LMFDB - Modular curve data - 48.48.1-48.b.1.11

Formats: - HTML - YAML - JSON - 2024-06-05T16:29:04.230400

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': '16A1', 'Glabel': None, 'RSZBlabel': '48.48.1.250', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [37, 0, 11, 1], 'canonical_generators': [[0, 1, 11, 2], [0, 1, 11, 34], [0, 7, 25, 18], [0, 47, 19, 44], [1, 0, 16, 1], [1, 16, 0, 1], [16, 21, 3, 22], [16, 33, 15, 22], [17, 16, 32, 33], [32, 45, 27, 38]], 'cm_discriminants': [], 'coarse_class': '48.24.1.b', 'coarse_class_num': 2, 'coarse_index': 24, 'coarse_label': '48.24.1.b.1', 'coarse_level': 48, 'coarse_num': 1, 'conductor': [[2, 5], [3, 2]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4]], 'cusp_widths': [[2, 2], [4, 1], [16, 1]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 11, 'generators': [[3, 17, 16, 17], [5, 19, 12, 17], [11, 20, 32, 15], [31, 41, 44, 27], [37, 23, 0, 11]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 48, '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, 16, 1], [12, 8, 2], [12, 32, 1], [16, 8, 2], [16, 16, 1], [16, 64, 1], [24, 16, 2], [24, 32, 1], [24, 128, 1], [48, 64, 2], [48, 128, 1], [48, 512, 1]], 'label': '48.48.1-48.b.1.11', 'lattice_labels': None, 'lattice_x': None, 'level': 48, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '5.66296048013594592988', '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, 32, 1], [12, 16, 2], [12, 64, 1], [16, 8, 2], [16, 16, 1], [16, 32, 1], [16, 128, 1], [24, 32, 2], [24, 64, 1], [24, 256, 1], [48, 64, 2], [48, 128, 1], [48, 256, 1], [48, 1024, 1]], 'parents': ['16.24.0-8.n.1.8', '24.24.0-8.n.1.5'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 24, 'psl2label': '16.24.1.a.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', '8.12.0.n.1', '12.12.0-4.c.1.1', '16.24.0-8.n.1.8', '24.24.0-8.n.1.5'], 'scalar_label': '4.2.1', 'simple': True, 'sl2label': '16.48.1-16.a.1.2', 'sl2level': 16, 'squarefree': True, 'trace_hash': 2083241323606420378, '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': '16A1', 'Glabel': None, 'RSZBlabel': '48.24.1.2', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [37, 0, 11, 1], 'canonical_generators': [[0, 1, 11, 2], [0, 1, 11, 34], [0, 1, 29, 4], [0, 7, 25, 18], [1, 0, 16, 1], [1, 16, 0, 1], [16, 3, 21, 10], [16, 21, 3, 22], [16, 33, 15, 22], [17, 16, 32, 33]], 'cm_discriminants': [], 'coarse_class': '48.24.1.b', 'coarse_class_num': 2, 'coarse_index': 24, 'coarse_label': '48.24.1.b.1', 'coarse_level': 48, 'coarse_num': 1, 'conductor': [[2, 5], [3, 2]], 'contains_negative_one': True, 'curve_label': '288.d3', 'cusp_orbits': [[1, 4]], 'cusp_widths': [[2, 2], [4, 1], [16, 1]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[9, 11, 16, 35], [17, 11, 16, 47], [23, 41, 20, 15], [29, 23, 20, 13], [31, 23, 40, 25], [31, 32, 24, 43]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 24, '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, 16, 1], [12, 8, 2], [12, 32, 1], [16, 8, 2], [16, 16, 1], [16, 64, 1], [24, 16, 2], [24, 32, 1], [24, 128, 1], [48, 64, 2], [48, 128, 1], [48, 512, 1]], 'label': '48.24.1.b.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '48.24.1.b.1'], 'lattice_x': [5000, 5000, 5000, 5000, 5000], 'level': 48, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '5.66296048013594592988', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['288.2.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, 8, 1], [4, 2, 2], [4, 8, 1], [6, 8, 1], [6, 16, 1], [8, 4, 2], [8, 8, 1], [8, 32, 1], [12, 16, 2], [12, 64, 1], [16, 16, 2], [16, 32, 1], [16, 128, 1], [24, 32, 2], [24, 64, 1], [24, 256, 1], [48, 128, 2], [48, 256, 1], [48, 1024, 1]], 'parents': ['8.12.0.n.1'], 'parents_conj': [[1, 36, 14, 7]], 'pointless': False, 'power': True, 'psl2index': 24, 'psl2label': '16.24.1.a.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', '8.12.0.n.1', '8.12.0.n.1', '8.12.0.n.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '16.24.1.a.1', 'sl2level': 16, 'squarefree': True, 'trace_hash': 2083241323606420378, '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-9*x*z^2'], 'modcurve': '48.24.1.b.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': ['62208*x^2*y^4*z^2+36864*x*y^6*z+314928*x*y^2*z^5+4096*y^8+531441*z^8', 'z^5*y^2*x'], 'degree': 24, 'domain_label': '48.24.1.b.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^4', '3^8'], '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

{'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['0:1:0', '0:0:1', '3:0:1', '-3:0:1']}, 'curve_genus': 1, 'curve_index': 24, 'curve_label': '48.24.1.b.1', 'curve_level': 48, '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}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi
Siegel

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Modular curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Galois groups
Sato-Tate groups
Abstract groups
Lattices

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Motives

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.