LMFDB - Modular curve data - 48.96.1-16.v.2.2

Formats: - HTML - YAML - JSON - 2024-06-02T08:15:38.174098

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': '16G1', 'Glabel': None, 'RSZBlabel': '48.96.1.1843', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [37, 0, 11, 1], 'canonical_generators': [[1, 0, 16, 1], [1, 16, 0, 1], [16, 3, 9, 46], [16, 9, 39, 22], [16, 21, 9, 4], [16, 33, 15, 22], [17, 16, 32, 33], [31, 0, 0, 47], [32, 9, 39, 38], [32, 27, 33, 14]], 'cm_discriminants': [], 'coarse_class': '16.48.1.v', 'coarse_class_num': 22, 'coarse_index': 48, 'coarse_label': '16.48.1.v.2', 'coarse_level': 16, 'coarse_num': 2, 'conductor': [[2, 5]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 2]], 'cusp_widths': [[2, 4], [4, 2], [16, 2]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 2, 'generators': [[1, 26, 16, 37], [1, 47, 44, 5], [17, 35, 16, 23], [27, 31, 28, 7], [43, 19, 40, 29]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 96, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 1, 2], [8, 2, 1], [8, 8, 1], [12, 4, 2], [12, 16, 1], [16, 2, 2], [16, 4, 1], [16, 16, 1], [24, 4, 2], [24, 8, 1], [24, 32, 1], [48, 8, 2], [48, 16, 1], [48, 64, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 2, 2], [8, 4, 1], [8, 8, 2], [12, 8, 2], [12, 32, 1], [16, 8, 4], [16, 32, 2], [24, 16, 2], [24, 32, 1], [24, 64, 2], [48, 64, 4], [48, 256, 2]], 'label': '48.96.1-16.v.2.2', 'lattice_labels': None, 'lattice_x': None, 'level': 48, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '3.46573590279972654709', '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, 8, 1], [4, 2, 2], [4, 8, 1], [6, 8, 1], [6, 16, 1], [8, 4, 2], [8, 8, 1], [8, 16, 2], [12, 16, 2], [12, 64, 1], [16, 16, 4], [16, 64, 2], [24, 32, 2], [24, 64, 1], [24, 128, 2], [48, 128, 4], [48, 512, 2]], 'parents': ['24.48.0-8.bb.2.8', '48.48.0-8.bb.2.4', '48.48.0-16.e.2.3', '48.48.0-16.e.2.10', '48.48.1-16.b.1.5', '48.48.1-16.b.1.15'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '16.48.1.b.1', 'psl2level': 16, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 4, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '4.6.0.c.1', '8.24.0.bb.2', '16.48.1.v.2', '24.48.0-8.bb.2.8'], 'scalar_label': '8.4.1', 'simple': True, 'sl2label': '16.96.1-16.b.1.2', 'sl2level': 16, 'squarefree': True, 'trace_hash': 1485208795141819780, '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': '16G1', 'Glabel': None, 'RSZBlabel': '16.48.1.56', 'RZBlabel': 'X335', 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2], 'canonical_conjugator': [1, 0, 15, 15], 'canonical_generators': [[0, 1, 15, 6], [0, 3, 9, 14], [0, 5, 9, 4], [0, 5, 15, 2], [0, 7, 9, 10], [0, 9, 7, 6]], 'cm_discriminants': [], 'coarse_class': '16.48.1.v', 'coarse_class_num': 22, 'coarse_index': 48, 'coarse_label': '16.48.1.v.2', 'coarse_level': 16, 'coarse_num': 2, 'conductor': [[2, 5]], 'contains_negative_one': True, 'curve_label': '32.a2', 'cusp_orbits': [[1, 4], [2, 2]], 'cusp_widths': [[2, 4], [4, 2], [16, 2]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[1, 10, 0, 1], [5, 3, 8, 9], [7, 3, 0, 1], [7, 12, 0, 7], [15, 13, 8, 15]], 'genus': 1, 'genus_minus_rank': 1, '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, 2, 2], [8, 4, 1], [8, 8, 2], [16, 8, 4], [16, 32, 2]], 'label': '16.48.1.v.2', '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.2', '16.24.0.e.2', '16.24.1.b.1', '16.48.1.v.2'], 'lattice_x': [5000, 5000, 5000, 5000, 1364, 5000, 8636, 5000], 'level': 16, 'level_is_squarefree': False, 'level_radical': 2, 'log_conductor': {'__RealLiteral__': 0, 'data': '3.46573590279972654709', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['32.2.a.a'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 1, '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], [4, 2, 2], [4, 8, 1], [8, 4, 2], [8, 8, 1], [8, 16, 2], [16, 16, 4], [16, 64, 2]], 'parents': ['8.24.0.bb.2', '16.24.0.e.2', '16.24.1.b.1'], 'parents_conj': [[1, 13, 4, 11], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '16.48.1.b.1', 'psl2level': 16, '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', '4.6.0.c.1', '8.24.0.bb.2'], 'scalar_label': '8.2.2', 'simple': True, 'sl2label': '16.48.1.b.1', 'sl2level': 16, 'squarefree': True, 'trace_hash': 1485208795141819780, 'traces': [0, 0, -2, 0, 0, 6, 2, 0, 0, -10, 0, -2, 10, 0, 0, 14, 0, -10, 0, 0, -6, 0, 0, 10, 18, -2, 0, 0, 6, -14, 0, 0, -22, 0, 14, 0, 22, 0, 0, -26, 0, -18, 0, -14, -2, 0, 0, 0, 0, 30, 26, 0, -30, 0, 2, 0, -26, 0, -18, 10, 0, -34, 0, 0, 26, 22, 0, 18, 0, -10, 34, 0, 0, 14, 0, 0, -34, 38, 2, -6, 0, 30, 0, 34, 0, 0, -14, 42, 38, 0, 0, 0, 0, 0, 0, 0, -10, -22, 0, -42, 0, 38, 0, 26, 0, 2, 0, -46, 0, 10, 0, -34, -38, 0, 0, 50, 0, 0, -26, 0, -50, -46, -2, 0, 0, -10, 30, 0, 0, 54, 0, 0, 0, -18, -38, 50, -34, 0, 22, 10, 0, -50, 0, 0, 54, 0, 46, 58, 0, 0, -58, 50, 0, 0, 0, 0, 0, -46, -38, -58, 0, 26, 0, 0, -62, 0, 0, 62]}

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-y^2*z-11*x*z^2+14*z^3'], 'modcurve': '16.48.1.v.2', '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': ['744*x^2*y^14-861743506*x^2*y^12*z^2+3946501303224*x^2*y^10*z^4-2404052725370889*x^2*y^8*z^6+450301688638460016*x^2*y^6*z^8-34266169928476438809*x^2*y^4*z^10+1121366330130233819844*x^2*y^2*z^12-13119880523481218023425*x^2*z^14-196876*x*y^14*z+20032110312*x*y^12*z^3-40645158196479*x*y^10*z^5+16765017079652202*x*y^8*z^7-2481637326273847576*x*y^6*z^9+160992383698961342616*x*y^4*z^11-4690996378190219311737*x*y^2*z^13+50228506469524739981310*x*z^15-y^16+21481872*y^14*z^2-317842308708*y^12*z^4+319718459371944*y^10*z^6-82473813056611532*y^8*z^8+8224738401779468256*y^6*z^10-365602252934307716394*y^4*z^12+7147543060259635457184*y^2*z^14-47977490845124607868921*z^16', 'y^2*(x^2*y^12-4*x^2*y^10*z^2-14*x^2*y^8*z^4+16*x^2*y^6*z^6+171*x^2*y^4*z^8+28*x^2*y^2*z^10+x^2*z^12+14*x*y^10*z^3-100*x*y^8*z^5+106*x*y^6*z^7+364*x*y^4*z^9+57*x*y^2*z^11+2*x*z^13-16*y^12*z^2+112*y^10*z^4-177*y^8*z^6+200*y^6*z^8-1108*y^4*z^10-192*y^2*z^12-7*z^14)'], 'degree': 48, 'domain_label': '16.48.1.v.2', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': None, '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: 1711575
{'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['2:0:1', '0:1:0', '1:2:1', '1:-2:1']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '16.48.1.v.2', '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: 1711576
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-1,-2:0,0:1,0', '3,0:0,2:1,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '16.48.1.v.2', '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}

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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
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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.