LMFDB - Higher genus family

Formats: - HTML - YAML - JSON - 2024-05-15T15:46:53.141752

Column	Type
braid	integer[]
cc	jsonb
cinv	jsonb
con	text
cyclic_trigonal	boolean
dim	smallint
eqn	jsonb
full_auto	text
full_label	text
g0	smallint
gen_vectors	jsonb
genus	smallint
group	text
group_order	integer
hyp_involution	jsonb
hyperelliptic	boolean
jacobian_decomp	jsonb
label	text
ndim	smallint
passport_label	text
r	smallint
realcc	integer[]
signH	text
signature	text
topological	integer[]
total_label	text

hgcwa_passports • Show schema

id: 12984
{'cc': [1, 1], 'con': '[10,16,26]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 2, 3, 1, 5, 6, 4, 8, 9, 7], [13, 14, 15, 16, 17, 18, 10, 11, 12, 22, 23, 24, 25, 26, 27, 19, 20, 21, 5, 6, 4, 8, 9, 7, 2, 3, 1], [18, 16, 17, 12, 10, 11, 15, 13, 14, 27, 25, 26, 21, 19, 20, 24, 22, 23, 7, 8, 9, 1, 2, 3, 4, 5, 6]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.1', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.1.1'}
id: 13049
{'cc': [2, 1], 'con': '[10,18,24]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 2, 3, 1, 5, 6, 4, 8, 9, 7], [14, 15, 13, 17, 18, 16, 11, 12, 10, 23, 24, 22, 26, 27, 25, 20, 21, 19, 6, 4, 5, 9, 7, 8, 3, 1, 2], [17, 18, 16, 11, 12, 10, 14, 15, 13, 26, 27, 25, 20, 21, 19, 23, 24, 22, 9, 7, 8, 3, 1, 2, 6, 4, 5]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.2', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.2.1'}
id: 13101
{'cc': [3, 1], 'con': '[10,20,22]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 2, 3, 1, 5, 6, 4, 8, 9, 7], [15, 13, 14, 18, 16, 17, 12, 10, 11, 24, 22, 23, 27, 25, 26, 21, 19, 20, 4, 5, 6, 7, 8, 9, 1, 2, 3], [16, 17, 18, 10, 11, 12, 13, 14, 15, 25, 26, 27, 19, 20, 21, 22, 23, 24, 8, 9, 7, 2, 3, 1, 5, 6, 4]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.3', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.3.1'}
id: 13147
{'cc': [4, 1], 'con': '[11,17,25]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[19, 20, 21, 22, 23, 24, 25, 26, 27, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16], [25, 26, 27, 19, 20, 21, 22, 23, 24, 8, 9, 7, 2, 3, 1, 5, 6, 4, 17, 18, 16, 11, 12, 10, 14, 15, 13], [23, 24, 22, 26, 27, 25, 20, 21, 19, 6, 4, 5, 9, 7, 8, 3, 1, 2, 15, 13, 14, 18, 16, 17, 12, 10, 11]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.4', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.4.1'}
id: 13182
{'cc': [5, 1], 'con': '[11,19,23]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[19, 20, 21, 22, 23, 24, 25, 26, 27, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16], [26, 27, 25, 20, 21, 19, 23, 24, 22, 9, 7, 8, 3, 1, 2, 6, 4, 5, 18, 16, 17, 12, 10, 11, 15, 13, 14], [22, 23, 24, 25, 26, 27, 19, 20, 21, 5, 6, 4, 8, 9, 7, 2, 3, 1, 14, 15, 13, 17, 18, 16, 11, 12, 10]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.5', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.5.1'}
id: 13209
{'cc': [6, 1], 'con': '[11,21,27]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[19, 20, 21, 22, 23, 24, 25, 26, 27, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16], [27, 25, 26, 21, 19, 20, 24, 22, 23, 7, 8, 9, 1, 2, 3, 4, 5, 6, 16, 17, 18, 10, 11, 12, 13, 14, 15], [24, 22, 23, 27, 25, 26, 21, 19, 20, 4, 5, 6, 7, 8, 9, 1, 2, 3, 13, 14, 15, 16, 17, 18, 10, 11, 12]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.6', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.6.1'}
id: 13234
{'cc': [7, 1], 'con': '[12,16,24]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 3, 1, 2, 6, 4, 5, 9, 7, 8], [13, 14, 15, 16, 17, 18, 10, 11, 12, 22, 23, 24, 25, 26, 27, 19, 20, 21, 5, 6, 4, 8, 9, 7, 2, 3, 1], [17, 18, 16, 11, 12, 10, 14, 15, 13, 26, 27, 25, 20, 21, 19, 23, 24, 22, 9, 7, 8, 3, 1, 2, 6, 4, 5]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.7', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.7.1'}
id: 13257
{'cc': [8, 1], 'con': '[12,18,22]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 3, 1, 2, 6, 4, 5, 9, 7, 8], [14, 15, 13, 17, 18, 16, 11, 12, 10, 23, 24, 22, 26, 27, 25, 20, 21, 19, 6, 4, 5, 9, 7, 8, 3, 1, 2], [16, 17, 18, 10, 11, 12, 13, 14, 15, 25, 26, 27, 19, 20, 21, 22, 23, 24, 8, 9, 7, 2, 3, 1, 5, 6, 4]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.8', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.8.1'}
id: 13276
{'cc': [9, 1], 'con': '[12,20,26]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 3, 1, 2, 6, 4, 5, 9, 7, 8], [15, 13, 14, 18, 16, 17, 12, 10, 11, 24, 22, 23, 27, 25, 26, 21, 19, 20, 4, 5, 6, 7, 8, 9, 1, 2, 3], [18, 16, 17, 12, 10, 11, 15, 13, 14, 27, 25, 26, 21, 19, 20, 24, 22, 23, 7, 8, 9, 1, 2, 3, 4, 5, 6]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.9', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.9.1'}
id: 13295
{'cc': [10, 1], 'con': '[13,17,23]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[20, 21, 19, 23, 24, 22, 26, 27, 25, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17], [25, 26, 27, 19, 20, 21, 22, 23, 24, 8, 9, 7, 2, 3, 1, 5, 6, 4, 17, 18, 16, 11, 12, 10, 14, 15, 13], [22, 23, 24, 25, 26, 27, 19, 20, 21, 5, 6, 4, 8, 9, 7, 2, 3, 1, 14, 15, 13, 17, 18, 16, 11, 12, 10]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.10', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.10.1'}
id: 13311
{'cc': [11, 1], 'con': '[13,19,27]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[20, 21, 19, 23, 24, 22, 26, 27, 25, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17], [26, 27, 25, 20, 21, 19, 23, 24, 22, 9, 7, 8, 3, 1, 2, 6, 4, 5, 18, 16, 17, 12, 10, 11, 15, 13, 14], [24, 22, 23, 27, 25, 26, 21, 19, 20, 4, 5, 6, 7, 8, 9, 1, 2, 3, 13, 14, 15, 16, 17, 18, 10, 11, 12]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.11', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.11.1'}
id: 13328
{'cc': [12, 1], 'con': '[13,21,25]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[20, 21, 19, 23, 24, 22, 26, 27, 25, 3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11, 15, 13, 14, 18, 16, 17], [27, 25, 26, 21, 19, 20, 24, 22, 23, 7, 8, 9, 1, 2, 3, 4, 5, 6, 16, 17, 18, 10, 11, 12, 13, 14, 15], [23, 24, 22, 26, 27, 25, 20, 21, 19, 6, 4, 5, 9, 7, 8, 3, 1, 2, 15, 13, 14, 18, 16, 17, 12, 10, 11]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.12', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.12.1'}
id: 13342
{'cc': [13, 1], 'con': '[14,16,22]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9], [13, 14, 15, 16, 17, 18, 10, 11, 12, 22, 23, 24, 25, 26, 27, 19, 20, 21, 5, 6, 4, 8, 9, 7, 2, 3, 1], [16, 17, 18, 10, 11, 12, 13, 14, 15, 25, 26, 27, 19, 20, 21, 22, 23, 24, 8, 9, 7, 2, 3, 1, 5, 6, 4]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.13', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.13.1'}
id: 13355
{'cc': [14, 1], 'con': '[14,18,26]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9], [14, 15, 13, 17, 18, 16, 11, 12, 10, 23, 24, 22, 26, 27, 25, 20, 21, 19, 6, 4, 5, 9, 7, 8, 3, 1, 2], [18, 16, 17, 12, 10, 11, 15, 13, 14, 27, 25, 26, 21, 19, 20, 24, 22, 23, 7, 8, 9, 1, 2, 3, 4, 5, 6]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.14', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.14.1'}
id: 13369
{'cc': [15, 1], 'con': '[14,20,24]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[12, 10, 11, 15, 13, 14, 18, 16, 17, 21, 19, 20, 24, 22, 23, 27, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9], [15, 13, 14, 18, 16, 17, 12, 10, 11, 24, 22, 23, 27, 25, 26, 21, 19, 20, 4, 5, 6, 7, 8, 9, 1, 2, 3], [17, 18, 16, 11, 12, 10, 14, 15, 13, 26, 27, 25, 20, 21, 19, 23, 24, 22, 9, 7, 8, 3, 1, 2, 6, 4, 5]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.15', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.15.1'}
id: 13381
{'cc': [16, 1], 'con': '[15,17,27]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[21, 19, 20, 24, 22, 23, 27, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [25, 26, 27, 19, 20, 21, 22, 23, 24, 8, 9, 7, 2, 3, 1, 5, 6, 4, 17, 18, 16, 11, 12, 10, 14, 15, 13], [24, 22, 23, 27, 25, 26, 21, 19, 20, 4, 5, 6, 7, 8, 9, 1, 2, 3, 13, 14, 15, 16, 17, 18, 10, 11, 12]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.16', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.16.1'}
id: 13392
{'cc': [17, 1], 'con': '[15,19,25]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[21, 19, 20, 24, 22, 23, 27, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [26, 27, 25, 20, 21, 19, 23, 24, 22, 9, 7, 8, 3, 1, 2, 6, 4, 5, 18, 16, 17, 12, 10, 11, 15, 13, 14], [23, 24, 22, 26, 27, 25, 20, 21, 19, 6, 4, 5, 9, 7, 8, 3, 1, 2, 15, 13, 14, 18, 16, 17, 12, 10, 11]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.17', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.17.1'}
id: 13403
{'cc': [18, 1], 'con': '[15,21,23]', 'dim': 0, 'eqn': [], 'full_auto': '[162,14]', 'full_label': '10.162-14.0.2-3-18', 'g0': 0, 'gen_vectors': [[21, 19, 20, 24, 22, 23, 27, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [27, 25, 26, 21, 19, 20, 24, 22, 23, 7, 8, 9, 1, 2, 3, 4, 5, 6, 16, 17, 18, 10, 11, 12, 13, 14, 15], [22, 23, 24, 25, 26, 27, 19, 20, 21, 5, 6, 4, 8, 9, 7, 2, 3, 1, 14, 15, 13, 17, 18, 16, 11, 12, 10]], 'genus': 10, 'group': '[27,2]', 'group_order': 27, 'jacobian_decomp': [[3, 1, 4], [3, 1, 5], [3, 1, 6], [1, 1, 10]], 'label': '10.27-2.0.9-9-9', 'ndim': 0, 'passport_label': '10.27-2.0.9-9-9.18', 'r': 3, 'signH': '[0,2,3,18]', 'signature': '[0,9,9,9]', 'total_label': '10.27-2.0.9-9-9.18.1'}

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.