LMFDB - Hilbert modular form data

Formats: - HTML - YAML - JSON - 2025-09-15T16:05:07.745890

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': 1, 'disc': 88, 'field_bad_primes': [2, 11], 'field_label': '2.2.88.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '2.2.88.1-81.5-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [3], 'level_ideal': '[81,81,2*w + 13]', 'level_label': '81.5', 'level_norm': 81, 'parallel_weight': 2, 'short_label': '81.5-a', 'weight': '[2, 2]'}

Column	Type
AL_eigenvalues	jsonb
hecke_eigenvalues	jsonb
hecke_polynomial	text
label	text

hmf_hecke • Show schema

{'AL_eigenvalues': [['[3,3,w + 5]', -1]], 'hecke_eigenvalues': [2, 0, 0, 4, 0, -3, 4, -4, -7, 0, -4, 5, -11, 0, -8, 7, 8, -4, -12, 15, 17, 7, -9, 16, 12, -16, -16, -18, 2, 4, -4, -19, 3, -12, 4, -20, 8, 1, -7, -16, -8, 4, 0, -7, -1, -16, -12, -28, -12, -17, 0, -3, -5, 0, -4, -16, 20, -28, 24, -15, 12, 24, 6, 13, -25, -1, 8, 20, 14, -9, 20, -4, -11, 32, 32, -21, -8, -19, -14, 5, 35, 20, -16, 13, 14, 28, 36, 9, 1, -15, 15, 32, 0, 40, 7, -16, 24, 16, 11, -36, 12, -9, -15, 29, 24, 16, -4, -12, -2, -31, 27, 8, -24, 16, 28, -8, 26, 33, -11, -5, 19, -2, -16, -37, 12, -12, 16, 41, 35, -5, -16, -12, -24, -20, -8, 16, 24, -24, 44, -16, -40, -45, 48, -16, 39, 9, -35, -48, -20, -48, 7, 49, 16, -52, -33, 17, -60, 12, 48, -29, 34, -36, 12, -57, 33, 18, -43, -4, 28, 20, 24, 49, -33, 60, -28, -48, 28, -44, -20, -1, -57, 8, -48, -34, 5, -5, 45, 22, -61, 40, -4, 24, 4, 20, -56, 9, -31, 9, -65, -48, 0, 0, -36, -54, -37, 68, -8, 10, 40, -12, -68, -44, 3, -34, -20, 32, -54, 38, -12, -44, 44, 16, 45, -59, 72, 76, -30, -14, 64, -8, 48, 49, 9, -8, 0, 64, 27, 35, 72, 48, -32, 48, 7, 23, 52, -48, -40, -44, -8, -52, -55, -16, 64, 11, -11, 17, -8, -27, -38, -48, -8, 65, -39, 38, -15, 12, -48, -29, 5, 40, -24, -60, 36, 12, 12, -19, 0, -24, -21, 11, 8, 40, -56, -33, -16, 8, 8, 16, 20, 52, 20, 72, -11, 19, -31, 41, -63, 1, -51, 27, 52, -56, 60, 24, 40, 24, -12, -48, -69, 64, -24, 76, -30, 59, 1, -90, -12, 44, 30, 1, 5, -16, -8, -11, -16, -44, -51, -36, 72, -16, 4, -76, 8, 72, 72, 55, -38, -76, -4, 13, -29, 36, 4, -17, -64, -52, -40, -70, -65, -44, 8, 56, -80, -68, -48, 56, -33, 79, 39, 12, 12, 0, 4, 16, 16, 56, -43, -88, -72, -52, 36, 60, -4, -25, 24, -12, 64, 9, 58, -8, -4, 34, -37, -56, -37, 40, -39, -48, 76, 69, 43, 69, 8, -40, -8, 36, -80, 18, 45, 8, -4, 9, 23, 80, -24, 40, -32, -16, -35, -95, 89, 31, 44, -52, 24, 75, 104, 40, 47, -79, -20, -64, 16, 12, -7, -7, -72, -39, -88, 24, -24, -4, -91, 5, 39, -15, -57, -87, -43, -37, 56, -88, -101, -3, 30, 39, -28, 8, -16, 60, -104, -40, -62, 67, -16, 40, -82, -2, 60, -68, -76, -4, 19, 38, -16, 79, -88, -52, 41, 0, -33, -79, -4, 56, -21, -13, -103, -48, 100, -76, 92, 0, -81, -65, 30, -2, -56, -96, -95, 56, 91, -40, 96, 28, 108, 60, 16, -24, -101, 106, 92, -40, 56, -8, 43, -24, -88, -4, 56, -96, 68, -36, -4, -52, 30, -30, 28, -112, -32, -24, -61, 27, 76, 60, 53, 14, -8, -68, 16, -64, 13, -45, -116, 92, 96, 81, 12, 4, 45, -61, 60, -40, 25, -65, 39, 33, 96, -8, -36, -48, -104, -72, -28, 28, -11, -37, 125, 75, -48, -112, -79, -7, 122, -90, -32, 68, 112, -88, -5, -21, 60, -20, -87, -16, 32, 16, -83, 75, -106, -45, 80, 80, -44, -120, 14, 14, -21, 56, -111, -81, -109, 43, -12, 120, -112, 36, -12, 80, -86, -39, -56, 64, 120, -60, 30, -30, -62, 91, -36, -60, -39, 111, 60, 8, 24, -8, 96, 0, 60, -92, 45, 67, 44, -96, -28, -64, 112, 19, 53, 77, -94, -25, -60, 28, 15, 113, 51, 69, 96, -28, -112, 67, -120, 12, -60, 28, -131, -67, -72, 16, 120, -124, -16, 32, -15, 26, -32, -28, 76, -20, 109, -32, -97, 129, -4, 32, 124, 96, -77, -99, -117, -85, 57, -94, -16, 16, 110, 92, -32, 104, 20, -24, -73, 85, 86, -55, -94, -72, -88, -24, 87, -9, 15, -60, 44, 52, -44, 51, -58, 84, -28, 50, -105, 36, -64, -9, 80, -5, 4, 100, -81, 129, -8, -76, 93, 42, 4, -56, 128, 51, -58, -91, 24, -48, 8, -51, 8, 28, 64, -16, 68, -132, -18, -143, -120, -36, 52, 136, -100, 4, -6, -137, -44, -24, -33, 57, 64, 73, 96, -4, -80, 84, 36, 32, 76, -88, -52, 100, 73, 88, -56, 84, 31, -106, -128, 144, -52, -116, -53, 43, 112, 97, -84, 20, 63, 81, 52, 84, -128, 19, 32, 16, -64, -29, 19, 72, 64, 137, 152, 68, -7, -119, -24, 36, 24, -136, 25, -151, -128, 16, -36, -20, 0, 100, 77, -101, -84, 48, -44, -68, 12, -120, -56, 20, -19, 3, -40, 4, 48, -40, -84, -104, -12, 112, -59, -131, -109, -42, -130, -63, 56, -104, -21, 43, 60, 100, 32, 60, 7, 32, 81, -126, -105, -65, -10, -81, 15, 87, 47, -10, -72, 36, -125, 104, 156, 12, -32, 48, 64, -32, -84, 8, -16, -4, -117, 149, -97, -40, 144, -120, -48, 144, 21, 51, 64, 87, -129, -87, 59, -147, 27, 117, 104, -88, 80, -76, -118, -60, 116, -92, 96, -73, 50, -14, 17, -92, 148, -17, -47, 44, -88, 143, 0, -27, 163, -12, 80, 8, -120, -124, -140, -108, -116, 144, -152, 51, 46, -140, 92, -90, 1, -37, 74, -8, -33, -52, 104, -132, -156, 15, 65, -156, -120, -8, 44, 111, -80, -24, 8, -50, 33, -37, 56, -29, 53, -40, 116, 50, 111, -102, 139, 123, -24, 55, -87, -68, 80, -45, -90, 112, -96, -131, 53, -7, -89, -150, -90, -16, -168, -17, -57, -52, -36, 74, -53, -166, -67, 156, 120, -28, -152, 81, -9, -131, 66, 48, -88, -142, 50, 32, 52, 11, 88, 20, 68, -63, -103, 12, -12, -27, -14, 60, -84, -28, -16, 18, -82, -84, 36, 33, -8, 132, -36, 4, 96, 92, -32, -16, -116, -5, 54, -128, -159, 7, 66, 20, -24, -48, -168, -93, -45, -52, 16, 4, 48, -69, 120, 96, 48, -32, 32, 130, 159, -27, 21, -61, -27, 172, 96, 140, 4, -97, 65, 60, 152, 57, 71, -104, 88, 81, 1, -85, 11, -99, 27, 93, 43, -28, 60, 35, -139, -20, -96, -32, 12, -8, 112, 24, 132, -10, 111, -33, 55, -32, -60, 19, -5, 132, 52, -140, -40, 92, 40, 13, -123, -76, 124, 85, -75, 153, -122, 36, 172, -159, 30, -4, -60, -182, -49, -45, -5, 91, -179, 160, -12, 100, 44, 172, 100, 123, -114, -108, -4, 28, 24, 8, 73, -128, 112, 80, 0, -59, 144, -69, -11, -86, -77, -113, 49, 139, -43, 48, 64, 144, -24, -92, -68, 88, -172, -25, 38, 104, 124, 128, 108, 104, 117, 108, -68, 85, 69, -88, -76, -118, 103, -56, -4, 20, -84, 30, 50, 76, 60, -31, -9, -144, -36, -96, 79, -108, -28, -72, 132, 24, -135, 54, -21, 32, 88, 96, -56, 142, 33, 164, 36, -8, -8, 160, -40, -80, -100, 60, -104, -65, 57, 124, 60, 120, 40, -72, 168, -132, -4, 154, 111, -132, -32, -3, 93, 132, -40, -59, 3, 56, 55, -51, 131, -111, -9, -45, 45, -144, 8, 56, -124], 'hecke_polynomial': 'x', 'label': '2.2.88.1-81.5-a'}

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

hmf_fields • Show schema

{'degree': 2, 'discriminant': 88, 'ideals': ['[1, 1, 1]', '[2, 2, -3*w + 14]', '[3, 3, -w + 5]', '[3, 3, w + 5]', '[4, 2, 2]', '[6, 6, -w + 4]', '[6, 6, -w - 4]', '[7, 7, 2*w + 9]', '[7, 7, 2*w - 9]', '[8, 4, -6*w + 28]', '[9, 3, 3]', '[9, 9, -4*w + 19]', '[9, 9, 4*w + 19]', '[11, 11, -7*w + 33]', '[12, 6, -2*w + 10]', '[12, 6, 2*w + 10]', '[13, 13, -w - 3]', '[13, 13, -w + 3]', '[14, 14, -w - 6]', '[14, 14, w - 6]', '[16, 4, 4]', '[18, 6, -9*w + 42]', '[18, 18, -w - 2]', '[18, 18, -w + 2]', '[21, 21, w + 1]', '[21, 21, 5*w - 23]', '[21, 21, 5*w + 23]', '[21, 21, w - 1]', '[22, 22, -w]', '[24, 12, -2*w + 8]', '[24, 12, -2*w - 8]', '[25, 5, -5]', '[26, 26, 5*w + 24]', '[26, 26, -5*w + 24]', '[27, 9, -3*w + 15]', '[27, 9, 3*w + 15]', '[27, 27, w + 7]', '[27, 27, -w + 7]', '[28, 14, 4*w + 18]', '[28, 14, 4*w - 18]', '[29, 29, 3*w + 13]', '[29, 29, -3*w + 13]', '[32, 8, -12*w + 56]', '[33, 33, -2*w + 11]', '[33, 33, 2*w + 11]', '[36, 6, 6]', '[36, 18, -8*w + 38]', '[36, 18, 8*w + 38]', '[39, 39, -8*w + 37]', '[39, 39, -2*w + 7]', '[39, 39, -2*w - 7]', '[39, 39, -8*w - 37]', '[42, 42, -w - 8]', '[42, 42, -11*w - 52]', '[42, 42, 11*w - 52]', '[42, 42, w - 8]', '[44, 22, -14*w + 66]', '[48, 12, -4*w + 20]', '[48, 12, 4*w + 20]', '[49, 7, 7]', '[49, 49, 6*w + 29]', '[49, 49, -6*w + 29]', '[50, 10, 15*w - 70]', '[52, 26, -2*w - 6]', '[52, 26, -2*w + 6]', '[54, 18, -3*w + 12]', '[54, 18, -3*w - 12]', '[54, 54, -7*w - 32]', '[54, 54, -7*w + 32]', '[56, 28, -2*w - 12]', '[56, 28, 2*w - 12]', '[58, 58, 3*w - 16]', '[58, 58, 3*w + 16]', '[59, 59, -w - 9]', '[59, 59, w - 9]', '[61, 61, 11*w - 51]', '[61, 61, 25*w - 117]', '[63, 21, 6*w + 27]', '[63, 21, 6*w - 27]', '[63, 63, 4*w + 17]', '[63, 63, 2*w - 5]', '[63, 63, 2*w + 5]', '[63, 63, 4*w - 17]', '[64, 8, 8]', '[66, 66, -5*w + 22]', '[66, 66, -5*w - 22]', '[67, 67, 9*w - 43]', '[67, 67, -9*w - 43]', '[72, 12, -18*w + 84]', '[72, 36, -2*w - 4]', '[72, 36, -2*w + 4]', '[75, 15, 5*w - 25]', '[75, 15, -5*w - 25]', '[77, 77, 3*w - 11]', '[77, 77, 3*w + 11]', '[78, 78, w + 10]', '[78, 78, 7*w + 34]', '[78, 78, -7*w + 34]', '[78, 78, -w + 10]', '[79, 79, 2*w - 3]', '[79, 79, -2*w - 3]', '[81, 9, 9]', '[81, 27, -12*w + 57]', '[81, 27, 12*w + 57]', '[81, 81, -2*w + 13]', '[81, 81, 2*w + 13]', '[84, 42, 2*w + 2]', '[84, 42, 10*w - 46]', '[84, 42, 10*w + 46]', '[84, 42, 2*w - 2]', '[87, 87, 14*w - 65]', '[87, 87, 2*w - 1]', '[87, 87, -2*w - 1]', '[87, 87, -14*w - 65]', '[88, 44, -2*w]', '[89, 89, 4*w - 21]', '[89, 89, -4*w - 21]', '[91, 91, -15*w - 71]', '[91, 91, -3*w - 17]', '[91, 91, 3*w - 17]', '[91, 91, 15*w - 71]', '[96, 24, -4*w + 16]', '[96, 24, -4*w - 16]', '[97, 97, -18*w + 85]', '[97, 97, 24*w - 113]', '[98, 14, -21*w + 98]', '[98, 98, -3*w - 10]', '[98, 98, -3*w + 10]', '[99, 33, -21*w + 99]', '[99, 99, w + 11]', '[99, 99, -w + 11]', '[100, 10, -10]', '[101, 101, -9*w - 41]', '[101, 101, -9*w + 41]', '[104, 52, 10*w + 48]', '[104, 52, -10*w + 48]', '[108, 18, -6*w + 30]', '[108, 18, 6*w + 30]', '[108, 54, 2*w + 14]', '[108, 54, -2*w + 14]', '[109, 109, 5*w + 21]', '[109, 109, -5*w + 21]', '[112, 28, 8*w + 36]', '[112, 28, 8*w - 36]', '[113, 113, -8*w - 39]', '[113, 113, 8*w - 39]', '[116, 58, 6*w + 26]', '[116, 58, -6*w + 26]', '[117, 39, -3*w - 9]', '[117, 39, -3*w + 9]', '[117, 117, -17*w + 79]', '[117, 117, -7*w + 31]', '[117, 117, -7*w - 31]', '[117, 117, -17*w - 79]', '[118, 118, 41*w - 192]', '[118, 118, 13*w - 60]', '[121, 11, 11]', '[122, 122, -w - 12]', '[122, 122, w - 12]', '[126, 42, -3*w - 18]', '[126, 42, 3*w - 18]', '[126, 126, 5*w - 26]', '[126, 126, 13*w - 62]', '[126, 126, -13*w - 62]', '[126, 126, -5*w - 26]', '[127, 127, 4*w - 15]', '[127, 127, -4*w - 15]', '[128, 16, -24*w + 112]', '[132, 66, -4*w + 22]', '[132, 66, 4*w + 22]', '[134, 134, 3*w - 8]', '[134, 134, 3*w + 8]', '[137, 137, 2*w - 15]', '[137, 137, -2*w - 15]', '[143, 143, -12*w + 55]', '[143, 143, -12*w - 55]', '[144, 12, 12]', '[144, 36, -16*w + 76]', '[144, 36, 16*w + 76]', '[147, 21, -7*w + 35]', '[147, 21, 7*w + 35]', '[147, 147, w + 13]', '[147, 147, -11*w + 53]', '[147, 147, 11*w + 53]', '[147, 147, -w + 13]', '[149, 149, -3*w - 7]', '[149, 149, 3*w - 7]', '[150, 30, 5*w - 20]', '[150, 30, 5*w + 20]', '[151, 151, 20*w - 93]', '[151, 151, 34*w - 159]', '[154, 154, -9*w - 44]', '[154, 154, 9*w - 44]', '[156, 78, -16*w + 74]', '[156, 78, -4*w + 14]', '[156, 78, -4*w - 14]', '[156, 78, -16*w - 74]', '[158, 158, 37*w - 174]', '[158, 158, -19*w + 90]', '[162, 18, -27*w + 126]', '[162, 54, -3*w - 6]', '[162, 54, -3*w + 6]', '[162, 162, -11*w - 50]', '[162, 162, -11*w + 50]', '[163, 163, 3*w - 19]', '[163, 163, -3*w - 19]', '[167, 167, 6*w + 25]', '[167, 167, 6*w - 25]', '[168, 84, -2*w - 16]', '[168, 84, -22*w - 104]', '[168, 84, 22*w - 104]', '[168, 84, 2*w - 16]', '[169, 13, 13]', '[169, 169, -6*w + 31]', '[169, 169, 6*w + 31]', '[173, 173, 3*w - 5]', '[173, 173, -3*w - 5]', '[174, 174, -w - 14]', '[174, 174, -25*w + 118]', '[174, 174, 31*w - 146]', '[174, 174, -w + 14]', '[175, 35, -10*w - 45]', '[175, 35, -10*w + 45]', '[176, 44, -28*w + 132]', '[177, 177, -4*w - 23]', '[177, 177, -14*w - 67]', '[177, 177, 14*w - 67]', '[177, 177, 4*w - 23]', '[178, 178, 7*w - 30]', '[178, 178, 7*w + 30]', '[179, 179, -5*w - 27]', '[179, 179, 5*w - 27]', '[182, 182, 9*w - 40]', '[182, 182, 3*w + 4]', '[182, 182, 3*w - 4]', '[182, 182, 9*w + 40]', '[183, 183, 4*w + 13]', '[183, 183, 8*w + 35]', '[183, 183, 8*w - 35]', '[183, 183, 4*w - 13]', '[189, 63, 3*w + 3]', '[189, 63, 15*w - 69]', '[189, 63, 15*w + 69]', '[189, 63, 3*w - 3]', '[189, 189, 23*w - 107]', '[189, 189, 5*w - 19]', '[189, 189, 5*w + 19]', '[189, 189, 23*w + 107]', '[192, 24, -8*w + 40]', '[192, 24, 8*w + 40]', '[194, 194, 3*w - 2]', '[194, 194, -3*w - 2]', '[196, 14, 14]', '[196, 98, 12*w + 58]', '[196, 98, -12*w + 58]', '[197, 197, -3*w - 1]', '[197, 197, 3*w - 1]', '[198, 66, -3*w]', '[198, 198, -19*w - 88]', '[198, 198, -19*w + 88]', '[200, 20, 30*w - 140]', '[201, 201, -10*w - 49]', '[201, 201, 2*w - 17]', '[201, 201, -2*w - 17]', '[201, 201, 10*w - 49]', '[202, 202, 3*w + 20]', '[202, 202, -3*w + 20]', '[203, 203, -w - 15]', '[203, 203, -17*w + 81]', '[203, 203, -17*w - 81]', '[203, 203, -w + 15]', '[208, 52, -4*w - 12]', '[208, 52, -4*w + 12]', '[216, 36, -6*w + 24]', '[216, 36, -6*w - 24]', '[216, 108, -14*w - 64]', '[216, 108, -14*w + 64]', '[218, 218, 7*w - 36]', '[218, 218, 7*w + 36]', '[224, 56, -4*w - 24]', '[224, 56, 4*w - 24]', '[225, 15, 15]', '[225, 45, 20*w - 95]', '[225, 45, -20*w - 95]', '[226, 226, 5*w + 18]', '[226, 226, 5*w - 18]', '[231, 231, 26*w - 121]', '[231, 231, 4*w - 11]', '[231, 231, 4*w + 11]', '[231, 231, 26*w + 121]', '[232, 116, 6*w - 32]', '[232, 116, 6*w + 32]', '[234, 78, 15*w + 72]', '[234, 78, -15*w + 72]', '[234, 234, w + 16]', '[234, 234, -5*w + 28]', '[234, 234, 5*w + 28]', '[234, 234, -w + 16]', '[236, 118, -2*w - 18]', '[236, 118, 2*w - 18]', '[237, 237, 7*w + 29]', '[237, 237, -13*w - 59]', '[237, 237, 13*w - 59]', '[237, 237, -7*w + 29]', '[239, 239, 60*w - 281]', '[239, 239, 18*w - 83]', '[242, 22, -33*w + 154]', '[243, 27, -9*w + 45]', '[243, 27, 9*w + 45]', '[243, 81, 3*w + 21]', '[243, 81, -3*w + 21]', '[243, 243, 23*w + 109]', '[243, 243, -23*w + 109]', '[244, 122, 22*w - 102]', '[244, 122, 50*w - 234]', '[251, 251, 13*w - 63]', '[251, 251, -85*w + 399]', '[252, 42, 12*w + 54]', '[252, 42, 12*w - 54]', '[252, 126, 8*w + 34]', '[252, 126, 4*w - 10]', '[252, 126, 4*w + 10]', '[252, 126, 8*w - 34]', '[254, 254, -11*w - 54]', '[254, 254, -11*w + 54]', '[256, 16, 16]', '[257, 257, -26*w + 123]', '[257, 257, 44*w - 207]', '[261, 87, 9*w + 39]', '[261, 87, -9*w + 39]', '[261, 261, 11*w - 49]', '[261, 261, 5*w - 17]', '[261, 261, -5*w - 17]', '[261, 261, -11*w - 49]', '[263, 263, 6*w - 23]', '[263, 263, -6*w - 23]', '[264, 132, -10*w + 44]', '[264, 132, -10*w - 44]', '[267, 267, -w - 17]', '[267, 267, -29*w - 137]', '[267, 267, 29*w - 137]', '[267, 267, w - 17]', '[268, 134, 18*w - 86]', '[268, 134, -18*w - 86]', '[271, 271, -4*w - 9]', '[271, 271, 4*w - 9]', '[273, 273, 8*w - 41]', '[273, 273, 32*w - 151]', '[273, 273, 4*w - 25]', '[273, 273, 2*w - 19]', '[273, 273, -2*w - 19]', '[273, 273, -4*w - 25]', '[273, 273, -32*w - 151]', '[273, 273, -8*w - 41]', '[274, 274, 17*w - 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483]', '[8867, 8867, 101*w - 483]', '[8887, 8887, 64*w - 285]', '[8887, 8887, -64*w - 285]', '[8951, 8951, 24*w - 61]', '[8951, 8951, -24*w - 61]', '[8963, 8963, 239*w - 1125]', '[8963, 8963, -167*w + 789]', '[8969, 8969, -80*w - 387]', '[8969, 8969, 80*w - 387]', '[9001, 9001, 18*w - 127]', '[9001, 9001, -18*w - 127]', '[9043, 9043, -87*w + 419]', '[9043, 9043, -87*w - 419]', '[9067, 9067, 21*w - 137]', '[9067, 9067, -21*w - 137]', '[9091, 9091, 345*w - 1621]', '[9091, 9091, -117*w + 557]', '[9103, 9103, 44*w + 183]', '[9103, 9103, -44*w + 183]', '[9127, 9127, 22*w - 39]', '[9127, 9127, -22*w - 39]', '[9151, 9151, 376*w - 1761]', '[9151, 9151, 110*w - 507]', '[9161, 9161, 68*w - 333]', '[9161, 9161, -68*w - 333]', '[9173, 9173, 21*w - 23]', '[9173, 9173, -21*w - 23]', '[9181, 9181, -85*w - 387]', '[9181, 9181, 85*w - 387]', '[9227, 9227, 97*w + 465]', '[9227, 9227, -97*w + 465]', '[9239, 9239, 78*w - 353]', '[9239, 9239, -78*w - 353]', '[9241, 9241, 342*w - 1607]', '[9241, 9241, -120*w + 571]', '[9319, 9319, 100*w + 459]', '[9319, 9319, -100*w + 459]', '[9337, 9337, -48*w - 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5]', '[9677, 9677, -21*w - 5]', '[9679, 9679, 28*w - 87]', '[9679, 9679, -28*w - 87]', '[9689, 9689, -154*w + 729]', '[9689, 9689, 280*w - 1317]', '[9719, 9719, -72*w - 323]', '[9719, 9719, 72*w - 323]', '[9739, 9739, 45*w - 233]', '[9739, 9739, -45*w - 233]', '[9743, 9743, -36*w - 137]', '[9743, 9743, 36*w - 137]', '[9767, 9767, 282*w - 1319]', '[9767, 9767, 156*w - 725]', '[9769, 9769, 96*w - 461]', '[9769, 9769, -450*w + 2113]', '[9781, 9781, -25*w - 63]', '[9781, 9781, 25*w - 63]', '[9817, 9817, 6*w - 103]', '[9817, 9817, -6*w - 103]', '[9829, 9829, 167*w - 777]', '[9829, 9829, 265*w - 1239]', '[9857, 9857, -106*w + 507]', '[9857, 9857, 106*w + 507]', '[9859, 9859, 51*w - 259]', '[9859, 9859, -51*w - 259]', '[9883, 9883, -27*w - 161]', '[9883, 9883, 27*w - 161]', '[9923, 9923, 271*w - 1275]', '[9923, 9923, -163*w + 771]', '[9931, 9931, 327*w - 1537]', '[9931, 9931, -135*w + 641]', '[9941, 9941, -111*w + 511]', '[9941, 9941, 111*w + 511]', '[9973, 9973, 49*w + 207]', '[9973, 9973, -49*w + 207]']}

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[]
maximal_cm_subfield	numeric[]
minimal_sibling	numeric[]
monogenic	smallint
narrow_class_group	bigint[]
narrow_class_number	bigint
num_ram	smallint
r2	smallint
ramps	numeric[]
rd	double precision
regulator	numeric
relative_class_number	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': [], 'class_number': 1, 'cm': False, 'coeffs': [-22, 0, 1], 'conductor': 88, 'degree': 2, 'dirichlet_group': [1, 43], 'disc_abs': 88, 'disc_rad': 22, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[1, 2]]], [5, [[2, 1]]], [7, [[1, 2]]], [11, [0]], [13, [[1, 2]]], [17, [[2, 1]]], [19, [[2, 1]]], [23, [[2, 1]]], [29, [[1, 2]]], [31, [[2, 1]]], [37, [[2, 1]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[2, 1]]], [53, [[2, 1]]], [59, [[1, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 9.38083151964686, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.88.1', 'local_algs': ['2.1.2.3a1.2', '11.1.2.1a1.1'], 'monogenic': 1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 0, 'ramps': [2, 11], 'rd': 9.38083151965, 'regulator': {'__RealLiteral__': 0, 'data': '5.97634446743', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( 42 a - 197 \\)'], '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 $\F_{q}$
Belyi maps

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.