]', '[160, 40, 4*w + 20]', '[162, 18, 9*w + 9]', '[162, 54, 3*w + 3]', '[162, 54, 3*w + 51]', '[162, 162, w + 53]', '[162, 162, w + 109]', '[163, 163, w + 50]', '[163, 163, w + 113]', '[165, 165, w + 55]', '[165, 165, w + 110]', '[169, 13, 13]', '[169, 169, -9*w + 68]', '[169, 169, 9*w + 68]', '[170, 170, -w - 15]', '[170, 170, w - 15]', '[171, 57, -3*w - 18]', '[171, 57, 3*w - 18]', '[171, 171, -14*w - 103]', '[171, 171, -2*w + 7]', '[171, 171, 2*w + 7]', '[171, 171, 14*w - 103]', '[173, 173, w + 48]', '[173, 173, w + 125]', '[176, 44, 12*w - 88]', '[178, 178, w + 77]', '[178, 178, w + 101]', '[180, 30, -12*w + 90]', '[180, 90, 2*w + 20]', '[180, 90, -2*w + 20]', '[181, 181, -3*w - 26]', '[181, 181, 3*w - 26]', '[184, 92, -2*w - 6]', '[184, 92, 2*w - 6]', '[187, 187, w + 66]', '[187, 187, w + 121]', '[188, 94, 2*w + 28]', '[188, 94, 2*w + 66]', '[190, 190, w + 25]', '[190, 190, w + 165]', '[192, 24, 8*w + 8]', '[192, 24, 8*w + 16]', '[193, 193, w + 21]', '[193, 193, w + 172]', '[195, 195, -7*w - 50]', '[195, 195, 2*w - 5]', '[195, 195, -2*w - 5]', '[195, 195, 7*w - 50]', '[196, 14, -14]', '[197, 197, w + 45]', '[197, 197, w + 152]', '[198, 66, 3*w + 33]', '[198, 198, w + 55]', '[198, 198, w + 143]', '[200, 20, 10*w + 10]', '[201, 201, -w - 16]', '[201, 201, -8*w - 61]', '[201, 201, 8*w - 61]', '[201, 201, w - 16]', '[204, 102, 2*w + 4]', '[204, 102, 4*w - 26]', '[204, 102, 4*w + 26]', '[204, 102, 2*w - 4]', '[206, 206, -3*w + 17]', '[206, 206, 3*w + 17]', '[207, 69, 3*w + 9]', '[207, 69, 3*w + 60]', '[207, 207, w + 26]', '[207, 207, w + 89]', '[207, 207, w + 118]', '[207, 207, w + 181]', '[208, 52, 4*w + 16]', '[208, 52, 4*w + 36]', '[209, 209, 4*w - 33]', '[209, 209, -40*w + 297]', '[211, 211, 2*w - 3]', '[211, 211, -2*w - 3]', '[216, 36, -6*w - 42]', '[216, 36, -6*w + 42]', '[216, 108, -2*w - 2]', '[216, 108, -2*w + 2]', '[219, 219, -5*w + 34]', '[219, 219, 2*w - 1]', '[219, 219, -2*w - 1]', '[219, 219, 5*w + 34]', '[220, 110, 2*w]', '[221, 221, 7*w - 54]', '[221, 221, 2*w - 21]', '[221, 221, 2*w + 21]', '[221, 221, 7*w + 54]', '[223, 223, w + 72]', '[223, 223, w + 151]', '[225, 15, 15]', '[225, 45, -5*w + 40]', '[225, 45, 5*w + 40]', '[228, 114, 2*w + 26]', '[228, 114, 2*w + 50]', '[228, 114, 2*w + 64]', '[228, 114, 2*w + 88]', '[229, 229, 6*w + 47]', '[229, 229, 6*w - 47]', '[230, 230, -9*w + 65]', '[230, 230, 21*w - 155]', '[233, 233, w + 88]', '[233, 233, w + 145]', '[234, 78, 3*w + 27]', '[234, 78, 3*w - 27]', '[234, 234, -w - 17]', '[234, 234, -11*w + 83]', '[234, 234, -11*w - 83]', '[234, 234, -w + 17]', '[235, 235, w + 80]', '[235, 235, w + 155]', '[237, 237, w + 23]', '[237, 237, w + 56]', '[237, 237, w + 181]', '[237, 237, w + 214]', '[239, 239, -3*w - 16]', '[239, 239, 3*w - 16]', '[240, 60, 4*w + 20]', '[240, 60, 4*w + 40]', '[242, 22, 11*w + 11]', '[243, 27, 9*w + 9]', '[243, 27, 9*w + 18]', '[243, 81, 3*w + 3]', '[243, 81, 3*w + 78]', '[243, 243, w + 28]', '[243, 243, w + 215]', '[245, 35, 14*w - 105]', '[247, 247, w + 82]', '[247, 247, w + 108]', '[247, 247, w + 139]', '[247, 247, w + 165]', '[250, 50, 5*w + 25]', '[253, 253, w + 66]', '[253, 253, w + 187]', '[255, 255, 4*w + 25]', '[255, 255, 11*w + 80]', '[255, 255, 11*w - 80]', '[255, 255, 4*w - 25]', '[256, 16, 16]', '[260, 130, 2*w + 60]', '[260, 130, 2*w + 70]', '[262, 262, w + 29]', '[262, 262, w + 233]', '[264, 132, -2*w - 22]', '[264, 132, 2*w - 22]', '[267, 267, w + 77]', '[267, 267, w + 101]', '[267, 267, w + 166]', '[267, 267, w + 190]', '[268, 134, 2*w + 32]', '[268, 134, 2*w + 102]', '[269, 269, -w - 18]', '[269, 269, w - 18]', '[270, 90, -3*w - 15]', '[270, 90, -3*w + 15]', '[270, 270, -13*w + 95]', '[270, 270, -13*w - 95]', '[271, 271, -8*w - 57]', '[271, 271, -8*w + 57]', '[272, 68, 4*w + 8]', '[272, 68, 4*w + 60]', '[275, 55, 15*w - 110]', '[276, 138, 10*w - 76]', '[276, 138, -4*w + 34]', '[276, 138, -4*w - 34]', '[276, 138, 10*w + 76]', '[277, 277, w + 71]', '[277, 277, w + 206]', '[278, 278, w + 65]', '[278, 278, w + 213]', '[282, 282, w + 61]', '[282, 282, w + 127]', '[282, 282, w + 155]', '[282, 282, w + 221]', '[285, 285, w + 25]', '[285, 285, w + 70]', '[285, 285, w + 215]', '[285, 285, w + 260]', '[286, 286, -5*w - 33]', '[286, 286, 5*w - 33]', '[288, 24, 12*w + 12]', '[288, 72, 4*w + 4]', '[288, 72, 4*w + 68]', '[289, 17, 17]', '[289, 289, -3*w + 28]', '[289, 289, 3*w + 28]', '[292, 146, 2*w + 72]', '[292, 146, 2*w + 74]', '[293, 293, w + 73]', '[293, 293, w + 220]', '[294, 42, 7*w + 49]', '[294, 42, 7*w - 49]', '[297, 99, 3*w + 33]', '[297, 99, 3*w + 66]', '[297, 297, w + 55]', '[297, 297, w + 242]', '[299, 299, -6*w + 41]', '[299, 299, 3*w - 14]', '[299, 299, 3*w + 14]', '[299, 299, -6*w - 41]', '[300, 30, 10*w + 10]', '[300, 30, 10*w + 20]', '[302, 302, w + 31]', '[302, 302, w + 271]', '[304, 76, -4*w - 24]', '[304, 76, 4*w - 24]', '[306, 102, 9*w - 69]', '[306, 102, -9*w - 69]', '[306, 306, -w - 19]', '[306, 306, 5*w - 41]', '[306, 306, -5*w - 41]', '[306, 306, w - 19]', '[309, 309, -19*w - 142]', '[309, 309, 2*w - 23]', '[309, 309, 2*w + 23]', '[309, 309, -19*w + 142]', '[312, 156, 2*w + 34]', '[312, 156, 2*w + 70]', '[312, 156, 2*w + 86]', '[312, 156, 2*w + 122]', '[316, 158, 10*w + 72]', '[316, 158, 10*w - 72]', '[320, 40, -16*w + 120]', '[323, 323, w + 32]', '[323, 323, w + 70]', '[323, 323, w + 253]', '[323, 323, w + 291]', '[324, 18, 18]', '[324, 54, -6*w + 48]', '[324, 54, 6*w + 48]', '[324, 162, 8*w + 62]', '[324, 162, -8*w + 62]', '[325, 65, 5*w + 20]', '[325, 65, 5*w + 45]', '[326, 326, -3*w - 13]', '[326, 326, 3*w - 13]', '[330, 330, -7*w - 55]', '[330, 330, 7*w - 55]', '[335, 335, w + 150]', '[335, 335, w + 185]', '[337, 337, w + 27]', '[337, 337, w + 310]', '[338, 26, 13*w + 13]', '[338, 338, w + 139]', '[338, 338, w + 199]', '[340, 170, 2*w + 30]', '[340, 170, 2*w + 140]', '[342, 114, 3*w + 39]', '[342, 114, 3*w + 75]', '[342, 342, w + 89]', '[342, 342, w + 127]', '[342, 342, w + 215]', '[342, 342, w + 253]', '[345, 345, -w - 20]', '[345, 345, 4*w + 35]', '[345, 345, 4*w - 35]', '[345, 345, -w + 20]', '[346, 346, -3*w - 29]', '[346, 346, 3*w - 29]', '[351, 117, 3*w + 12]', '[351, 117, 12*w + 87]', '[351, 117, -12*w + 87]', '[351, 117, -3*w + 12]', '[351, 351, 4*w - 23]', '[351, 351, 5*w - 32]', '[351, 351, -5*w - 32]', '[351, 351, -4*w - 23]', '[352, 88, 4*w + 44]', '[356, 178, -2*w - 24]', '[356, 178, 2*w - 24]', '[359, 359, 9*w + 64]', '[359, 359, 9*w - 64]', '[360, 60, 6*w + 30]', '[360, 180, 2*w + 70]', '[360, 180, 2*w + 110]', '[361, 19, 19]', '[361, 361, -24*w + 179]', '[361, 361, -12*w + 91]', '[362, 362, w + 69]', '[362, 362, w + 293]', '[363, 33, 11*w + 11]', '[363, 33, 11*w + 22]', '[365, 365, w + 110]', '[365, 365, w + 255]', '[367, 367, w + 34]', '[367, 367, w + 333]', '[368, 92, 4*w + 12]', '[368, 92, 4*w + 80]', '[373, 373, w + 146]', '[373, 373, w + 227]', '[374, 374, -3*w + 11]', '[374, 374, -3*w - 11]', '[375, 75, 5*w + 25]', '[375, 75, 5*w + 50]', '[376, 188, 14*w - 102]', '[376, 188, 14*w + 102]', '[380, 190, -6*w + 40]', '[380, 190, 54*w - 400]', '[383, 383, w + 173]', '[383, 383, w + 210]', '[384, 48, -8*w - 56]', '[384, 48, -8*w + 56]', '[386, 386, -w - 21]', '[386, 386, w - 21]', '[389, 389, -5*w - 42]', '[389, 389, 5*w - 42]', '[390, 390, w + 35]', '[390, 390, w + 95]', '[390, 390, w + 295]', '[390, 390, w + 355]', '[391, 391, 7*w - 48]', '[391, 391, -16*w + 117]', '[391, 391, 16*w + 117]', '[391, 391, -7*w - 48]', '[392, 28, 14*w + 14]', '[393, 393, w + 29]', '[393, 393, w + 160]', '[393, 393, w + 233]', '[393, 393, w + 364]', '[394, 394, 15*w - 113]', '[394, 394, 15*w + 113]', '[395, 395, 3*w + 10]', '[395, 395, 3*w - 10]', '[396, 66, 18*w - 132]', '[396, 198, 4*w - 22]', '[396, 198, 4*w + 22]', '[400, 20, 20]', '[401, 401, 29*w - 216]', '[401, 401, 11*w - 84]', '[402, 402, w + 83]', '[402, 402, w + 185]', '[402, 402, w + 217]', '[402, 402, w + 319]', '[405, 45, -18*w + 135]', '[405, 135, 3*w + 30]', '[405, 135, -3*w + 30]', '[405, 405, -2*w + 25]', '[405, 405, 2*w + 25]', '[408, 204, 2*w + 38]', '[408, 204, 2*w + 98]', '[408, 204, 2*w + 106]', '[408, 204, 2*w + 166]', '[412, 206, 2*w + 80]', '[412, 206, 2*w + 126]', '[414, 138, -3*w - 9]', '[414, 138, 3*w - 9]', '[414, 414, 5*w + 31]', '[414, 414, 11*w - 79]', '[414, 414, -11*w - 79]', '[414, 414, -5*w + 31]', '[416, 104, 4*w + 36]', '[416, 104, 4*w - 36]', '[417, 417, w + 65]', '[417, 417, w + 74]', '[417, 417, w + 343]', '[417, 417, w + 352]', '[418, 418, w + 165]', '[418, 418, w + 253]', '[421, 421, -6*w + 49]', '[421, 421, -6*w - 49]', '[422, 422, w + 107]', '[422, 422, w + 315]', '[423, 141, 3*w + 42]', '[423, 141, 3*w + 99]', '[423, 423, w + 80]', '[423, 423, w + 127]', '[423, 423, w + 296]', '[423, 423, w + 343]', '[425, 85, 5*w + 10]', '[425, 85, 5*w + 75]', '[429, 429, -w - 22]', '[429, 429, -10*w + 77]', '[429, 429, -10*w - 77]', '[429, 429, -w + 22]', '[431, 431, 3*w - 8]', '[431, 431, -3*w - 8]', '[432, 36, 12*w + 12]', '[432, 36, 12*w + 24]', '[432, 108, 4*w + 4]', '[432, 108, 4*w + 104]', '[437, 437, w + 89]', '[437, 437, w + 158]', '[437, 437, w + 279]', '[437, 437, w + 348]', '[438, 438, w + 37]', '[438, 438, w + 109]', '[438, 438, w + 329]', '[438, 438, w + 401]', '[439, 439, -4*w - 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49]', '[9977, 9977, w + 3278]', '[9977, 9977, w + 6699]', '[9979, 9979, -59*w + 426]', '[9979, 9979, -22*w - 129]', '[9979, 9979, -22*w + 129]', '[9979, 9979, -59*w - 426]', '[9981, 3327, 39*w - 306]', '[9981, 3327, 39*w + 306]', '[9981, 9981, -38*w + 299]', '[9981, 9981, 2*w - 101]', '[9981, 9981, 2*w + 101]', '[9981, 9981, -38*w - 299]', '[9984, 624, 16*w + 64]', '[9984, 624, 64*w + 464]', '[9984, 624, -64*w + 464]', '[9984, 624, -16*w + 64]', '[9985, 9985, w + 2685]', '[9985, 9985, w + 7300]', '[9986, 9986, -11*w - 129]', '[9986, 9986, 11*w - 129]', '[9995, 9995, 198*w - 1465]', '[9995, 9995, -42*w + 295]', '[9996, 714, -14*w - 28]', '[9996, 714, -28*w + 182]', '[9996, 714, -28*w - 182]', '[9996, 714, -14*w + 28]', '[10000, 100, 100]'], 'label': '2.2.220.1', 'narrow_class_no': 4, 'primes': ['[2, 2, w + 1]', '[3, 3, w + 1]', '[3, 3, w + 2]', '[5, 5, -2*w + 15]', '[11, 11, 3*w - 22]', '[13, 13, w + 4]', '[13, 13, w + 9]', '[17, 17, w + 2]', '[17, 17, w + 15]', '[19, 19, -w - 6]', '[19, 19, w - 6]', '[23, 23, w + 3]', '[23, 23, w + 20]', '[47, 47, w + 14]', '[47, 47, w + 33]', '[49, 7, -7]', '[67, 67, w + 16]', '[67, 67, w + 51]', '[73, 73, w + 36]', '[73, 73, w + 37]', '[79, 79, 5*w + 36]', '[79, 79, 5*w - 36]', '[89, 89, -w - 12]', '[89, 89, w - 12]', '[103, 103, w + 40]', '[103, 103, w + 63]', '[131, 131, -6*w - 43]', '[131, 131, -6*w + 43]', '[139, 139, 2*w - 9]', '[139, 139, -2*w - 9]', '[151, 151, 4*w - 27]', '[151, 151, 4*w + 27]', '[163, 163, w + 50]', '[163, 163, w + 113]', '[173, 173, w + 48]', '[173, 173, w + 125]', '[181, 181, -3*w - 26]', '[181, 181, 3*w - 26]', '[193, 193, w + 21]', '[193, 193, w + 172]', '[197, 197, w + 45]', '[197, 197, w + 152]', '[211, 211, 2*w - 3]', '[211, 211, -2*w - 3]', '[223, 223, w + 72]', '[223, 223, w + 151]', '[229, 229, 6*w + 47]', '[229, 229, 6*w - 47]', '[233, 233, w + 88]', '[233, 233, w + 145]', '[239, 239, -3*w - 16]', '[239, 239, 3*w - 16]', '[269, 269, -w - 18]', '[269, 269, w - 18]', '[271, 271, -8*w - 57]', '[271, 271, -8*w + 57]', '[277, 277, w + 71]', '[277, 277, w + 206]', '[293, 293, w + 73]', '[293, 293, w + 220]', '[337, 337, w + 27]', '[337, 337, w + 310]', '[359, 359, 9*w + 64]', '[359, 359, 9*w - 64]', '[367, 367, w + 34]', '[367, 367, w + 333]', '[373, 373, w + 146]', '[373, 373, w + 227]', '[383, 383, w + 173]', '[383, 383, w + 210]', '[389, 389, -5*w - 42]', '[389, 389, 5*w - 42]', '[401, 401, 29*w - 216]', '[401, 401, 11*w - 84]', '[421, 421, -6*w + 49]', '[421, 421, -6*w - 49]', '[431, 431, 3*w - 8]', '[431, 431, -3*w - 8]', '[439, 439, -4*w - 21]', '[439, 439, 4*w - 21]', '[443, 443, w + 99]', '[443, 443, w + 344]', '[449, 449, -8*w - 63]', '[449, 449, -8*w + 63]', '[457, 457, w + 91]', '[457, 457, w + 366]', '[463, 463, w + 38]', '[463, 463, w + 425]', '[467, 467, w + 191]', '[467, 467, w + 276]', '[479, 479, -3*w - 4]', '[479, 479, 3*w - 4]', '[487, 487, w + 223]', '[487, 487, w + 264]', '[491, 491, 3*w - 2]', '[491, 491, -3*w - 2]', '[509, 509, 2*w - 27]', '[509, 509, -2*w - 27]', '[521, 521, -w - 24]', '[521, 521, w - 24]', '[557, 557, w + 75]', '[557, 557, w + 482]', '[571, 571, 11*w + 78]', '[571, 571, 11*w - 78]', '[587, 587, w + 246]', '[587, 587, w + 341]', '[593, 593, w + 184]', '[593, 593, w + 409]', '[613, 613, w + 235]', '[613, 613, w + 378]', '[641, 641, -4*w - 39]', '[641, 641, 4*w - 39]', '[643, 643, w + 174]', '[643, 643, w + 469]', '[647, 647, w + 257]', '[647, 647, w + 390]', '[659, 659, -18*w + 131]', '[659, 659, 30*w - 221]', '[661, 661, 3*w - 34]', '[661, 661, -3*w - 34]', '[673, 673, w + 196]', '[673, 673, w + 477]', '[677, 677, w + 240]', '[677, 677, w + 437]', '[683, 683, w + 136]', '[683, 683, w + 547]', '[709, 709, 21*w - 158]', '[709, 709, 27*w - 202]', '[727, 727, w + 339]', '[727, 727, w + 388]', '[733, 733, w + 39]', '[733, 733, w + 694]', '[739, 739, 10*w - 69]', '[739, 739, 10*w + 69]', '[811, 811, 35*w - 258]', '[811, 811, -19*w + 138]', '[823, 823, w + 177]', '[823, 823, w + 646]', '[829, 829, -6*w - 53]', '[829, 829, 6*w - 53]', '[841, 29, -29]', '[853, 853, w + 316]', '[853, 853, w + 537]', '[857, 857, w + 270]', '[857, 857, w + 587]', '[863, 863, w + 405]', '[863, 863, w + 458]', '[877, 877, w + 377]', '[877, 877, w + 500]', '[881, 881, -19*w + 144]', '[881, 881, -37*w + 276]', '[883, 883, w + 52]', '[883, 883, w + 831]', '[907, 907, w + 350]', '[907, 907, w + 557]', '[919, 919, -8*w - 51]', '[919, 919, 8*w - 51]', '[929, 929, 5*w - 48]', '[929, 929, -5*w - 48]', '[937, 937, w + 176]', '[937, 937, w + 761]', '[947, 947, w + 252]', '[947, 947, w + 695]', '[953, 953, w + 334]', '[953, 953, w + 619]', '[961, 31, -31]', '[983, 983, w + 277]', '[983, 983, w + 706]', '[997, 997, w + 371]', '[997, 997, w + 626]']}

Column	Type
class_group	jsonb
class_number	numeric
cm	boolean
coeffs	numeric[]
conductor	numeric
degree	smallint
disc_abs	numeric
disc_rad	numeric
disc_sign	smallint
embeddings_gen_imag	double precision[]
embeddings_gen_real	double precision[]
gal_is_abelian	boolean
gal_is_cyclic	boolean
gal_is_solvable	boolean
galois_disc_exponents	numeric[]
galois_label	text
galt	integer
grd	double precision
index	integer
inessentialp	integer[]
is_galois	boolean
is_minimal_sibling	boolean
iso_number	smallint
label	text
local_algs	text[]
minimal_sibling	numeric[]
monogenic	smallint
num_ram	smallint
r2	smallint
ramps	numeric[]
rd	double precision
regulator	numeric
subfield_mults	integer[]
subfields	text[]
torsion_order	smallint
used_grh	boolean
dirichlet_group	bigint[]
frobs	jsonb
res	jsonb
source	text
subfield_inclusions	smallint[]
torsion_gen	text
units	jsonb
unitsGmodule	jsonb
unitsType	text
zk	jsonb

nf_fields • Show schema

{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-55, 0, 1], 'conductor': 220, 'degree': 2, 'dirichlet_group': [1, 219], 'disc_abs': 220, 'disc_rad': 110, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[1, 2]]], [5, [0]], [7, [[2, 1]]], [11, [0]], [13, [[1, 2]]], [17, [[1, 2]]], [19, [[1, 2]]], [23, [[1, 2]]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[2, 1]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 14.832396974191326, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.220.1', 'local_algs': ['2.2.2.1', '5.2.1.1', '11.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 5, 11], 'rd': 14.8323969742, 'regulator': {'__RealLiteral__': 0, 'data': '5.18175198713', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 12 a - 89 \\)'], 'used_grh': False, 'zk': ['1', 'a']}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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