LMFDB - Modular curve data - 16.96.0-16.z.1.2

Formats: - HTML - YAML - JSON - 2024-05-18T02:08:52.775693

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': '16H0', 'Glabel': '256.6025', 'RSZBlabel': '16.96.0.98', 'RZBlabel': 'X230e', 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2], 'canonical_conjugator': [5, 0, 11, 1], 'canonical_generators': [[0, 1, 11, 14], [0, 1, 15, 2], [0, 9, 3, 14], [0, 9, 5, 12], [0, 9, 7, 2]], 'cm_discriminants': [], 'coarse_class': '16.48.0.z', 'coarse_class_num': 26, 'coarse_index': 48, 'coarse_label': '16.48.0.z.1', 'coarse_level': 16, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 4]], 'cusp_widths': [[1, 4], [2, 2], [4, 2], [16, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 2, 'generators': [[5, 13, 8, 9], [9, 0, 8, 15], [9, 12, 0, 3]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 96, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [16, 2, 2], [16, 4, 1], [16, 16, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 2], [8, 2, 1], [8, 4, 1], [8, 16, 1], [16, 4, 2], [16, 8, 3], [16, 64, 1]], 'label': '16.96.0-16.z.1.2', 'lattice_labels': None, 'lattice_x': None, 'level': 16, 'level_is_squarefree': False, 'level_radical': 2, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 1, 'num_known_degree1_noncm_points': 7, 'num_known_degree1_noncusp_points': 7, 'num_known_degree1_points': 8, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 2, 1], [4, 8, 1], [8, 1, 4], [8, 2, 2], [8, 8, 1], [8, 32, 1], [16, 4, 4], [16, 8, 2], [16, 16, 2], [16, 128, 1]], 'parents': ['8.48.0-8.bb.1.1', '16.48.0-8.bb.1.2', '16.48.0-16.e.2.2', '16.48.0-16.e.2.7', '16.48.0-16.h.1.2', '16.48.0-16.h.1.16'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 48, 'psl2label': '16.48.0.b.1', 'psl2level': 16, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 2, 'reductions': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.48.0-8.bb.1.1'], 'scalar_label': '8.4.1', 'simple': None, 'sl2label': '16.96.0-16.b.1.2', 'sl2level': 16, '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': '16H0', 'Glabel': None, 'RSZBlabel': '16.48.0.102', 'RZBlabel': 'X230', 'SZlabel': '16H0-16e', 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2], 'canonical_conjugator': [5, 0, 11, 1], 'canonical_generators': [[0, 1, 11, 14], [0, 1, 15, 2], [0, 7, 9, 14], [0, 7, 11, 4], [0, 7, 13, 2], [0, 9, 7, 2]], 'cm_discriminants': [], 'coarse_class': '16.48.0.z', 'coarse_class_num': 26, 'coarse_index': 48, 'coarse_label': '16.48.0.z.1', 'coarse_level': 16, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 4]], 'cusp_widths': [[1, 4], [2, 2], [4, 2], [16, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[1, 0, 8, 5], [7, 4, 8, 3], [11, 1, 0, 9], [11, 13, 8, 15]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [16, 2, 2], [16, 4, 1], [16, 16, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 1, 2], [4, 4, 1], [8, 1, 2], [8, 2, 1], [8, 4, 1], [8, 16, 1], [16, 4, 2], [16, 8, 3], [16, 64, 1]], 'label': '16.48.0.z.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '8.24.0.bb.1', '16.24.0.e.2', '16.24.0.h.1', '16.48.0.z.1'], 'lattice_x': [5901, 5901, 5901, 5901, 2008, 5901, 8882, 5901], 'level': 16, 'level_is_squarefree': False, 'level_radical': 2, 'log_conductor': None, 'models': 1, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 1, 'num_known_degree1_noncm_points': 7, 'num_known_degree1_noncusp_points': 7, 'num_known_degree1_points': 8, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 2], [4, 8, 1], [8, 2, 2], [8, 4, 1], [8, 8, 1], [8, 32, 1], [16, 8, 2], [16, 16, 3], [16, 128, 1]], 'parents': ['8.24.0.bb.1', '16.24.0.e.2', '16.24.0.h.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1], [1, 13, 12, 7]], 'pointless': False, 'power': None, 'psl2index': 48, 'psl2label': '16.48.0.b.1', 'psl2level': 16, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 2, 'reductions': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1'], 'scalar_label': '8.2.2', 'simple': None, 'sl2label': '16.48.0.b.1', 'sl2level': 16, 'squarefree': None, 'trace_hash': 0, 'traces': []}

modcurve 16.48.0.z.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^48*(x^16-16*x^14*y^2+48*x^12*y^4+64*x^10*y^6-160*x^8*y^8+256*x^6*y^10+768*x^4*y^12-1024*x^2*y^14+256*y^16)^3', 'y^16*x^64*(x^2-2*y^2)^4*(x^2+2*y^2)^2*(x^2-4*x*y+2*y^2)*(x^2+4*x*y+2*y^2)'], 'degree': 48, 'domain_label': '16.48.0.z.1', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['1', '2^8'], '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: 1540
{'Elabel': '42.a5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 42, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.z.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 15.7880705667147, 'jinv': '-7189057/16128', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 1711506
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['-2,1:1,0', '0,1:1,0']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.z.1', 'curve_level': 16, 'curve_name': None, 'cusp': True, 'degree': 2, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '2.2.8.1', 'upload_id': None}
id: 1848193
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['0:1', '1:0']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.z.1', 'curve_level': 16, '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: 8997
{'Elabel': '714.f5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 714, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.z.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 45.0927944453665, 'jinv': '38331145780597164097/55468445663232', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 70153
{'Elabel': '10626.p6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 10626, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.z.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 46.2762652751398, 'jinv': '125177609053596564863/73635189229502208', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 147111
{'Elabel': '29274.bj6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 29274, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.z.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 59.6371808423632, 'jinv': '-79450851511794083168203777/59901777677855490048', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 691234
{'Elabel': '227010.bk4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 227010, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.z.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 74.793591496411, 'jinv': '303699494199600230500999432823041/2621771300039062500000000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 728845
{'Elabel': '243474.y4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 243474, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.z.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 82.3620528273534, 'jinv': '588010472756223448971259933329689857/921126937566439960215552', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 1103659
{'Elabel': '420546.br4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 420546, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '16.48.0.z.1', 'curve_level': 16, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 67.8056561036079, 'jinv': '280299477128278939052609797057/72101228095800836352', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}

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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.