LMFDB - Modular curve data - 40.120.3-10.a.1.2

Formats: - HTML - YAML - JSON - 2024-05-25T04:21:03.199909

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': '10A3', 'Glabel': None, 'RSZBlabel': '40.120.3.21', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [21, 27, 5, 38], 'canonical_generators': [[1, 0, 10, 1], [1, 2, 2, 5], [1, 10, 0, 1], [3, 0, 6, 7], [7, 6, 6, 9], [19, 0, 0, 39], [29, 30, 10, 9], [31, 0, 0, 1]], 'cm_discriminants': [], 'coarse_class': '10.60.3.a', 'coarse_class_num': 1, 'coarse_index': 60, 'coarse_label': '10.60.3.a.1', 'coarse_level': 10, 'coarse_num': 1, 'conductor': [[2, 4], [5, 6]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[2, 3]], 'cusp_widths': [[10, 6]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': [1, 1], 'factorization': [], 'fine_num': 2, 'generators': [[3, 22, 18, 11], [11, 32, 8, 19], [23, 6, 14, 17], [23, 14, 16, 39], [33, 22, 4, 37], [37, 20, 38, 23]], 'genus': 3, 'genus_minus_rank': 3, 'has_obstruction': 0, 'index': 120, 'isogeny_orbits': [[2, 1, 3], [4, 2, 3], [5, 6, 1], [8, 4, 3], [10, 6, 3], [20, 12, 3], [40, 24, 3]], 'kummer_orbits': [[2, 1, 3], [4, 2, 3], [5, 12, 1], [8, 8, 3], [10, 12, 3], [20, 48, 3], [40, 192, 3]], 'label': '40.120.3-10.a.1.2', 'lattice_labels': None, 'lattice_x': None, 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '12.42921619684438348527', 'prec': 77}, 'models': None, 'mults': [2, 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': 0, 'obstructions': None, 'orbits': [[2, 1, 3], [4, 4, 3], [5, 24, 1], [8, 16, 3], [10, 24, 3], [20, 96, 3], [40, 384, 3]], 'parents': ['40.12.0-2.a.1.1'], 'parents_conj': None, 'pointless': None, 'power': False, 'psl2index': 60, 'psl2label': '10.60.3.a.1', 'psl2level': 10, 'q_gonality': None, 'q_gonality_bounds': [3, 4], 'qbar_gonality': 3, 'qbar_gonality_bounds': [3, 3], 'rank': 0, 'rational_cusps': 0, 'reductions': ['2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '5.10.0.a.1', '10.60.3.a.1', '10.60.3.a.1'], 'scalar_label': '4.2.1', 'simple': False, 'sl2label': '20.120.3-10.a.1.2', 'sl2level': 20, 'squarefree': False, 'trace_hash': 910338553619709655, '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': '10A3', 'Glabel': '48.5', 'RSZBlabel': '10.60.3.1', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [9, 0, 0, 1], 'canonical_generators': [[1, 2, 2, 5], [3, 0, 6, 7], [7, 6, 6, 9]], 'cm_discriminants': [], 'coarse_class': '10.60.3.a', 'coarse_class_num': 1, 'coarse_index': 60, 'coarse_label': '10.60.3.a.1', 'coarse_level': 10, 'coarse_num': 1, 'conductor': [[2, 4], [5, 6]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 3]], 'cusp_widths': [[10, 6]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': [1, 1], 'factorization': ['2.6.0.a.1', '5.10.0.a.1'], 'fine_num': 0, 'generators': [[3, 2, 2, 7], [7, 8, 8, 1]], 'genus': 3, 'genus_minus_rank': 3, 'has_obstruction': 0, 'index': 60, 'isogeny_orbits': [[2, 1, 3], [5, 6, 1], [10, 6, 3]], 'kummer_orbits': [[2, 1, 3], [5, 12, 1], [10, 12, 3]], 'label': '10.60.3.a.1', 'lattice_labels': ['1.1.0.a.1', '2.2.0.a.1', '2.3.0.a.1', '2.6.0.a.1', '5.10.0.a.1', '10.20.1.a.1', '10.30.1.a.1', '10.60.3.a.1'], 'lattice_x': [5635, 8373, 2421, 2421, 6309, 6309, 1071, 3254], 'level': 10, 'level_is_squarefree': True, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '12.42921619684438348527', 'prec': 77}, 'models': 1, 'mults': [2, 1], 'name': None, 'newforms': ['50.2.a.b', '100.2.a.a'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 0, 'obstructions': [], 'orbits': [[2, 1, 3], [5, 24, 1], [10, 24, 3]], 'parents': ['2.6.0.a.1', '10.20.1.a.1', '10.30.1.a.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': None, 'power': False, 'psl2index': 60, 'psl2label': '10.60.3.a.1', 'psl2level': 10, 'q_gonality': None, 'q_gonality_bounds': [3, 4], 'qbar_gonality': 3, 'qbar_gonality_bounds': [3, 3], 'rank': 0, 'rational_cusps': 0, 'reductions': ['2.6.0.a.1', '5.10.0.a.1'], 'scalar_label': '1.1.1', 'simple': False, 'sl2label': '10.60.3.a.1', 'sl2level': 10, 'squarefree': False, 'trace_hash': 910338553619709655, 'traces': [2, 0, 0, -6, -6, 6, 12, 6, -18, 6, 0, -6, 0, 18, -18, -6, 12, 6, 24, 12, -24, -12, 12, 24, -6, -30, -6, 12, -18, 24, -6, 24, -12, 6, -6, 24, 18, -12, -42, 54, -42, -6, -48, 12, 18, 48, -42, 18, -18, 54, -6, -24, 48, 54, 42, 6, 18, 24, -90, -30, -36, 18, -36, -24, -30, -18, 42, 24, 36, -30, -30, 84, 78, -78, -78, -18, 54, 54, -36, -24, 6, -30, 0, 36, -72, 12, -24, -60, 54, -6, 6, 36, -30, 24, 36, -54, -54, -12, -96, 78, -60, 6, 66, 0, -48, 48, 72, 0, 60, -36, -42, 66, 42, 60, -24, 66, -6, -66, -54, 66, 42, -6, 78, 120, 42, -6, 6, -84, -18, 30, 60, -18, 60, -42, 36, 12, 78, 30, -126, -66, -72, 30, -30, 96, 42, -48, -102, -12, 6, 42, 30, -54, -96, -42, 102, 36, -36, 18, 48, 6, 78, 84, -42, -30, -132, 6, -120, 30]}

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': ['2*x^4-3*x^3*y-5*x^2*y^2-4*x*y^3-2*y^4+3*x^3*z-18*x^2*y*z-17*x*y^2*z+4*y^3*z-5*x^2*z^2+17*x*y*z^2-6*y^2*z^2+4*x*z^3+4*y*z^3-2*z^4'], 'modcurve': '10.60.3.a.1', 'model_type': 0, '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': ['942686181*x^3*y^12+7521205212*x^3*y^11*z+21841462746*x^3*y^10*z^2+26279261420*x^3*y^9*z^3+8553933195*x^3*y^8*z^4-3838235848*x^3*y^7*z^5-2749142676*x^3*y^6*z^6-3838235848*x^3*y^5*z^7+8553933195*x^3*y^4*z^8+26279261420*x^3*y^3*z^9+21841462746*x^3*y^2*z^10+7521205212*x^3*y*z^11+942686181*x^3*z^12+1161438453*x^2*y^13+12366492993*x^2*y^12*z+50057826552*x^2*y^11*z^2+93833940112*x^2*y^10*z^3+74146673325*x^2*y^9*z^4+6215553441*x^2*y^8*z^5-10741951784*x^2*y^7*z^6+10741951784*x^2*y^6*z^7-6215553441*x^2*y^5*z^8-74146673325*x^2*y^4*z^9-93833940112*x^2*y^3*z^10-50057826552*x^2*y^2*z^11-12366492993*x^2*y*z^12-1161438453*x^2*z^13+816387768*x*y^14+8576491653*x*y^13*z+32274478260*x*y^12*z^2+46701809818*x*y^11*z^3-1555516012*x*y^10*z^4-60480360469*x*y^9*z^5-28296834304*x*y^8*z^6+12444669420*x*y^7*z^7-28296834304*x*y^6*z^8-60480360469*x*y^5*z^9-1555516012*x*y^4*z^10+46701809818*x*y^3*z^11+32274478260*x*y^2*z^12+8576491653*x*y*z^13+816387768*x*z^14+345044610*y^15+1836929070*y^14*z+2535309000*y^13*z^2+365319900*y^12*z^3+2866112280*y^11*z^4+6122843860*y^10*z^5-713164710*y^9*z^6-1091471650*y^8*z^7+1091471650*y^7*z^8+713164710*y^6*z^9-6122843860*y^5*z^10-2866112280*y^4*z^11-365319900*y^3*z^12-2535309000*y^2*z^13-1836929070*y*z^14-345044610*z^15', '436429*x^3*y^12-32512*x^3*y^11*z-2136286*x^3*y^10*z^2+3087680*x^3*y^9*z^3-598845*x^3*y^8*z^4-3040832*x^3*y^7*z^5+4626076*x^3*y^6*z^6-3040832*x^3*y^5*z^7-598845*x^3*y^4*z^8+3087680*x^3*y^3*z^9-2136286*x^3*y^2*z^10-32512*x^3*y*z^11+436429*x^3*z^12+537693*x^2*y^13+1395853*x^2*y^12*z-3482508*x^2*y^11*z^2-2075228*x^2*y^10*z^3+11077825*x^2*y^9*z^4-13186479*x^2*y^8*z^5+10001136*x^2*y^7*z^6-10001136*x^2*y^6*z^7+13186479*x^2*y^5*z^8-11077825*x^2*y^4*z^9+2075228*x^2*y^3*z^10+3482508*x^2*y^2*z^11-1395853*x^2*y*z^12-537693*x^2*z^13+377976*x*y^14+927181*x*y^13*z-3365160*x*y^12*z^2-1424414*x*y^11*z^3+12384616*x*y^10*z^4-15132733*x*y^9*z^5+6603592*x*y^8*z^6-738020*x*y^7*z^7+6603592*x*y^6*z^8-15132733*x*y^5*z^9+12384616*x*y^4*z^10-1424414*x*y^3*z^11-3365160*x*y^2*z^12+927181*x*y*z^13+377976*x*z^14+159762*y^15-436218*y^14*z+105520*y^13*z^2+1873220*y^12*z^3-5294352*y^11*z^4+8188412*y^10*z^5-8953166*y^9*z^6+8392350*y^8*z^7-8392350*y^7*z^8+8953166*y^6*z^9-8188412*y^5*z^10+5294352*y^4*z^11-1873220*y^3*z^12-105520*y^2*z^13+436218*y*z^14-159762*z^15'], 'degree': 60, 'domain_label': '10.60.3.a.1', 'domain_model_type': 0, 'dont_display': False, 'factored': True, 'leading_coefficients': ['5^2', '1'], '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': 3, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['-3,2:2,-1:1,0', '1,-1:-1,0:1,0', '0,1:2,-1:1,0']}, 'curve_genus': 3, 'curve_index': 60, 'curve_label': '10.60.3.a.1', 'curve_level': 10, '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': '2.2.5.1', '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
Higher genus families
Abelian varieties over $\F_{q}$
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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.