LMFDB - Modular curve data - 60.144.1-60.cf.1.2

Formats: - HTML - YAML - JSON - 2024-06-01T17:34:37.804720

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': '10K1', 'Glabel': None, 'RSZBlabel': '60.144.1.303', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 5], 'canonical_conjugator': [28, 3, 17, 29], 'canonical_generators': [[0, 1, 23, 52], [0, 1, 29, 58], [0, 19, 1, 52], [0, 41, 49, 38], [11, 10, 50, 51], [31, 42, 48, 7], [59, 0, 50, 59], [59, 50, 0, 59]], 'cm_discriminants': [], 'coarse_class': '60.72.1.cf', 'coarse_class_num': 58, 'coarse_index': 72, 'coarse_label': '60.72.1.cf.1', 'coarse_level': 60, 'coarse_num': 1, 'conductor': [[2, 4], [3, 2], [5, 2]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 3], [4, 1]], 'cusp_widths': [[2, 6], [10, 6]], 'cusps': 12, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 2, 'generators': [[1, 10, 52, 39], [9, 5, 56, 49], [37, 20, 42, 19], [59, 15, 54, 1]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 144, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [5, 1, 1], [5, 5, 1], [6, 4, 1], [6, 8, 1], [10, 1, 1], [10, 2, 1], [10, 5, 1], [10, 10, 1], [12, 8, 1], [12, 16, 1], [15, 4, 1], [15, 20, 1], [20, 2, 1], [20, 4, 1], [20, 10, 1], [20, 20, 1], [30, 4, 1], [30, 8, 1], [30, 20, 1], [30, 40, 1], [60, 8, 1], [60, 16, 1], [60, 40, 1], [60, 80, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [5, 1, 2], [5, 10, 1], [6, 4, 1], [6, 8, 1], [10, 1, 2], [10, 2, 2], [10, 10, 1], [10, 20, 1], [12, 16, 1], [12, 32, 1], [15, 8, 2], [15, 80, 1], [20, 4, 2], [20, 8, 2], [20, 40, 1], [20, 80, 1], [30, 8, 2], [30, 16, 2], [30, 80, 1], [30, 160, 1], [60, 32, 2], [60, 64, 2], [60, 320, 1], [60, 640, 1]], 'label': '60.144.1-60.cf.1.2', 'lattice_labels': None, 'lattice_x': None, 'level': 60, 'level_is_squarefree': False, 'level_radical': 30, 'log_conductor': {'__RealLiteral__': 0, 'data': '8.18868912444420136966', 'prec': 74}, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': 1, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 1, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 4, 1], [4, 8, 1], [5, 2, 2], [5, 20, 1], [6, 8, 1], [6, 16, 1], [10, 2, 2], [10, 4, 2], [10, 20, 1], [10, 40, 1], [12, 32, 1], [12, 64, 1], [15, 16, 2], [15, 160, 1], [20, 8, 2], [20, 16, 2], [20, 80, 1], [20, 160, 1], [30, 16, 2], [30, 32, 2], [30, 160, 1], [30, 320, 1], [60, 64, 2], [60, 128, 2], [60, 640, 1], [60, 1280, 1]], 'parents': ['20.72.0-10.a.2.12', '60.72.0-10.a.2.5'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 72, 'psl2label': '10.72.1.a.1', 'psl2level': 10, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '5.12.0.a.1', '5.12.0.a.1', '10.36.0.a.2', '10.36.0.a.2', '20.72.0-10.a.2.12'], 'scalar_label': '5.4.1', 'simple': True, 'sl2label': '20.144.1-10.a.1.2', 'sl2level': 20, 'squarefree': True, 'trace_hash': 494513997903162760, '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': '10K1', 'Glabel': None, 'RSZBlabel': '60.72.1.26', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 5], 'canonical_conjugator': [28, 3, 57, 49], 'canonical_generators': [[0, 1, 23, 52], [0, 1, 29, 58], [0, 19, 1, 52], [0, 19, 11, 22], [1, 0, 10, 1], [1, 10, 0, 1], [11, 10, 50, 51], [31, 42, 48, 7]], 'cm_discriminants': [], 'coarse_class': '60.72.1.cf', 'coarse_class_num': 58, 'coarse_index': 72, 'coarse_label': '60.72.1.cf.1', 'coarse_level': 60, 'coarse_num': 1, 'conductor': [[2, 4], [3, 2], [5, 2]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 3], [4, 1]], 'cusp_widths': [[2, 6], [10, 6]], 'cusps': 12, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[13, 45, 28, 59], [17, 10, 52, 21], [41, 50, 14, 49], [43, 40, 38, 31], [57, 5, 58, 51]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 72, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [5, 1, 1], [5, 5, 1], [6, 4, 1], [6, 8, 1], [10, 1, 1], [10, 2, 1], [10, 5, 1], [10, 10, 1], [12, 8, 1], [12, 16, 1], [15, 4, 1], [15, 20, 1], [20, 2, 1], [20, 4, 1], [20, 10, 1], [20, 20, 1], [30, 4, 1], [30, 8, 1], [30, 20, 1], [30, 40, 1], [60, 8, 1], [60, 16, 1], [60, 40, 1], [60, 80, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [5, 1, 2], [5, 10, 1], [6, 4, 1], [6, 8, 1], [10, 1, 2], [10, 2, 2], [10, 10, 1], [10, 20, 1], [12, 16, 1], [12, 32, 1], [15, 8, 2], [15, 80, 1], [20, 4, 2], [20, 8, 2], [20, 40, 1], [20, 80, 1], [30, 8, 2], [30, 16, 2], [30, 80, 1], [30, 160, 1], [60, 32, 2], [60, 64, 2], [60, 320, 1], [60, 640, 1]], 'label': '60.72.1.cf.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '5.6.0.a.1', '5.12.0.a.1', '10.18.0.a.1', '10.36.0.a.2', '60.2.0.a.1', '60.6.0.a.1', '60.12.0.bo.1', '60.12.1.n.1', '60.24.1.bd.1', '60.36.0.e.1', '60.36.1.bf.1', '60.72.1.cf.1'], 'lattice_x': [5907, 8159, 4121, 3324, 8297, 6566, 5907, 7418, 742, 5907, 1896, 3874, 9258, 5220], 'level': 60, 'level_is_squarefree': False, 'level_radical': 30, 'log_conductor': {'__RealLiteral__': 0, 'data': '8.18868912444420136966', 'prec': 74}, 'models': None, 'mults': [1], 'name': None, 'newforms': ['3600.2.a.be'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': 1, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 1, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 4, 1], [4, 8, 1], [5, 2, 2], [5, 20, 1], [6, 8, 1], [6, 16, 1], [10, 2, 2], [10, 4, 2], [10, 20, 1], [10, 40, 1], [12, 32, 1], [12, 64, 1], [15, 16, 2], [15, 160, 1], [20, 8, 2], [20, 16, 2], [20, 80, 1], [20, 160, 1], [30, 16, 2], [30, 32, 2], [30, 160, 1], [30, 320, 1], [60, 64, 2], [60, 128, 2], [60, 640, 1], [60, 1280, 1]], 'parents': ['10.36.0.a.2', '60.24.1.bd.1', '60.36.0.e.1', '60.36.1.bf.1'], 'parents_conj': [[45, 41, 14, 5], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': True, 'psl2index': 72, 'psl2label': '10.72.1.a.1', 'psl2level': 10, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '5.12.0.a.1', '5.12.0.a.1', '10.36.0.a.2', '10.36.0.a.2', '10.36.0.a.2'], 'scalar_label': '5.2.1', 'simple': True, 'sl2label': '10.72.1.a.1', 'sl2level': 10, 'squarefree': True, 'trace_hash': 494513997903162760, 'traces': [0, 0, 0, 2, 0, -2, -6, 4, -6, -6, 4, -2, -6, -10, 6, -6, 12, 2, 2, -12, -2, -8, -6, 6, -2, -6, 14, 6, 2, -6, 2, 0, 18, 4, 6, -20, 22, -10, -18, -6, -12, -10, -12, -26, 18, -8, 16, -10, 6, 14, -6, -24, 14, 0, -6, 18, -18, -20, -26, -6, 14, -30, 2, 12, 22, -6, -8, -2, 30, -10, 18, 24, -22, -26, 28, -6, 6, -2, 30, -34, 36, 26, 36, -2, -8, -6, -6, -26, -30, 14, 30, -24, 26, 0, 4, 18, -6, 6, 14, 14, 26, -30, 18, -30, -8, 22, 6, 18, 0, -10, -22, -2, -6, -20, 28, 18, 14, -42, 42, 36, -22, 46, 18, 42, -8, 30, -34, -24, -46, 22, -20, -6, 4, 22, -42, 2, -30, 26, 42, 6, 16, 54, 38, 30, 2, -48, -50, 18, 4, -6, -26, 18, 14, -18, -46, 12, 16, 42, 22, 18, -18, -6, -22, -24, 18, 18, 4, -26]}

modcurve 60.72.1.cf.1 does not appear in modcurve_models
domain_label 60.72.1.cf.1 does not appear in modcurve_modelmaps

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

{'Elabel': '11550.f1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 11550, 'coordinates': None, 'curve_genus': 1, 'curve_index': 72, 'curve_label': '60.72.1.cf.1', 'curve_level': 60, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 53.9178262574465, 'jinv': '260744057755293612689909/8504954620259328', '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.