LMFDB - Modular curve data - 24.96.1-24.ix.1.22

Formats: - HTML - YAML - JSON - 2024-06-11T21:24:54.604489

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': '24G1', 'Glabel': '768.1035859', 'RSZBlabel': '24.96.1.97', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [17, 8, 7, 23], 'canonical_generators': [[0, 1, 7, 18], [0, 1, 23, 10], [0, 5, 19, 2], [0, 13, 11, 10], [0, 17, 7, 2], [0, 19, 17, 22], [0, 23, 13, 14], [0, 23, 19, 8]], 'cm_discriminants': [], 'coarse_class': '24.48.1.ix', 'coarse_class_num': 232, 'coarse_index': 48, 'coarse_label': '24.48.1.ix.1', 'coarse_level': 24, 'coarse_num': 1, 'conductor': [[2, 6], [3, 1]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 2]], 'cusp_widths': [[1, 2], [2, 1], [3, 2], [6, 1], [8, 1], [24, 1]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['3.4.0.a.1', '8.24.0-8.p.1.7'], 'fine_num': 22, 'generators': [[11, 9, 12, 23], [19, 15, 20, 23], [19, 18, 4, 7], [23, 6, 8, 13], [23, 18, 4, 11]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 96, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 2, 2], [8, 8, 1], [12, 1, 2], [12, 3, 2], [12, 4, 1], [12, 12, 1], [24, 2, 2], [24, 6, 2], [24, 8, 1], [24, 24, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 4, 2], [8, 16, 1], [12, 2, 2], [12, 6, 2], [12, 8, 1], [12, 24, 1], [24, 8, 2], [24, 24, 2], [24, 32, 1], [24, 96, 1]], 'label': '24.96.1-24.ix.1.22', 'lattice_labels': None, 'lattice_x': None, 'level': 24, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '5.25749537202778154790', 'prec': 74}, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 1, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [3, 2, 1], [3, 6, 1], [4, 2, 2], [4, 8, 1], [6, 2, 1], [6, 4, 1], [6, 6, 1], [6, 12, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [12, 4, 2], [12, 12, 2], [12, 16, 1], [12, 48, 1], [24, 8, 2], [24, 16, 1], [24, 24, 2], [24, 48, 1], [24, 64, 1], [24, 192, 1]], 'parents': ['8.24.0-8.p.1.7', '24.48.0-12.g.1.13', '24.48.0-12.g.1.19'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '24.48.1.a.1', 'psl2level': 24, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '8.24.0-8.p.1.7', '12.24.0.g.1'], 'scalar_label': '4.2.1', 'simple': True, 'sl2label': '24.96.1-24.a.1.2', 'sl2level': 24, 'squarefree': True, 'trace_hash': 255172822239056233, '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': '24G1', 'Glabel': None, 'RSZBlabel': '24.48.1.66', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [17, 8, 7, 23], 'canonical_generators': [[0, 1, 5, 16], [0, 1, 7, 18], [0, 1, 11, 10], [0, 1, 23, 10], [0, 5, 7, 2], [0, 5, 19, 2], [0, 7, 17, 22], [0, 13, 11, 10]], 'cm_discriminants': [], 'coarse_class': '24.48.1.ix', 'coarse_class_num': 232, 'coarse_index': 48, 'coarse_label': '24.48.1.ix.1', 'coarse_level': 24, 'coarse_num': 1, 'conductor': [[2, 6], [3, 1]], 'contains_negative_one': True, 'curve_label': '192.d4', 'cusp_orbits': [[1, 4], [2, 2]], 'cusp_widths': [[1, 2], [2, 1], [3, 2], [6, 1], [8, 1], [24, 1]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['3.4.0.a.1', '8.12.0.p.1'], 'fine_num': 0, 'generators': [[1, 6, 8, 17], [7, 6, 20, 19], [7, 9, 0, 11], [13, 21, 0, 17], [17, 3, 16, 13], [23, 15, 20, 17]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 2, 2], [8, 8, 1], [12, 1, 2], [12, 3, 2], [12, 4, 1], [12, 12, 1], [24, 2, 2], [24, 6, 2], [24, 8, 1], [24, 24, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 4, 2], [8, 16, 1], [12, 2, 2], [12, 6, 2], [12, 8, 1], [12, 24, 1], [24, 8, 2], [24, 24, 2], [24, 32, 1], [24, 96, 1]], 'label': '24.48.1.ix.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '8.12.0.p.1', '12.24.0.g.1', '24.48.1.ix.1'], 'lattice_x': [3122, 4616, 1674, 7557, 3349, 8778, 5611, 7195], 'level': 24, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '5.25749537202778154790', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['192.2.a.d'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 1, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 2, 1], [3, 6, 1], [4, 2, 2], [4, 8, 1], [6, 2, 1], [6, 4, 1], [6, 6, 1], [6, 12, 1], [8, 8, 2], [8, 32, 1], [12, 4, 2], [12, 12, 2], [12, 16, 1], [12, 48, 1], [24, 16, 2], [24, 48, 2], [24, 64, 1], [24, 192, 1]], 'parents': ['8.12.0.p.1', '12.24.0.g.1'], 'parents_conj': [[1, 0, 0, 1], [3, 5, 2, 17]], 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '24.48.1.a.1', 'psl2level': 24, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '8.12.0.p.1', '12.24.0.g.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '24.48.1.a.1', 'sl2level': 24, 'squarefree': True, 'trace_hash': 255172822239056233, 'traces': [0, 1, 2, 0, -4, 2, 2, 4, -8, -6, 8, -6, -6, -4, 0, 2, -4, 2, 4, 8, 10, -8, 4, -6, 2, 18, 16, 12, 2, 18, -8, 4, -6, 12, -14, -16, 2, -12, 24, -6, -12, -6, 0, 2, 18, 16, 20, -8, -12, -22, 10, -16, 18, -20, 2, -8, 10, 8, 26, 26, 28, 18, -12, -24, -6, -6, -20, 18, 12, -30, 2, -24, -8, 10, -20, 0, 2, -14, -30, -6, -12, 10, 32, -14, 0, -20, -14, -22, 26, 8, 36, -16, -32, 12, -12, 24, -6, 26, -4, 18, -44, 26, -28, 10, -36, 2, 44, -14, 24, -38, -40, -38, 42, 44, 16, -14, -12, 8, -6, -12, 10, 34, 2, -4, 4, -6, 10, -32, 48, -14, 4, -8, 24, -38, -22, 2, 18, -28, -22, 26, -4, -30, -16, 28, 50, -24, 10, 42, 12, -32, 18, 50, 4, 8, -4, 16, 16, 50, 42, -6, -12, -54, -16, -36, -30, -24, 40, 26]}

Column	Type
dont_display	boolean
equation	text[]
modcurve	text
model_type	smallint
number_variables	smallint
smooth	boolean
upload_id	bigint

modcurve_models • Show schema

{'dont_display': False, 'equation': ['x^3+x^2*z-y^2*z-17*x*z^2+15*z^3'], 'modcurve': '24.48.1.ix.1', 'model_type': 5, 'number_variables': 3, 'smooth': True, 'upload_id': None}

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': ['32*x^2*y^14-49440*x^2*y^12*z^2+41204736*x^2*y^10*z^4-17975260160*x^2*y^8*z^6+4069732843520*x^2*y^6*z^8-499381945565184*x^2*y^4*z^10+27895158454353920*x^2*y^2*z^12-554111127877844992*x^2*z^14-464*x*y^14*z+559680*x*y^12*z^3-325064448*x*y^10*z^5+115976615936*x*y^8*z^7-23689694150656*x*y^6*z^9+2510607340929024*x*y^4*z^11-123361399543955456*x*y^2*z^13+2219694395765030912*x*z^15-y^16+4464*y^14*z^2-4953120*y^12*z^4+2282817280*y^10*z^6-583111623680*y^8*z^8+88557304872960*y^6*z^10-6321869422133248*y^4*z^12+188088919423713280*y^2*z^14-1672083105113964544*z^16', 'z^2*y^2*(x^2*y^10-2912*x^2*y^8*z^2+550592*x^2*y^6*z^4-22712320*x^2*y^4*z^6-524288*x^2*y^2*z^8-2097152*x^2*z^10-26*x*y^10*z+20336*x*y^8*z^3-2680448*x*y^6*z^5+90521600*x*y^4*z^7-2228224*x*y^2*z^9-8388608*x*z^11+321*y^10*z^2-96208*y^8*z^4+5896128*y^6*z^6-68038656*y^4*z^8+1703936*y^2*z^10+10485760*z^12)'], 'degree': 48, 'domain_label': '24.48.1.ix.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-1', '2^4'], '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: 1720619
{'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['0:1:0', '-5:0:1', '1:0:1', '3:0:1']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '24.48.1.ix.1', 'curve_level': 24, '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: 1720620
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['7,0:0,12:1,0', '-1,0:0,-4:1,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '24.48.1.ix.1', 'curve_level': 24, '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}

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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.