LMFDB - Modular curve data - 40.48.0-8.n.1.3

Formats: - HTML - YAML - JSON - 2024-05-09T21:06:11.434184

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': '4G0', 'Glabel': None, 'RSZBlabel': '40.48.0.629', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [11, 20, 15, 21], 'canonical_generators': [[1, 0, 8, 1], [1, 8, 0, 1], [9, 8, 32, 33], [11, 0, 0, 11], [16, 25, 25, 36], [16, 25, 35, 16], [19, 20, 20, 19], [23, 0, 0, 39], [24, 15, 5, 4], [39, 0, 20, 39], [39, 20, 0, 39]], 'cm_discriminants': [], 'coarse_class': '8.24.0.n', 'coarse_class_num': 14, 'coarse_index': 24, 'coarse_label': '8.24.0.n.1', 'coarse_level': 8, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[2, 3]], 'cusp_widths': [[4, 6]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 3, 'generators': [[13, 4, 36, 37], [23, 33, 14, 5], [25, 7, 2, 35], [37, 12, 34, 7]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 3], [5, 6, 1], [8, 4, 3], [10, 6, 1], [10, 12, 1], [20, 12, 3], [40, 24, 3]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 3], [5, 12, 1], [8, 8, 3], [10, 12, 1], [10, 24, 1], [20, 48, 3], [40, 192, 3]], 'label': '40.48.0-8.n.1.3', 'lattice_labels': None, 'lattice_x': None, 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 6, 'num_known_degree1_noncusp_points': 6, 'num_known_degree1_points': 7, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [4, 4, 3], [5, 24, 1], [8, 16, 3], [10, 24, 1], [10, 48, 1], [20, 96, 3], [40, 384, 3]], 'parents': [], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 24, 'psl2label': '4.24.0.a.1', 'psl2level': 4, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.12.0.f.1', '4.12.0.f.1', '8.24.0.n.1'], 'scalar_label': '8.2.1', 'simple': None, 'sl2label': '8.48.0-4.a.1.3', 'sl2level': 8, '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': '4G0', 'Glabel': '64.202', 'RSZBlabel': '8.24.0.80', 'RZBlabel': 'X76', 'SZlabel': '4G0-8b', 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2], 'canonical_conjugator': [1, 0, 7, 7], 'canonical_generators': [[0, 1, 1, 4], [0, 1, 3, 0], [0, 1, 3, 4], [1, 0, 4, 1], [1, 4, 0, 1], [3, 0, 0, 3], [5, 4, 4, 5]], 'cm_discriminants': [], 'coarse_class': '8.24.0.n', 'coarse_class_num': 14, 'coarse_index': 24, 'coarse_label': '8.24.0.n.1', 'coarse_level': 8, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 3]], 'cusp_widths': [[4, 6]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[1, 0, 4, 1], [5, 5, 2, 3], [7, 0, 6, 5], [7, 3, 2, 5]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 24, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 3], [8, 4, 3]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 3], [8, 8, 3]], 'label': '8.24.0.n.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.e.1', '4.12.0.f.1', '8.2.0.a.1', '8.6.0.a.1', '8.6.0.c.1', '8.12.0.f.1', '8.12.0.t.1', '8.24.0.n.1'], 'lattice_x': [2159, 3460, 5587, 8508, 857, 1016, 3301, 3301, 5587, 5587], 'level': 8, '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': 6, 'num_known_degree1_noncusp_points': 6, 'num_known_degree1_points': 7, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [4, 4, 3], [8, 16, 3]], 'parents': ['4.12.0.f.1', '8.12.0.f.1', '8.12.0.t.1'], 'parents_conj': [[0, 1, 1, 7], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': None, 'psl2index': 24, 'psl2label': '4.24.0.a.1', 'psl2level': 4, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 0, 'reductions': ['2.3.0.a.1', '4.12.0.f.1'], 'scalar_label': '1.1.1', 'simple': None, 'sl2label': '4.24.0.a.1', 'sl2level': 4, 'squarefree': None, 'trace_hash': 0, 'traces': []}

modcurve 8.24.0.n.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+y)^24*(x^4+40*x^3*y+132*x^2*y^2-176*x*y^3-188*y^4)^3*(5*x^4+8*x^3*y+84*x^2*y^2+272*x*y^3+596*y^4)^3', '(x+y)^24*(x^2+2*y^2)^4*(x^2-4*x*y-14*y^2)^4*(x^2+8*x*y+34*y^2)^4'], 'degree': 24, 'domain_label': '8.24.0.n.1', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-2^6', '3^4'], '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: 1644334
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['-4,3:1,0']}, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '8.24.0.n.1', 'curve_level': 8, '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': '2.0.8.1', 'upload_id': None}
id: 1847977
{'Elabel': None, 'ainvs': None, 'cardinality': 0, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['-1:1']}, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '8.24.0.n.1', 'curve_level': 8, '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: 9378
{'Elabel': '768.b2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 768, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '8.24.0.n.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 8.98719682066197, 'jinv': '-8000/81', 'jorig': '-8000/81', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 58726
{'Elabel': '8448.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 8448, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '8.24.0.n.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 31.7283775693936, 'jinv': '-60180985892672/96059601', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 346820
{'Elabel': '91392.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 91392, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '8.24.0.n.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 30.7211648063262, 'jinv': '21980236097728/16243247601', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 675624
{'Elabel': '220416.k2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 220416, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '8.24.0.n.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 46.1917326821948, 'jinv': '-115030925350366472000/3605642329094001', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 1055047
{'Elabel': '397056.d2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 397056, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '8.24.0.n.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 52.1451192774434, 'jinv': '44293251299122732024000/555888858426015750801', 'jorig': '44293251299122732024000/555888858426015750801', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
id: 1166496
{'Elabel': '452352.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 452352, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '8.24.0.n.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 46.4509265818076, 'jinv': '149066856688334627008/5180852818018039761', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}

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Hilbert	Bianchi
Siegel

Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.