LMFDB - Higher genus passport

Formats: - HTML - YAML - JSON - 2025-06-12T21:13:56.069216

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: 154
{'cc': [1, 1], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[5, 6, 8, 7, 1, 2, 4, 3], [3, 4, 1, 2, 7, 8, 5, 6], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.1'}
id: 163
{'cc': [1, 2], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[6, 5, 7, 8, 2, 1, 3, 4], [3, 4, 1, 2, 7, 8, 5, 6], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.2'}
id: 174
{'cc': [1, 3], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[8, 7, 5, 6, 4, 3, 1, 2], [3, 4, 1, 2, 7, 8, 5, 6], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.3'}
id: 186
{'cc': [1, 4], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[7, 8, 6, 5, 3, 4, 2, 1], [3, 4, 1, 2, 7, 8, 5, 6], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.4'}
id: 195
{'cc': [1, 5], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[3, 4, 1, 2, 7, 8, 5, 6], [5, 6, 8, 7, 1, 2, 4, 3], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.5'}
id: 204
{'cc': [1, 6], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[4, 3, 2, 1, 8, 7, 6, 5], [5, 6, 8, 7, 1, 2, 4, 3], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.6'}
id: 216
{'cc': [1, 7], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[8, 7, 5, 6, 4, 3, 1, 2], [5, 6, 8, 7, 1, 2, 4, 3], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.7'}
id: 222
{'cc': [1, 8], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[7, 8, 6, 5, 3, 4, 2, 1], [5, 6, 8, 7, 1, 2, 4, 3], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.8'}
id: 228
{'cc': [1, 9], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[5, 6, 8, 7, 1, 2, 4, 3], [4, 3, 2, 1, 8, 7, 6, 5], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.9'}
id: 240
{'cc': [1, 10], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[6, 5, 7, 8, 2, 1, 3, 4], [4, 3, 2, 1, 8, 7, 6, 5], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.10'}
id: 242
{'cc': [1, 11], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[8, 7, 5, 6, 4, 3, 1, 2], [4, 3, 2, 1, 8, 7, 6, 5], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.11'}
id: 250
{'cc': [1, 12], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[7, 8, 6, 5, 3, 4, 2, 1], [4, 3, 2, 1, 8, 7, 6, 5], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.12'}
id: 256
{'cc': [1, 13], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[3, 4, 1, 2, 7, 8, 5, 6], [6, 5, 7, 8, 2, 1, 3, 4], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.13'}
id: 264
{'cc': [1, 14], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[4, 3, 2, 1, 8, 7, 6, 5], [6, 5, 7, 8, 2, 1, 3, 4], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.14'}
id: 268
{'cc': [1, 15], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[8, 7, 5, 6, 4, 3, 1, 2], [6, 5, 7, 8, 2, 1, 3, 4], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.15'}
id: 272
{'cc': [1, 16], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[7, 8, 6, 5, 3, 4, 2, 1], [6, 5, 7, 8, 2, 1, 3, 4], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.16'}
id: 280
{'cc': [1, 17], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[3, 4, 1, 2, 7, 8, 5, 6], [8, 7, 5, 6, 4, 3, 1, 2], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.17'}
id: 286
{'cc': [1, 18], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[5, 6, 8, 7, 1, 2, 4, 3], [8, 7, 5, 6, 4, 3, 1, 2], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.18'}
id: 290
{'cc': [1, 19], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[4, 3, 2, 1, 8, 7, 6, 5], [8, 7, 5, 6, 4, 3, 1, 2], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.19'}
id: 298
{'cc': [1, 20], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[6, 5, 7, 8, 2, 1, 3, 4], [8, 7, 5, 6, 4, 3, 1, 2], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.20'}
id: 302
{'cc': [1, 21], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[3, 4, 1, 2, 7, 8, 5, 6], [7, 8, 6, 5, 3, 4, 2, 1], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.21'}
id: 312
{'cc': [1, 22], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[5, 6, 8, 7, 1, 2, 4, 3], [7, 8, 6, 5, 3, 4, 2, 1], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.22'}
id: 314
{'cc': [1, 23], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[4, 3, 2, 1, 8, 7, 6, 5], [7, 8, 6, 5, 3, 4, 2, 1], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.23'}
id: 324
{'cc': [1, 24], 'con': '[2]', 'dim': 1, 'full_auto': '[16,11]', 'full_label': '3.16-11.0.2-2-2-4', 'g0': 1, 'gen_vectors': [[6, 5, 7, 8, 2, 1, 3, 4], [7, 8, 6, 5, 3, 4, 2, 1], [2, 1, 4, 3, 6, 5, 8, 7]], 'genus': 3, 'group': '[8,3]', 'group_order': 8, 'jacobian_decomp': [[1, 1, 1], [1, 2, 5]], 'label': '3.8-3.1.2', 'passport_label': '3.8-3.1.2.1', 'r': 1, 'signH': '[0,2,2,2,4]', 'signature': '[1,2]', 'total_label': '3.8-3.1.2.1.24'}

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.