LMFDB - Hilbert modular form data

Formats: - HTML - YAML - JSON - 2024-05-15T18:20:16.293872

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': 6, 'dimension': 1, 'disc': 1229312, 'field_bad_primes': [2, 7], 'field_label': '6.6.1229312.1', 'is_CM': 'no', 'is_base_change': 'yes', 'label': '6.6.1229312.1-8.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [2], 'level_ideal': '[8, 2, -1/4*w^5 + 2*w^3 - 3*w]', 'level_label': '8.1', 'level_norm': 8, 'parallel_weight': 2, 'short_label': '8.1-c', 'weight': '[2, 2, 2, 2, 2, 2]'}

Column	Type
AL_eigenvalues	jsonb
hecke_eigenvalues	jsonb
hecke_polynomial	text
label	text

hmf_hecke • Show schema

{'AL_eigenvalues': [['[8, 2, -1/4*w^5 + 2*w^3 - 3*w]', 1]], 'hecke_eigenvalues': [-1, -1, -1, 0, 0, 0, 0, 0, 0, 12, 12, -9, 12, -9, -9, 14, -7, 14, -7, 14, -7, -9, -9, -9, -9, -9, -9, 2, 2, 2, 2, 2, 2, 21, 0, 0, 21, 21, 0, -16, -16, -16, 14, 14, 14, 14, 14, 14, -12, -12, -12, 30, 30, 30, 30, -12, -12, 30, 30, -12, 5, 5, 26, 5, 26, 26, -7, 14, 14, -7, -7, 14, 9, 9, -33, 9, -33, -33, -16, 26, 26, -16, -16, 26, 21, -21, 21, -21, 21, -21, -28, -28, -28, -28, -28, -28, -30, -30, -30, 12, 12, 12, -37, -37, 5, -37, 5, 5, 23, -19, 23, -19, 23, -19, 35, 35, 35, 35, 35, 35, -44, 9, -12, 9, -12, 9, -12, 14, 14, 14, 14, 14, 14, 21, 21, -21, 21, -21, -21, 2, 2, 2, 42, 42, 42, 21, 21, 21, -12, -12, -12, -12, -12, -12, 14, 56, 14, 56, 14, 56, -12, 30, 30, -12, -12, 30, 23, 23, 44, 23, 44, 44], 'hecke_polynomial': 'x', 'label': '6.6.1229312.1-8.1-c'}

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

hmf_fields • Show schema

{'degree': 6, 'discriminant': 1229312, 'ideals': ['[1, 1, 1]', '[7, 7, -1/4*w^5 - 1/4*w^4 + 2*w^3 + 2*w^2 - 3*w - 3]', '[7, 7, -1/4*w^5 + 1/4*w^4 + 2*w^3 - 2*w^2 - 3*w + 3]', '[8, 2, -1/4*w^5 + 2*w^3 - 3*w]', '[41, 41, -1/4*w^4 - 1/2*w^3 + 3/2*w^2 + 3*w - 1]', '[41, 41, -1/2*w^2 - w + 2]', '[41, 41, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 2*w^2 - 5*w - 2]', '[41, 41, 1/4*w^5 - 1/4*w^4 - 5/2*w^3 + 2*w^2 + 5*w - 2]', '[41, 41, 1/2*w^2 - w - 2]', '[41, 41, -1/4*w^4 + 1/2*w^3 + 3/2*w^2 - 3*w - 1]', '[49, 7, -1/2*w^4 + 7/2*w^2 - 3]', '[49, 7, 1/4*w^5 + 1/4*w^4 - 3/2*w^3 - 3/2*w^2 - 1]', '[49, 7, 1/4*w^5 - 2*w^3 + 1/2*w^2 + 4*w]', '[56, 14, 1/4*w^5 - 2*w^3 + 2*w - 2]', '[56, 14, 1/4*w^5 - 5/2*w^3 + 6*w + 2]', '[64, 2, 2]', '[71, 71, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + w^2 - 5*w + 1]', '[71, 71, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 3/2*w^2 - 6*w - 2]', '[71, 71, 1/4*w^4 - 1/2*w^3 - 5/2*w^2 + 3*w + 4]', '[71, 71, 1/4*w^4 + 1/2*w^3 - 5/2*w^2 - 3*w + 4]', '[71, 71, 1/2*w^4 - 7/2*w^2 + w + 3]', '[71, 71, -1/4*w^5 + 1/4*w^4 + 5/2*w^3 - w^2 - 5*w - 1]', '[97, 97, 1/4*w^5 - 5/2*w^3 - 1/2*w^2 + 5*w]', '[97, 97, -1/4*w^4 + 3/2*w^2 + w + 1]', '[97, 97, -1/4*w^4 + 1/2*w^3 + 2*w^2 - 3*w - 4]', '[97, 97, 1/4*w^4 + 1/2*w^3 - 2*w^2 - 3*w + 4]', '[97, 97, 1/4*w^4 - 3/2*w^2 + w - 1]', '[97, 97, -1/4*w^5 + 5/2*w^3 - 1/2*w^2 - 5*w]', '[113, 113, 1/2*w^5 + 1/4*w^4 - 9/2*w^3 - 2*w^2 + 8*w + 1]', '[113, 113, -1/4*w^5 + 1/2*w^4 + 2*w^3 - 3*w^2 - 3*w - 1]', '[113, 113, -1/2*w^5 + 1/2*w^4 + 9/2*w^3 - 7/2*w^2 - 8*w + 3]', '[113, 113, 1/2*w^5 + 1/2*w^4 - 9/2*w^3 - 7/2*w^2 + 8*w + 3]', '[113, 113, -1/4*w^5 - 1/2*w^4 + 3*w^3 + 4*w^2 - 8*w - 5]', '[113, 113, -1/2*w^5 + 1/4*w^4 + 9/2*w^3 - 2*w^2 - 8*w + 1]', '[127, 127, 1/2*w^3 + 1/2*w^2 - 3*w]', '[127, 127, -1/4*w^5 + 1/4*w^4 + 5/2*w^3 - 3/2*w^2 - 5*w - 1]', '[127, 127, -1/4*w^4 + 2*w^2 + w - 4]', '[127, 127, -1/4*w^4 + 2*w^2 - w - 4]', '[127, 127, 1/4*w^5 + 1/4*w^4 - 5/2*w^3 - 3/2*w^2 + 5*w - 1]', '[127, 127, -1/2*w^3 + 1/2*w^2 + 3*w]', '[167, 167, 1/4*w^5 + 1/4*w^4 - 2*w^3 - 2*w^2 + 4*w + 5]', '[167, 167, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 4*w^2 + 4*w + 5]', '[167, 167, -1/4*w^5 + 1/2*w^4 + 5/2*w^3 - 3*w^2 - 5*w - 1]', '[167, 167, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 3*w^2 + 5*w - 1]', '[167, 167, 1/4*w^5 - 1/2*w^4 - 5/2*w^3 + 4*w^2 + 4*w - 5]', '[167, 167, -1/4*w^5 + 1/4*w^4 + 2*w^3 - 2*w^2 - 4*w + 5]', '[169, 13, -1/2*w^4 + 7/2*w^2 - 4]', '[169, 13, 1/4*w^4 - w^2 - 2]', '[169, 13, 1/4*w^4 - 5/2*w^2 + 3]', '[223, 223, -1/4*w^5 + 2*w^3 - 1/2*w^2 - 3*w + 5]', '[223, 223, 1/4*w^5 - 1/4*w^4 - 2*w^3 + 3/2*w^2 + 3*w - 4]', '[223, 223, 1/2*w^5 - 1/2*w^4 - 4*w^3 + 7/2*w^2 + 5*w - 4]', '[223, 223, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 7/2*w^2 - 5*w - 4]', '[223, 223, -1/4*w^5 - 1/4*w^4 + 2*w^3 + 3/2*w^2 - 3*w - 4]', '[223, 223, 1/4*w^5 - 2*w^3 - 1/2*w^2 + 3*w + 5]', '[239, 239, 1/4*w^5 - 1/2*w^4 - 3/2*w^3 + 7/2*w^2 + w - 3]', '[239, 239, 1/2*w^5 - 1/2*w^4 - 5*w^3 + 7/2*w^2 + 11*w - 3]', '[239, 239, -1/2*w^4 + 9/2*w^2 + w - 6]', '[239, 239, 1/2*w^4 - 9/2*w^2 + w + 6]', '[239, 239, 1/2*w^5 + 1/2*w^4 - 5*w^3 - 7/2*w^2 + 11*w + 3]', '[239, 239, -1/4*w^5 - 1/2*w^4 + 3/2*w^3 + 7/2*w^2 - w - 3]', '[281, 281, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 3*w^2 + 4*w + 1]', '[281, 281, 1/2*w^4 - 1/2*w^3 - 4*w^2 + 4*w + 5]', '[281, 281, 1/4*w^5 - 3*w^3 - w^2 + 8*w + 3]', '[281, 281, 1/4*w^5 - 3*w^3 + w^2 + 8*w - 3]', '[281, 281, 1/2*w^4 + 1/2*w^3 - 4*w^2 - 4*w + 5]', '[281, 281, -1/4*w^5 + 1/2*w^4 + 5/2*w^3 - 3*w^2 - 4*w + 1]', '[287, 287, 1/4*w^5 - 1/4*w^4 - 3/2*w^3 + 2*w^2 - 3]', '[287, 287, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 3*w^2 - 5*w - 1]', '[287, 287, -1/4*w^5 + 1/4*w^4 + 2*w^3 - 3/2*w^2 - 4*w]', '[287, 287, -1/2*w^5 + 9/2*w^3 + 1/2*w^2 - 8*w - 1]', '[287, 287, 1/2*w^5 - 1/2*w^4 - 9/2*w^3 + 4*w^2 + 9*w - 5]', '[287, 287, -1/4*w^5 + 3/2*w^3 - w^2 - w + 3]', '[287, 287, -1/4*w^5 + 3/2*w^3 + w^2 - w - 3]', '[287, 287, 1/2*w^5 + 1/2*w^4 - 9/2*w^3 - 4*w^2 + 9*w + 5]', '[287, 287, -1/2*w^5 + 9/2*w^3 - 1/2*w^2 - 8*w + 1]', '[287, 287, 1/4*w^5 + 1/4*w^4 - 2*w^3 - 3/2*w^2 + 4*w]', '[287, 287, -1/2*w^5 + 1/2*w^4 + 4*w^3 - 3*w^2 - 5*w + 1]', '[287, 287, -1/4*w^5 - 1/4*w^4 + 3/2*w^3 + 2*w^2 - 3]', '[328, 82, -1/2*w^4 + 4*w^2 + w - 4]', '[328, 82, -1/4*w^5 + 1/2*w^4 + 5/2*w^3 - 3*w^2 - 5*w + 2]', '[328, 82, -1/2*w^3 - w^2 + 3*w + 4]', '[328, 82, -1/2*w^3 + w^2 + 3*w - 4]', '[328, 82, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 3*w^2 + 5*w + 2]', '[328, 82, 1/2*w^4 - 4*w^2 + w + 4]', '[337, 337, 3/4*w^4 + 1/2*w^3 - 11/2*w^2 - 3*w + 6]', '[337, 337, -1/2*w^5 + 4*w^3 - w^2 - 6*w + 5]', '[337, 337, 1/2*w^5 - 1/4*w^4 - 4*w^3 + 3/2*w^2 + 5*w - 3]', '[337, 337, -1/2*w^5 - 1/4*w^4 + 4*w^3 + 3/2*w^2 - 5*w - 3]', '[337, 337, -1/4*w^5 + 1/4*w^4 + 3*w^3 - w^2 - 8*w - 3]', '[337, 337, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 3*w^2 + 6*w + 3]', '[343, 7, -1/2*w^5 + 4*w^3 - 6*w - 1]', '[343, 7, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 5/2*w^2 - 4*w - 4]', '[343, 7, -1/2*w^5 + 4*w^3 - 6*w + 1]', '[343, 7, -1/2*w^3 + 1/2*w^2 + 4*w - 4]', '[392, 14, -1/2*w^3 + 4*w]', '[392, 14, -1/4*w^5 - 1/2*w^4 + 3/2*w^3 + 3*w^2 - w - 4]', '[392, 14, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 4*w^2 + 5*w + 2]', '[433, 433, 1/4*w^5 + 1/4*w^4 - 2*w^3 - 2*w^2 + w + 2]', '[433, 433, 1/4*w^5 - 3*w^3 - 1/2*w^2 + 9*w + 2]', '[433, 433, -1/4*w^5 + 1/4*w^4 + 3*w^3 - 3/2*w^2 - 7*w + 1]', '[433, 433, 1/4*w^5 + 1/4*w^4 - 3*w^3 - 3/2*w^2 + 7*w + 1]', '[433, 433, -1/4*w^5 + 3*w^3 - 1/2*w^2 - 9*w + 2]', '[433, 433, -1/4*w^5 + 1/4*w^4 + 2*w^3 - 2*w^2 - w + 2]', '[448, 14, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 4*w^2 - 6*w - 6]', '[448, 14, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 3*w^2 + 6*w]', '[449, 449, 1/4*w^5 - 1/2*w^4 - 2*w^3 + 3*w^2 + 4*w - 1]', '[449, 449, -1/2*w^5 + 1/4*w^4 + 4*w^3 - 3/2*w^2 - 5*w + 2]', '[449, 449, 1/4*w^5 - 1/2*w^4 - 3/2*w^3 + 4*w^2 - 5]', '[449, 449, -1/4*w^5 - 1/2*w^4 + 3/2*w^3 + 4*w^2 - 5]', '[449, 449, 1/2*w^5 + 1/4*w^4 - 4*w^3 - 3/2*w^2 + 5*w + 2]', '[449, 449, -1/4*w^5 - 1/2*w^4 + 2*w^3 + 3*w^2 - 4*w - 1]', '[463, 463, -1/4*w^5 + 5/2*w^3 + 1/2*w^2 - 7*w - 3]', '[463, 463, -1/2*w^5 - 1/4*w^4 + 9/2*w^3 + 2*w^2 - 7*w - 1]', '[463, 463, -1/4*w^4 + w^3 + 3/2*w^2 - 5*w - 2]', '[463, 463, -1/4*w^4 - w^3 + 3/2*w^2 + 5*w - 2]', '[463, 463, 1/2*w^5 - 1/4*w^4 - 9/2*w^3 + 2*w^2 + 7*w - 1]', '[463, 463, -1/4*w^5 + 5/2*w^3 - 1/2*w^2 - 7*w + 3]', '[497, 497, -1/4*w^5 + 1/4*w^4 + 5/2*w^3 - 3/2*w^2 - 7*w]', '[497, 497, w^5 - 3/4*w^4 - 9*w^3 + 6*w^2 + 18*w - 10]', '[497, 497, -1/4*w^5 + 1/4*w^4 + 3/2*w^3 - w^2 - 4]', '[497, 497, -3/4*w^5 - 1/4*w^4 + 15/2*w^3 + 7/2*w^2 - 15*w - 8]', '[497, 497, -1/2*w^5 - 1/4*w^4 + 5*w^3 + 2*w^2 - 10*w - 2]', '[497, 497, 3/4*w^5 + 3/4*w^4 - 15/2*w^3 - 7*w^2 + 16*w + 12]', '[497, 497, -3/4*w^5 + 3/4*w^4 + 15/2*w^3 - 7*w^2 - 16*w + 12]', '[497, 497, 1/4*w^5 - 1/2*w^4 - 5/2*w^3 + 7/2*w^2 + 7*w - 6]', '[497, 497, 3/4*w^5 - 1/4*w^4 - 15/2*w^3 + 7/2*w^2 + 15*w - 8]', '[497, 497, 1/4*w^5 + 1/4*w^4 - 3/2*w^3 - w^2 - 4]', '[497, 497, -1/4*w^5 - 1/2*w^4 + 3/2*w^3 + 5/2*w^2 + w + 2]', '[497, 497, 1/4*w^5 + 1/4*w^4 - 5/2*w^3 - 3/2*w^2 + 7*w]', '[503, 503, 1/4*w^5 - 3/2*w^3 + 1/2*w^2 - 4]', '[503, 503, -1/2*w^5 - 1/2*w^4 + 9/2*w^3 + 7/2*w^2 - 9*w - 3]', '[503, 503, 3/4*w^4 - 11/2*w^2 + w + 6]', '[503, 503, -3/4*w^4 + 11/2*w^2 + w - 6]', '[503, 503, -1/2*w^5 + 1/2*w^4 + 9/2*w^3 - 7/2*w^2 - 9*w + 3]', '[503, 503, -1/4*w^5 + 3/2*w^3 + 1/2*w^2 - 4]', '[512, 4, -1/2*w^5 + 4*w^3 - 6*w]', '[568, 142, 1/4*w^5 + 1/2*w^4 - 3*w^3 - 4*w^2 + 8*w + 4]', '[568, 142, 1/4*w^5 - 1/2*w^4 - 2*w^3 + 4*w^2 + 4*w - 6]', '[568, 142, -1/4*w^5 + 5/2*w^3 + w^2 - 4*w - 4]', '[568, 142, 1/4*w^5 - 5/2*w^3 + w^2 + 4*w - 4]', '[568, 142, -1/2*w^4 - 1/2*w^3 + 3*w^2 + 4*w - 2]', '[568, 142, -1/4*w^5 + 1/2*w^4 + 3*w^3 - 4*w^2 - 8*w + 4]', '[601, 601, 1/4*w^5 + 1/4*w^4 - 2*w^3 - 3/2*w^2 + 4*w - 2]', '[601, 601, -1/2*w^5 + 9/2*w^3 - 1/2*w^2 - 8*w - 1]', '[601, 601, 1/4*w^5 + 1/4*w^4 - 3/2*w^3 - 2*w^2 + 5]', '[601, 601, 1/4*w^5 - 1/4*w^4 - 3/2*w^3 + 2*w^2 - 5]', '[601, 601, -1/2*w^5 + 9/2*w^3 + 1/2*w^2 - 8*w + 1]', '[601, 601, -1/4*w^5 + 1/4*w^4 + 2*w^3 - 3/2*w^2 - 4*w - 2]', '[617, 617, -1/2*w^4 + 1/2*w^3 + 7/2*w^2 - 3*w - 5]', '[617, 617, 1/4*w^4 - w^2 + w - 3]', '[617, 617, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 5/2*w^2 - 5*w - 2]', '[617, 617, -1/4*w^5 + 1/4*w^4 + 5/2*w^3 - 5/2*w^2 - 5*w + 2]', '[617, 617, 1/4*w^4 - w^2 - w - 3]', '[617, 617, -1/2*w^4 - 1/2*w^3 + 7/2*w^2 + 3*w - 5]', '[631, 631, -1/4*w^5 + 1/4*w^4 + 3*w^3 - w^2 - 8*w]', '[631, 631, 1/2*w^5 - 7/2*w^3 - 1/2*w^2 + 3*w + 2]', '[631, 631, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 7/2*w^2 + 4*w + 2]', '[631, 631, -1/4*w^5 + 1/2*w^4 + 5/2*w^3 - 7/2*w^2 - 4*w + 2]', '[631, 631, -1/2*w^5 + 7/2*w^3 - 1/2*w^2 - 3*w + 2]', '[631, 631, 3/4*w^5 - 1/4*w^4 - 13/2*w^3 + 3/2*w^2 + 11*w - 1]', '[673, 673, -1/4*w^5 - 3/4*w^4 + 2*w^3 + 6*w^2 - 3*w - 7]', '[673, 673, -1/4*w^5 + 2*w^3 + 3/2*w^2 - 3*w - 5]', '[673, 673, 1/4*w^5 - 3/4*w^4 - 2*w^3 + 9/2*w^2 + 3*w - 2]', '[673, 673, 1/4*w^5 + 3/4*w^4 - 2*w^3 - 9/2*w^2 + 3*w + 2]', '[673, 673, 1/4*w^5 - 2*w^3 + 3/2*w^2 + 3*w - 5]', '[673, 673, 1/2*w^4 - 3*w^2 + w - 1]', '[679, 679, -1/4*w^5 + 1/4*w^4 + 7/2*w^3 - 1/2*w^2 - 10*w - 3]', '[679, 679, 1/4*w^5 - 2*w^3 - w^2 + 2*w + 3]', '[679, 679, 3/4*w^5 - 1/4*w^4 - 13/2*w^3 + 5/2*w^2 + 12*w - 5]', '[679, 679, w^5 + w^4 - 9*w^3 - 17/2*w^2 + 17*w + 13]', '[679, 679, 1/2*w^2 - w - 5]', '[679, 679, -3/4*w^5 - w^4 + 6*w^3 + 7*w^2 - 8*w - 7]', '[679, 679, 3/4*w^5 - w^4 - 6*w^3 + 7*w^2 + 8*w - 7]', '[679, 679, 1/2*w^2 + w - 5]', '[679, 679, -w^5 + w^4 + 9*w^3 - 17/2*w^2 - 17*w + 13]', '[679, 679, 3/4*w^5 + 1/4*w^4 - 13/2*w^3 - 5/2*w^2 + 12*w + 5]', '[679, 679, -1/4*w^5 + 2*w^3 - w^2 - 2*w + 3]', '[679, 679, -1/4*w^5 - 1/4*w^4 + 7/2*w^3 + 1/2*w^2 - 10*w + 3]', '[727, 727, 1/4*w^5 - 1/4*w^4 - 5/2*w^3 + 2*w^2 + 7*w - 2]', '[727, 727, 1/2*w^5 + 1/4*w^4 - 9/2*w^3 - 3/2*w^2 + 7*w + 1]', '[727, 727, -w^3 - 1/2*w^2 + 5*w + 2]', '[727, 727, w^3 - 1/2*w^2 - 5*w + 2]', '[727, 727, 1/2*w^5 - 1/4*w^4 - 9/2*w^3 + 3/2*w^2 + 7*w - 1]', '[727, 727, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 2*w^2 - 7*w - 2]', '[729, 3, -3]', '[743, 743, 1/4*w^5 + 3/4*w^4 - 5/2*w^3 - 11/2*w^2 + 5*w + 7]', '[743, 743, 1/2*w^3 - 1/2*w^2 - 4*w - 1]', '[743, 743, 1/2*w^4 - 1/2*w^3 - 5/2*w^2 + 3*w - 2]', '[743, 743, 1/2*w^4 + 1/2*w^3 - 5/2*w^2 - 3*w - 2]', '[743, 743, -1/2*w^3 - 1/2*w^2 + 4*w - 1]', '[743, 743, -1/4*w^5 + 3/4*w^4 + 5/2*w^3 - 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5]', '[1849, 43, 1/2*w^4 - 9/2*w^2 + 5]', '[1849, 43, 1/4*w^4 - 1/2*w^2 - 4]', '[1889, 1889, -1/4*w^4 - w^3 + w^2 + 6*w + 1]', '[1889, 1889, -1/2*w^5 + 1/2*w^4 + 5*w^3 - 7/2*w^2 - 10*w + 3]', '[1889, 1889, -1/4*w^4 + 5/2*w^2 - 2*w - 4]', '[1889, 1889, -1/4*w^4 + 5/2*w^2 + 2*w - 4]', '[1889, 1889, -1/2*w^5 - 1/2*w^4 + 5*w^3 + 7/2*w^2 - 10*w - 3]', '[1889, 1889, -1/4*w^4 + w^3 + w^2 - 6*w + 1]', '[1912, 478, -1/2*w^3 - w^2 + 4*w]', '[1912, 478, -1/2*w^4 - 1/2*w^3 + 5*w^2 + 4*w - 10]', '[1912, 478, 1/4*w^5 - 1/2*w^4 - 7/2*w^3 + 3*w^2 + 11*w - 2]', '[1912, 478, 1/4*w^5 + 1/2*w^4 - 7/2*w^3 - 3*w^2 + 11*w + 2]', '[1912, 478, -1/2*w^4 + 1/2*w^3 + 5*w^2 - 4*w - 10]', '[1912, 478, -1/2*w^3 + w^2 + 4*w]', '[1967, 1967, 3/4*w^4 + w^3 - 4*w^2 - 7*w - 1]', '[1967, 1967, w^5 - 5/4*w^4 - 19/2*w^3 + 10*w^2 + 20*w - 15]', '[1967, 1967, 1/2*w^5 - 1/4*w^4 - 5*w^3 + 9*w + 3]', '[1967, 1967, -3/4*w^5 + 1/4*w^4 + 13/2*w^3 - 2*w^2 - 12*w + 1]', '[1967, 1967, 5/4*w^5 - 3/4*w^4 - 25/2*w^3 + 8*w^2 + 26*w - 15]', '[1967, 1967, 1/2*w^5 - 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w^2 - 6*w - 1]', '[2591, 2591, 1/2*w^5 - 1/2*w^4 - 4*w^3 + 4*w^2 + 6*w - 9]', '[2591, 2591, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 4*w^2 + 6*w + 9]', '[2591, 2591, -1/2*w^5 + 3/4*w^4 + 5*w^3 - 5*w^2 - 12*w + 5]', '[2591, 2591, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 3*w^2 + 6*w - 3]', '[2617, 2617, 1/2*w^5 - 1/4*w^4 - 5*w^3 + 3/2*w^2 + 10*w + 1]', '[2617, 2617, -1/4*w^4 + 2*w^2 - 2*w - 4]', '[2617, 2617, w^3 + 1/2*w^2 - 6*w]', '[2617, 2617, -w^3 + 1/2*w^2 + 6*w]', '[2617, 2617, -1/4*w^4 + 2*w^2 + 2*w - 4]', '[2617, 2617, -1/2*w^5 - 1/4*w^4 + 5*w^3 + 3/2*w^2 - 10*w + 1]', '[2624, 82, -1/2*w^4 - w^3 + 3*w^2 + 6*w - 2]', '[2624, 82, -w^2 - 2*w + 4]', '[2624, 82, -1/2*w^5 - 1/2*w^4 + 5*w^3 + 4*w^2 - 10*w - 4]', '[2624, 82, 1/2*w^5 - 1/2*w^4 - 5*w^3 + 4*w^2 + 10*w - 4]', '[2624, 82, w^2 - 2*w - 4]', '[2624, 82, -1/2*w^4 + w^3 + 3*w^2 - 6*w - 2]', '[2633, 2633, 1/2*w^5 - 3/4*w^4 - 7/2*w^3 + 5*w^2 + 4*w - 2]', '[2633, 2633, -3/4*w^5 - 1/4*w^4 + 11/2*w^3 + w^2 - 5*w]', '[2633, 2633, 1/4*w^5 - 5/2*w^3 + 4*w - 5]', '[2633, 2633, -1/4*w^5 + 5/2*w^3 - 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11/2*w^3 - 2*w^2 + 7*w + 2]', '[9799, 9799, -5/4*w^5 - 1/4*w^4 + 23/2*w^3 - 23*w + 7]', '[9799, 9799, 1/2*w^5 - 3/4*w^4 - 3*w^3 + 5/2*w^2 + 2*w + 2]', '[9799, 9799, -3/4*w^5 - 1/4*w^4 + 15/2*w^3 + 2*w^2 - 19*w + 3]', '[9799, 9799, -1/2*w^5 + 3/2*w^4 + 4*w^3 - 12*w^2 - 6*w + 17]', '[9799, 9799, 3/4*w^5 - 3/4*w^4 - 13/2*w^3 + 6*w^2 + 7*w - 2]', '[9799, 9799, -w^5 + 1/4*w^4 + 17/2*w^3 - 3*w^2 - 12*w + 12]', '[9799, 9799, -w^4 - 3/2*w^3 + 5*w^2 + 8*w + 1]', '[9799, 9799, -3/2*w^5 - w^4 + 12*w^3 + 11/2*w^2 - 17*w + 1]', '[9799, 9799, -w^5 + 9*w^3 - 1/2*w^2 - 15*w + 1]', '[9799, 9799, 3/2*w^5 - 1/4*w^4 - 13*w^3 + 7/2*w^2 + 23*w - 8]', '[9799, 9799, 1/2*w^5 + 3/4*w^4 - 7/2*w^3 - 7*w^2 + 2*w + 12]', '[9799, 9799, 1/2*w^5 - 3/4*w^4 - 5*w^3 + 5*w^2 + 8*w - 10]', '[9799, 9799, 1/2*w^5 - 9/2*w^3 + w^2 + 8*w + 1]', '[9799, 9799, 1/2*w^5 - 3/4*w^4 - 4*w^3 + 7*w^2 + 4*w - 10]', '[9799, 9799, -1/2*w^5 + 1/4*w^4 + 6*w^3 - 3/2*w^2 - 17*w]', '[9848, 2462, 1/2*w^5 - 1/2*w^4 - 5*w^3 + 5*w^2 + 11*w - 6]', '[9848, 2462, -1/2*w^4 + 1/2*w^3 + 2*w^2 - w + 4]', '[9848, 2462, 1/4*w^5 + w^4 - 3/2*w^3 - 7*w^2 - w + 8]', '[9848, 2462, 1/4*w^5 - w^4 - 3/2*w^3 + 7*w^2 - w - 8]', '[9848, 2462, 1/2*w^4 + 1/2*w^3 - 2*w^2 - w - 4]', '[9848, 2462, -1/2*w^5 - 1/2*w^4 + 5*w^3 + 5*w^2 - 11*w - 6]', '[9857, 9857, -1/2*w^5 - 1/2*w^4 + 5*w^3 + 7/2*w^2 - 10*w - 9]', '[9857, 9857, -1/4*w^5 + 1/4*w^4 + 7/2*w^3 - w^2 - 9*w - 3]', '[9857, 9857, 1/4*w^4 - 5/2*w^2 - 2*w - 2]', '[9857, 9857, 1/4*w^4 - 5/2*w^2 + 2*w - 2]', '[9857, 9857, 1/2*w^5 + 3/2*w^4 - 4*w^3 - 10*w^2 + 4*w + 7]', '[9857, 9857, 1/2*w^5 - 1/2*w^4 - 5*w^3 + 7/2*w^2 + 10*w - 9]', '[9871, 9871, 1/2*w^5 + 3/2*w^4 - 7/2*w^3 - 10*w^2 + 3*w + 7]', '[9871, 9871, w^5 + 5/4*w^4 - 9*w^3 - 19/2*w^2 + 17*w + 9]', '[9871, 9871, 1/2*w^5 - 1/2*w^4 - 4*w^3 + w^2 + 7*w + 5]', '[9871, 9871, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 5/2*w^2 - 4*w + 2]', '[9871, 9871, -3/4*w^5 - w^4 + 13/2*w^3 + 9*w^2 - 11*w - 13]', '[9871, 9871, -1/2*w^5 + 3/2*w^4 + 7/2*w^3 - 10*w^2 - 3*w + 7]', '[9967, 9967, -w - 5]', '[9967, 9967, 1/2*w^3 - 3*w - 5]', '[9967, 9967, -1/4*w^5 + 5/2*w^3 - 5*w + 5]', '[9967, 9967, -1/4*w^5 + 5/2*w^3 - 5*w - 5]', '[9967, 9967, -1/2*w^3 + 3*w - 5]', '[9967, 9967, w - 5]'], 'label': '6.6.1229312.1', 'narrow_class_no': 1, 'primes': ['[7, 7, -1/4*w^5 - 1/4*w^4 + 2*w^3 + 2*w^2 - 3*w - 3]', '[7, 7, -1/4*w^5 + 1/4*w^4 + 2*w^3 - 2*w^2 - 3*w + 3]', '[8, 2, -1/4*w^5 + 2*w^3 - 3*w]', '[41, 41, -1/4*w^4 - 1/2*w^3 + 3/2*w^2 + 3*w - 1]', '[41, 41, -1/2*w^2 - w + 2]', '[41, 41, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 2*w^2 - 5*w - 2]', '[41, 41, 1/4*w^5 - 1/4*w^4 - 5/2*w^3 + 2*w^2 + 5*w - 2]', '[41, 41, 1/2*w^2 - w - 2]', '[41, 41, -1/4*w^4 + 1/2*w^3 + 3/2*w^2 - 3*w - 1]', '[71, 71, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + w^2 - 5*w + 1]', '[71, 71, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 3/2*w^2 - 6*w - 2]', '[71, 71, 1/4*w^4 - 1/2*w^3 - 5/2*w^2 + 3*w + 4]', '[71, 71, 1/4*w^4 + 1/2*w^3 - 5/2*w^2 - 3*w + 4]', '[71, 71, 1/2*w^4 - 7/2*w^2 + w + 3]', '[71, 71, -1/4*w^5 + 1/4*w^4 + 5/2*w^3 - w^2 - 5*w - 1]', '[97, 97, 1/4*w^5 - 5/2*w^3 - 1/2*w^2 + 5*w]', '[97, 97, -1/4*w^4 + 3/2*w^2 + w + 1]', '[97, 97, -1/4*w^4 + 1/2*w^3 + 2*w^2 - 3*w - 4]', '[97, 97, 1/4*w^4 + 1/2*w^3 - 2*w^2 - 3*w + 4]', '[97, 97, 1/4*w^4 - 3/2*w^2 + w - 1]', '[97, 97, -1/4*w^5 + 5/2*w^3 - 1/2*w^2 - 5*w]', '[113, 113, 1/2*w^5 + 1/4*w^4 - 9/2*w^3 - 2*w^2 + 8*w + 1]', '[113, 113, -1/4*w^5 + 1/2*w^4 + 2*w^3 - 3*w^2 - 3*w - 1]', '[113, 113, -1/2*w^5 + 1/2*w^4 + 9/2*w^3 - 7/2*w^2 - 8*w + 3]', '[113, 113, 1/2*w^5 + 1/2*w^4 - 9/2*w^3 - 7/2*w^2 + 8*w + 3]', '[113, 113, -1/4*w^5 - 1/2*w^4 + 3*w^3 + 4*w^2 - 8*w - 5]', '[113, 113, -1/2*w^5 + 1/4*w^4 + 9/2*w^3 - 2*w^2 - 8*w + 1]', '[127, 127, 1/2*w^3 + 1/2*w^2 - 3*w]', '[127, 127, -1/4*w^5 + 1/4*w^4 + 5/2*w^3 - 3/2*w^2 - 5*w - 1]', '[127, 127, -1/4*w^4 + 2*w^2 + w - 4]', '[127, 127, -1/4*w^4 + 2*w^2 - w - 4]', '[127, 127, 1/4*w^5 + 1/4*w^4 - 5/2*w^3 - 3/2*w^2 + 5*w - 1]', '[127, 127, -1/2*w^3 + 1/2*w^2 + 3*w]', '[167, 167, 1/4*w^5 + 1/4*w^4 - 2*w^3 - 2*w^2 + 4*w + 5]', '[167, 167, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 4*w^2 + 4*w + 5]', '[167, 167, -1/4*w^5 + 1/2*w^4 + 5/2*w^3 - 3*w^2 - 5*w - 1]', '[167, 167, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 3*w^2 + 5*w - 1]', '[167, 167, 1/4*w^5 - 1/2*w^4 - 5/2*w^3 + 4*w^2 + 4*w - 5]', '[167, 167, -1/4*w^5 + 1/4*w^4 + 2*w^3 - 2*w^2 - 4*w + 5]', '[169, 13, -1/2*w^4 + 7/2*w^2 - 4]', '[169, 13, 1/4*w^4 - w^2 - 2]', '[169, 13, 1/4*w^4 - 5/2*w^2 + 3]', '[223, 223, -1/4*w^5 + 2*w^3 - 1/2*w^2 - 3*w + 5]', '[223, 223, 1/4*w^5 - 1/4*w^4 - 2*w^3 + 3/2*w^2 + 3*w - 4]', '[223, 223, 1/2*w^5 - 1/2*w^4 - 4*w^3 + 7/2*w^2 + 5*w - 4]', '[223, 223, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 7/2*w^2 - 5*w - 4]', '[223, 223, -1/4*w^5 - 1/4*w^4 + 2*w^3 + 3/2*w^2 - 3*w - 4]', '[223, 223, 1/4*w^5 - 2*w^3 - 1/2*w^2 + 3*w + 5]', '[239, 239, 1/4*w^5 - 1/2*w^4 - 3/2*w^3 + 7/2*w^2 + w - 3]', '[239, 239, 1/2*w^5 - 1/2*w^4 - 5*w^3 + 7/2*w^2 + 11*w - 3]', '[239, 239, -1/2*w^4 + 9/2*w^2 + w - 6]', '[239, 239, 1/2*w^4 - 9/2*w^2 + w + 6]', '[239, 239, 1/2*w^5 + 1/2*w^4 - 5*w^3 - 7/2*w^2 + 11*w + 3]', '[239, 239, -1/4*w^5 - 1/2*w^4 + 3/2*w^3 + 7/2*w^2 - w - 3]', '[281, 281, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 3*w^2 + 4*w + 1]', '[281, 281, 1/2*w^4 - 1/2*w^3 - 4*w^2 + 4*w + 5]', '[281, 281, 1/4*w^5 - 3*w^3 - w^2 + 8*w + 3]', '[281, 281, 1/4*w^5 - 3*w^3 + w^2 + 8*w - 3]', '[281, 281, 1/2*w^4 + 1/2*w^3 - 4*w^2 - 4*w + 5]', '[281, 281, -1/4*w^5 + 1/2*w^4 + 5/2*w^3 - 3*w^2 - 4*w + 1]', '[337, 337, 3/4*w^4 + 1/2*w^3 - 11/2*w^2 - 3*w + 6]', '[337, 337, -1/2*w^5 + 4*w^3 - w^2 - 6*w + 5]', '[337, 337, 1/2*w^5 - 1/4*w^4 - 4*w^3 + 3/2*w^2 + 5*w - 3]', '[337, 337, -1/2*w^5 - 1/4*w^4 + 4*w^3 + 3/2*w^2 - 5*w - 3]', '[337, 337, -1/4*w^5 + 1/4*w^4 + 3*w^3 - w^2 - 8*w - 3]', '[337, 337, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 3*w^2 + 6*w + 3]', '[433, 433, 1/4*w^5 + 1/4*w^4 - 2*w^3 - 2*w^2 + w + 2]', '[433, 433, 1/4*w^5 - 3*w^3 - 1/2*w^2 + 9*w + 2]', '[433, 433, -1/4*w^5 + 1/4*w^4 + 3*w^3 - 3/2*w^2 - 7*w + 1]', '[433, 433, 1/4*w^5 + 1/4*w^4 - 3*w^3 - 3/2*w^2 + 7*w + 1]', '[433, 433, -1/4*w^5 + 3*w^3 - 1/2*w^2 - 9*w + 2]', '[433, 433, -1/4*w^5 + 1/4*w^4 + 2*w^3 - 2*w^2 - w + 2]', '[449, 449, 1/4*w^5 - 1/2*w^4 - 2*w^3 + 3*w^2 + 4*w - 1]', '[449, 449, -1/2*w^5 + 1/4*w^4 + 4*w^3 - 3/2*w^2 - 5*w + 2]', '[449, 449, 1/4*w^5 - 1/2*w^4 - 3/2*w^3 + 4*w^2 - 5]', '[449, 449, -1/4*w^5 - 1/2*w^4 + 3/2*w^3 + 4*w^2 - 5]', '[449, 449, 1/2*w^5 + 1/4*w^4 - 4*w^3 - 3/2*w^2 + 5*w + 2]', '[449, 449, -1/4*w^5 - 1/2*w^4 + 2*w^3 + 3*w^2 - 4*w - 1]', '[463, 463, -1/4*w^5 + 5/2*w^3 + 1/2*w^2 - 7*w - 3]', '[463, 463, -1/2*w^5 - 1/4*w^4 + 9/2*w^3 + 2*w^2 - 7*w - 1]', '[463, 463, -1/4*w^4 + w^3 + 3/2*w^2 - 5*w - 2]', '[463, 463, -1/4*w^4 - w^3 + 3/2*w^2 + 5*w - 2]', '[463, 463, 1/2*w^5 - 1/4*w^4 - 9/2*w^3 + 2*w^2 + 7*w - 1]', '[463, 463, -1/4*w^5 + 5/2*w^3 - 1/2*w^2 - 7*w + 3]', '[503, 503, 1/4*w^5 - 3/2*w^3 + 1/2*w^2 - 4]', '[503, 503, -1/2*w^5 - 1/2*w^4 + 9/2*w^3 + 7/2*w^2 - 9*w - 3]', '[503, 503, 3/4*w^4 - 11/2*w^2 + w + 6]', '[503, 503, -3/4*w^4 + 11/2*w^2 + w - 6]', '[503, 503, -1/2*w^5 + 1/2*w^4 + 9/2*w^3 - 7/2*w^2 - 9*w + 3]', '[503, 503, -1/4*w^5 + 3/2*w^3 + 1/2*w^2 - 4]', '[601, 601, 1/4*w^5 + 1/4*w^4 - 2*w^3 - 3/2*w^2 + 4*w - 2]', '[601, 601, -1/2*w^5 + 9/2*w^3 - 1/2*w^2 - 8*w - 1]', '[601, 601, 1/4*w^5 + 1/4*w^4 - 3/2*w^3 - 2*w^2 + 5]', '[601, 601, 1/4*w^5 - 1/4*w^4 - 3/2*w^3 + 2*w^2 - 5]', '[601, 601, -1/2*w^5 + 9/2*w^3 + 1/2*w^2 - 8*w + 1]', '[601, 601, -1/4*w^5 + 1/4*w^4 + 2*w^3 - 3/2*w^2 - 4*w - 2]', '[617, 617, -1/2*w^4 + 1/2*w^3 + 7/2*w^2 - 3*w - 5]', '[617, 617, 1/4*w^4 - w^2 + w - 3]', '[617, 617, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 5/2*w^2 - 5*w - 2]', '[617, 617, -1/4*w^5 + 1/4*w^4 + 5/2*w^3 - 5/2*w^2 - 5*w + 2]', '[617, 617, 1/4*w^4 - w^2 - w - 3]', '[617, 617, -1/2*w^4 - 1/2*w^3 + 7/2*w^2 + 3*w - 5]', '[631, 631, -1/4*w^5 + 1/4*w^4 + 3*w^3 - w^2 - 8*w]', '[631, 631, 1/2*w^5 - 7/2*w^3 - 1/2*w^2 + 3*w + 2]', '[631, 631, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 7/2*w^2 + 4*w + 2]', '[631, 631, -1/4*w^5 + 1/2*w^4 + 5/2*w^3 - 7/2*w^2 - 4*w + 2]', '[631, 631, -1/2*w^5 + 7/2*w^3 - 1/2*w^2 - 3*w + 2]', '[631, 631, 3/4*w^5 - 1/4*w^4 - 13/2*w^3 + 3/2*w^2 + 11*w - 1]', '[673, 673, -1/4*w^5 - 3/4*w^4 + 2*w^3 + 6*w^2 - 3*w - 7]', '[673, 673, -1/4*w^5 + 2*w^3 + 3/2*w^2 - 3*w - 5]', '[673, 673, 1/4*w^5 - 3/4*w^4 - 2*w^3 + 9/2*w^2 + 3*w - 2]', '[673, 673, 1/4*w^5 + 3/4*w^4 - 2*w^3 - 9/2*w^2 + 3*w + 2]', '[673, 673, 1/4*w^5 - 2*w^3 + 3/2*w^2 + 3*w - 5]', '[673, 673, 1/2*w^4 - 3*w^2 + w - 1]', '[727, 727, 1/4*w^5 - 1/4*w^4 - 5/2*w^3 + 2*w^2 + 7*w - 2]', '[727, 727, 1/2*w^5 + 1/4*w^4 - 9/2*w^3 - 3/2*w^2 + 7*w + 1]', '[727, 727, -w^3 - 1/2*w^2 + 5*w + 2]', '[727, 727, w^3 - 1/2*w^2 - 5*w + 2]', '[727, 727, 1/2*w^5 - 1/4*w^4 - 9/2*w^3 + 3/2*w^2 + 7*w - 1]', '[727, 727, -1/4*w^5 - 1/4*w^4 + 5/2*w^3 + 2*w^2 - 7*w - 2]', '[729, 3, -3]', '[743, 743, 1/4*w^5 + 3/4*w^4 - 5/2*w^3 - 11/2*w^2 + 5*w + 7]', '[743, 743, 1/2*w^3 - 1/2*w^2 - 4*w - 1]', '[743, 743, 1/2*w^4 - 1/2*w^3 - 5/2*w^2 + 3*w - 2]', '[743, 743, 1/2*w^4 + 1/2*w^3 - 5/2*w^2 - 3*w - 2]', '[743, 743, -1/2*w^3 - 1/2*w^2 + 4*w - 1]', '[743, 743, -1/4*w^5 + 3/4*w^4 + 5/2*w^3 - 11/2*w^2 - 5*w + 7]', '[769, 769, 1/4*w^5 - 1/4*w^4 - 2*w^3 + 2*w^2 + 3*w - 6]', '[769, 769, 1/4*w^5 - 3/4*w^4 - 5/2*w^3 + 11/2*w^2 + 6*w - 7]', '[769, 769, -1/4*w^4 + 1/2*w^3 + 3*w^2 - 2*w - 4]', '[769, 769, 1/4*w^4 + 1/2*w^3 - 3*w^2 - 2*w + 4]', '[769, 769, -1/4*w^5 - 3/4*w^4 + 5/2*w^3 + 11/2*w^2 - 6*w - 7]', '[769, 769, 1/4*w^5 + 1/4*w^4 - 2*w^3 - 2*w^2 + 3*w + 6]', '[839, 839, 1/4*w^5 + 1/2*w^4 - 5/2*w^3 - 5/2*w^2 + 6*w + 1]', '[839, 839, -1/4*w^5 + 1/4*w^4 + 5/2*w^3 - w^2 - 5*w - 4]', '[839, 839, 1/4*w^5 - 1/4*w^4 - 2*w^3 + 3*w^2 + 2*w - 7]', '[839, 839, -1/4*w^5 - 1/4*w^4 + 2*w^3 + 3*w^2 - 2*w - 7]', '[839, 839, 1/4*w^5 + 1/4*w^4 - 5/2*w^3 - w^2 + 5*w - 4]', '[839, 839, -1/4*w^5 + 1/2*w^4 + 5/2*w^3 - 5/2*w^2 - 6*w + 1]', '[841, 29, -3/4*w^4 + 11/2*w^2 - 6]', '[841, 29, -1/2*w^4 + 5/2*w^2 + 1]', '[841, 29, 3/4*w^4 - 5*w^2 + 4]', '[881, 881, -1/4*w^4 + w^3 + 3/2*w^2 - 5*w - 1]', '[881, 881, -1/4*w^5 + 5/2*w^3 - 1/2*w^2 - 7*w + 2]', '[881, 881, 1/2*w^5 + 1/4*w^4 - 9/2*w^3 - 2*w^2 + 7*w + 2]', '[881, 881, -1/2*w^5 + 1/4*w^4 + 9/2*w^3 - 2*w^2 - 7*w + 2]', '[881, 881, 1/4*w^5 - 5/2*w^3 - 1/2*w^2 + 7*w + 2]', '[881, 881, -1/4*w^4 - w^3 + 3/2*w^2 + 5*w - 1]', '[911, 911, -1/2*w^5 + 1/4*w^4 + 9/2*w^3 - 2*w^2 - 8*w]', '[911, 911, -1/4*w^5 + 1/2*w^4 + 2*w^3 - 4*w^2 - 2*w + 7]', '[911, 911, -1/2*w^4 + 1/2*w^3 + 3*w^2 - 2*w + 1]', '[911, 911, -1/2*w^4 - 1/2*w^3 + 3*w^2 + 2*w + 1]', '[911, 911, 1/4*w^5 + 1/2*w^4 - 2*w^3 - 4*w^2 + 2*w + 7]', '[911, 911, 1/2*w^5 + 1/4*w^4 - 9/2*w^3 - 2*w^2 + 8*w]', '[937, 937, -1/4*w^5 - 1/4*w^4 + 3*w^3 + 3/2*w^2 - 9*w - 1]', '[937, 937, 1/4*w^5 - 1/4*w^4 - 3*w^3 + 2*w^2 + 7*w - 2]', '[937, 937, 1/4*w^5 - 1/4*w^4 - 3/2*w^3 + 5/2*w^2 - 5]', '[937, 937, -1/4*w^5 - 1/4*w^4 + 3/2*w^3 + 5/2*w^2 - 5]', '[937, 937, -1/4*w^5 - 1/4*w^4 + 3*w^3 + 2*w^2 - 7*w - 2]', '[937, 937, -1/4*w^5 + 1/4*w^4 + 3*w^3 - 3/2*w^2 - 9*w + 1]', '[953, 953, -1/4*w^4 + 1/2*w^3 + 3*w^2 - 3*w - 6]', '[953, 953, -1/2*w^4 - 1/2*w^3 + 9/2*w^2 + 2*w - 7]', '[953, 953, -1/2*w^5 + 1/4*w^4 + 5*w^3 - 5/2*w^2 - 11*w + 3]', '[953, 953, -1/4*w^5 - 3/4*w^4 + 5/2*w^3 + 5*w^2 - 6*w - 3]', '[953, 953, -1/2*w^4 + 1/2*w^3 + 9/2*w^2 - 2*w - 7]', '[953, 953, 1/4*w^5 + 1/2*w^4 - 3/2*w^3 - 7/2*w^2 - w + 4]', '[967, 967, -1/4*w^5 - 1/2*w^4 + 3/2*w^3 + 7/2*w^2 - w - 7]', '[967, 967, 1/2*w^4 - 7/2*w^2 + 2*w + 7]', '[967, 967, 1/2*w^5 + 1/4*w^4 - 5*w^3 - w^2 + 10*w - 5]', '[967, 967, -1/2*w^5 + 1/4*w^4 + 5*w^3 - w^2 - 10*w - 5]', '[967, 967, 1/2*w^5 + 1/4*w^4 - 4*w^3 - 2*w^2 + 3*w + 2]', '[967, 967, 1/4*w^5 - 1/2*w^4 - 3/2*w^3 + 7/2*w^2 + w - 7]']}

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': [], 'class_number': 1, 'cm': False, 'coeffs': [-8, 0, 24, 0, -10, 0, 1], 'conductor': 56, 'degree': 6, 'dirichlet_group': [1, 37, 25, 9, 29, 53], 'disc_abs': 1229312, 'disc_rad': 14, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[6, 1]]], [5, [[6, 1]]], [7, [0]], [11, [[6, 1]]], [13, [[2, 3]]], [17, [[3, 2]]], [19, [[6, 1]]], [23, [[3, 2]]], [29, [[2, 3]]], [31, [[3, 2]]], [37, [[6, 1]]], [41, [[1, 6]]], [43, [[2, 3]]], [47, [[3, 2]]], [53, [[6, 1]]], [59, [[6, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [9, 4], 'galois_label': '6T1', 'galt': 1, 'grd': 10.350079527967589, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '6.6.1229312.1', 'local_algs': ['2.6.9.1', '7.3.2.2', '7.3.2.2'], 'monogenic': 0, 'num_ram': 2, 'r2': 0, 'ramps': [2, 7], 'rd': 10.350079528, 'regulator': {'__RealLiteral__': 0, 'data': '8.7234383498', 'prec': 40}, 'res': {'sex': ['1,-2,-1,1', '-2,0,1', '0,1']}, 'subfield_mults': [1, 1], 'subfields': ['-2.0.1', '1.-2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{2} - 2 \\)', '\\( \\frac{1}{4} a^{4} - \\frac{3}{2} a^{2} + 1 \\)', '\\( \\frac{1}{4} a^{5} - 2 a^{3} + 3 a + 1 \\)', '\\( \\frac{1}{4} a^{5} - \\frac{1}{4} a^{4} - 2 a^{3} + \\frac{3}{2} a^{2} + 3 a - 1 \\)', '\\( \\frac{1}{4} a^{5} - 2 a^{3} + \\frac{1}{2} a^{2} + 3 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2', '1/2*a^3', '1/4*a^4', '1/4*a^5']}

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

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