LMFDB - Modular curve data - 12.32.0-12.a.1.1

Formats: - HTML - YAML - JSON - 2024-06-03T03:04:54.011034

Column	Type
CPlabel	text
Glabel	text
RSZBlabel	text
RZBlabel	text
SZlabel	text
Slabel	text
all_degree1_points_known	boolean
bad_primes	integer[]
canonical_conjugator	integer[]
canonical_generators	integer[]
cm_discriminants	integer[]
coarse_class	text
coarse_class_num	integer
coarse_index	integer
coarse_label	text
coarse_level	integer
coarse_num	integer
conductor	integer[]
contains_negative_one	boolean
curve_label	text
cusp_orbits	integer[]
cusp_widths	integer[]
cusps	integer
determinant_label	text
dims	integer[]
factorization	text[]
fine_num	integer
generators	integer[]
genus	integer
genus_minus_rank	integer
has_obstruction	smallint
index	integer
isogeny_orbits	integer[]
kummer_orbits	integer[]
label	text
lattice_labels	text[]
lattice_x	integer[]
level	integer
level_is_squarefree	boolean
level_radical	integer
log_conductor	numeric
models	smallint
mults	integer[]
name	text
newforms	text[]
nu2	integer
nu3	integer
num_bad_primes	integer
num_known_degree1_noncm_points	integer
num_known_degree1_noncusp_points	integer
num_known_degree1_points	integer
obstructions	integer[]
orbits	integer[]
parents	text[]
parents_conj	integer[]
pointless	boolean
power	boolean
psl2index	integer
psl2label	text
psl2level	integer
q_gonality	integer
q_gonality_bounds	integer[]
qbar_gonality	integer
qbar_gonality_bounds	integer[]
rank	integer
rational_cusps	integer
reductions	text[]
scalar_label	text
simple	boolean
sl2label	text
sl2level	integer
squarefree	boolean
trace_hash	bigint
traces	integer[]

{'CPlabel': '12B0', 'Glabel': '144.190', 'RSZBlabel': '12.32.0.3', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [7, 0, 8, 5], 'canonical_generators': [[0, 1, 1, 9], [0, 1, 7, 3], [0, 5, 7, 11], [0, 7, 1, 3], [0, 11, 1, 11], [9, 11, 7, 2]], 'cm_discriminants': [], 'coarse_class': '12.16.0.a', 'coarse_class_num': 1, 'coarse_index': 16, 'coarse_label': '12.16.0.a.1', 'coarse_level': 12, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2]], 'cusp_widths': [[4, 1], [12, 1]], 'cusps': 2, 'determinant_label': '1.1.1', 'dims': None, 'factorization': ['3.8.0-3.a.1.1', '4.4.0-2.a.1.1'], 'fine_num': 1, 'generators': [[2, 5, 9, 1], [8, 9, 9, 1]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 32, 'isogeny_orbits': [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 6, 1], [6, 3, 1], [6, 9, 1], [12, 6, 1], [12, 18, 1]], 'kummer_orbits': [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 6, 1], [6, 3, 1], [6, 9, 1], [12, 12, 1], [12, 36, 1]], 'label': '12.32.0-12.a.1.1', 'lattice_labels': None, 'lattice_x': None, 'level': 12, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 4, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 14, 'num_known_degree1_noncusp_points': 14, 'num_known_degree1_points': 15, 'obstructions': None, 'orbits': [[2, 3, 1], [3, 2, 1], [3, 3, 2], [4, 12, 1], [6, 6, 1], [6, 9, 2], [12, 24, 1], [12, 36, 2]], 'parents': ['6.16.0-6.a.1.1', '12.16.0-6.a.1.3'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 16, 'psl2label': '12.16.0.a.1', 'psl2level': 12, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 2, 'reductions': ['2.2.0.a.1', '3.8.0-3.a.1.1', '4.4.0-2.a.1.1', '6.16.0-6.a.1.1'], 'scalar_label': '12.4.1', 'simple': None, 'sl2label': '12.32.0-12.a.1.1', 'sl2level': 12, 'squarefree': None, 'trace_hash': 0, 'traces': None}

Column	Type
CPlabel	text
Glabel	text
RSZBlabel	text
RZBlabel	text
SZlabel	text
Slabel	text
all_degree1_points_known	boolean
bad_primes	integer[]
canonical_conjugator	integer[]
canonical_generators	integer[]
cm_discriminants	integer[]
coarse_class	text
coarse_class_num	integer
coarse_index	integer
coarse_label	text
coarse_level	integer
coarse_num	integer
conductor	integer[]
contains_negative_one	boolean
curve_label	text
cusp_orbits	integer[]
cusp_widths	integer[]
cusps	integer
determinant_label	text
dims	integer[]
factorization	text[]
fine_num	integer
generators	integer[]
genus	integer
genus_minus_rank	integer
has_obstruction	smallint
index	integer
isogeny_orbits	integer[]
kummer_orbits	integer[]
label	text
lattice_labels	text[]
lattice_x	integer[]
level	integer
level_is_squarefree	boolean
level_radical	integer
log_conductor	numeric
models	smallint
mults	integer[]
name	text
newforms	text[]
nu2	integer
nu3	integer
num_bad_primes	integer
num_known_degree1_noncm_points	integer
num_known_degree1_noncusp_points	integer
num_known_degree1_points	integer
obstructions	integer[]
orbits	integer[]
parents	text[]
parents_conj	integer[]
pointless	boolean
power	boolean
psl2index	integer
psl2label	text
psl2level	integer
q_gonality	integer
q_gonality_bounds	integer[]
qbar_gonality	integer
qbar_gonality_bounds	integer[]
rank	integer
rational_cusps	integer
reductions	text[]
scalar_label	text
simple	boolean
sl2label	text
sl2level	integer
squarefree	boolean
trace_hash	bigint
traces	integer[]

gps_gl2zhat_fine • Show schema

{'CPlabel': '12B0', 'Glabel': '288.1037', 'RSZBlabel': '12.16.0.9', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [7, 0, 8, 5], 'canonical_generators': [[0, 1, 1, 9], [0, 1, 7, 3], [0, 1, 11, 1], [0, 5, 11, 9], [0, 7, 5, 1], [3, 1, 5, 10]], 'cm_discriminants': [], 'coarse_class': '12.16.0.a', 'coarse_class_num': 1, 'coarse_index': 16, 'coarse_label': '12.16.0.a.1', 'coarse_level': 12, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 2]], 'cusp_widths': [[4, 1], [12, 1]], 'cusps': 2, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[5, 10, 0, 5], [7, 0, 0, 11], [10, 3, 9, 5]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 16, 'isogeny_orbits': [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 6, 1], [6, 3, 1], [6, 9, 1], [12, 6, 1], [12, 18, 1]], 'kummer_orbits': [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 6, 1], [6, 3, 1], [6, 9, 1], [12, 12, 1], [12, 36, 1]], 'label': '12.16.0.a.1', 'lattice_labels': ['1.1.0.a.1', '2.2.0.a.1', '3.4.0.a.1', '6.8.0.a.1', '12.16.0.a.1'], 'lattice_x': [4885, 7643, 2126, 4885, 4885], 'level': 12, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': None, 'models': 1, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 4, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 14, 'num_known_degree1_noncusp_points': 14, 'num_known_degree1_points': 15, 'obstructions': [], 'orbits': [[2, 3, 1], [3, 2, 1], [3, 6, 1], [4, 12, 1], [6, 6, 1], [6, 18, 1], [12, 24, 1], [12, 72, 1]], 'parents': ['6.8.0.a.1'], 'parents_conj': [[1, 0, 0, 1]], 'pointless': False, 'power': None, 'psl2index': 16, 'psl2label': '12.16.0.a.1', 'psl2level': 12, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 2, 'reductions': ['2.2.0.a.1', '2.2.0.a.1', '3.4.0.a.1', '6.8.0.a.1'], 'scalar_label': '12.2.1', 'simple': None, 'sl2label': '12.16.0.a.1', 'sl2level': 12, 'squarefree': None, 'trace_hash': 0, 'traces': []}

modcurve 12.16.0.a.1 does not appear in modcurve_models

Column	Type
codomain_label	text
codomain_model_type	smallint
coordinates	text[]
degree	integer
domain_label	text
domain_model_type	smallint
dont_display	boolean
factored	boolean
leading_coefficients	text[]
upload_id	bigint

modcurve_modelmaps • Show schema

{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['x^16*(27*x^4+16*y^4)^3*(243*x^4+16*y^4)', 'y^4*x^28'], 'degree': 16, 'domain_label': '12.16.0.a.1', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['1', '2^4*3^6'], 'upload_id': None}

Column	Type
Elabel	text
ainvs	text
cardinality	integer
cm	smallint
conductor_norm	numeric
coordinates	jsonb
curve_genus	integer
curve_index	integer
curve_label	text
curve_level	integer
curve_name	text
cusp	boolean
degree	smallint
isolated	smallint
j_field	text
j_height	double precision
jinv	text
jorig	text
quo_info	smallint[]
residue_field	text
upload_id	bigint

modcurve_points • Show schema

id: 5063
{'Elabel': '324.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 324, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 8.84101431048389, 'jinv': '6912', 'jorig': '6912', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 56040
{'Elabel': '7938.m1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 7938, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 16.0209741016143, 'jinv': '9074457/4096', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 1709683
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['0:1', '1:0']}, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': True, 'degree': 1, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 3459
{'Elabel': '196.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 196, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 19.8237091860548, 'jinv': '406749952', 'jorig': '406749952', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 31830
{'Elabel': '3698.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 3698, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 20.4316843007922, 'jinv': '747081097/4096', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 56014
{'Elabel': '7938.b1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 7938, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 16.0209741016143, 'jinv': '9074457/4096', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 202666
{'Elabel': '44652.e2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 44652, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 15.4937817558188, 'jinv': '5356288/729', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 350480
{'Elabel': '92450.ba1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 92450, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 20.4316843007922, 'jinv': '747081097/4096', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 247895
{'Elabel': '58482.b2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 58482, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 17.9157367395026, 'jinv': '60353937/16', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 247914
{'Elabel': '58482.o1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 58482, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 17.9157367395026, 'jinv': '60353937/16', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 530437
{'Elabel': '160178.d1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 160178, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 24.2832651848978, 'jinv': '35163174217/16777216', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 1010442
{'Elabel': '374978.b1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 374978, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 30.8684597304697, 'jinv': '25468403731777/16', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 1066818
{'Elabel': '402486.y2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 402486, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 16.8404284087802, 'jinv': '20592313/11664', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 1066823
{'Elabel': '402486.bh2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 402486, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 16.8404284087802, 'jinv': '20592313/11664', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 1240661
{'Elabel': '491172.h2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 491172, 'coordinates': None, 'curve_genus': 0, 'curve_index': 16, 'curve_label': '12.16.0.a.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 38.3883126770402, 'jinv': '46971276760146688/10673289', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}

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Classical	Maass
Hilbert	Bianchi
Siegel

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Modular curves
Higher genus families
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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.