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gps_gl2zhat_fine • Show schema
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{'CPlabel': '12P1', 'Glabel': '48.43', 'RSZBlabel': '12.96.1.94', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [11, 0, 2, 11], 'canonical_generators': [[1, 3, 10, 11], [1, 8, 10, 3], [5, 10, 8, 9], [9, 2, 4, 5], [9, 4, 2, 7], [11, 10, 8, 3]], 'cm_discriminants': [-3], 'coarse_class': '12.48.1.o', 'coarse_class_num': 15, 'coarse_index': 48, 'coarse_label': '12.48.1.o.1', 'coarse_level': 12, 'coarse_num': 1, 'conductor': [[2, 4], [3, 1]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[2, 4]], 'cusp_widths': [[2, 2], [4, 2], [6, 2], [12, 2]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 3, 'generators': [[5, 5, 0, 7], [5, 8, 6, 11], [7, 9, 6, 5]], '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, 2, 1], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [12, 2, 1], [12, 4, 1], [12, 6, 1], [12, 12, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 2, 1], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [12, 4, 1], [12, 8, 1], [12, 12, 1], [12, 24, 1]], 'label': '12.96.1-12.o.1.3', 'lattice_labels': None, 'lattice_x': None, 'level': 12, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '3.87120101090789092906', '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': 1, 'num_known_degree1_points': 1, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [3, 2, 1], [3, 6, 1], [4, 4, 1], [4, 8, 1], [6, 2, 1], [6, 4, 1], [6, 6, 1], [6, 12, 1], [12, 8, 1], [12, 12, 2], [12, 16, 1], [12, 48, 1]], 'parents': ['12.48.0-6.b.1.1', '12.48.0-6.b.1.3', '12.48.0-12.i.1.4', '12.48.0-12.i.1.7', '12.48.1-12.l.1.8', '12.48.1-12.l.1.11'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '12.48.1.a.1', 'psl2level': 12, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 0, 'reductions': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.e.1', '6.24.0.b.1'], 'scalar_label': '3.2.1', 'simple': True, 'sl2label': '12.96.1-12.a.1.4', 'sl2level': 12, 'squarefree': True, 'trace_hash': 1588924079463638771, 'traces': None}
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gps_gl2zhat_fine • Show schema
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{'CPlabel': '12P1', 'Glabel': '96.219', 'RSZBlabel': '12.48.1.23', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [11, 0, 2, 11], 'canonical_generators': [[1, 2, 4, 9], [1, 3, 10, 11], [1, 8, 10, 3], [3, 8, 10, 5], [3, 10, 8, 7], [5, 10, 8, 9]], 'cm_discriminants': [-3], 'coarse_class': '12.48.1.o', 'coarse_class_num': 15, 'coarse_index': 48, 'coarse_label': '12.48.1.o.1', 'coarse_level': 12, 'coarse_num': 1, 'conductor': [[2, 4], [3, 1]], 'contains_negative_one': True, 'curve_label': '48.a4', 'cusp_orbits': [[2, 4]], 'cusp_widths': [[2, 2], [4, 2], [6, 2], [12, 2]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[1, 5, 0, 11], [7, 2, 0, 7], [7, 3, 6, 5], [11, 7, 0, 1]], '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, 2, 1], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [12, 2, 1], [12, 4, 1], [12, 6, 1], [12, 12, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 2, 1], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [12, 4, 1], [12, 8, 1], [12, 12, 1], [12, 24, 1]], 'label': '12.48.1.o.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '3.4.0.a.1', '4.6.0.e.1', '6.2.0.a.1', '6.6.0.a.1', '6.8.0.b.1', '6.12.0.a.1', '6.24.0.b.1', '12.6.0.b.1', '12.12.0.l.1', '12.24.0.i.1', '12.24.1.l.1', '12.48.1.o.1'], 'lattice_x': [6831, 4208, 8989, 2705, 6831, 5710, 8279, 5000, 6366, 738, 1721, 1011, 4016, 3251], 'level': 12, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '3.87120101090789092906', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['48.2.a.a'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 1, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 2, 1], [3, 6, 1], [4, 4, 1], [4, 8, 1], [6, 2, 1], [6, 4, 1], [6, 6, 1], [6, 12, 1], [12, 8, 1], [12, 16, 1], [12, 24, 1], [12, 48, 1]], 'parents': ['6.24.0.b.1', '12.12.0.l.1', '12.24.0.i.1', '12.24.1.l.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '12.48.1.a.1', 'psl2level': 12, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 0, 'reductions': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.e.1', '6.24.0.b.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '12.48.1.a.1', 'sl2level': 12, 'squarefree': True, 'trace_hash': 1588924079463638771, '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]}
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modcurve_models • Show schema
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{'dont_display': False, 'equation': ['x^3+x^2*z-y^2*z-4*x*z^2-4*z^3'], 'modcurve': '12.48.1.o.1', 'model_type': 5, 'number_variables': 3, 'smooth': True, 'upload_id': None}
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modcurve_modelmaps • Show schema
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{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['z*y^3*(10*x^2*y^18-736*x^2*y^17*z+22521*x^2*y^16*z^2-358728*x^2*y^15*z^3+2781864*x^2*y^14*z^4-814176*x^2*y^13*z^5-172920424*x^2*y^12*z^6+1417448524*x^2*y^11*z^7-5826164904*x^2*y^10*z^8+33645519104*x^2*y^9*z^9-253889232493*x^2*y^8*z^10+1009427991420*x^2*y^7*z^11-3060016345436*x^2*y^6*z^12+16138912702352*x^2*y^5*z^13-41979023814276*x^2*y^4*z^14+68357139681740*x^2*y^3*z^15-410141445663110*x^2*y^2*z^16-1283918200896377*x^2*z^18-25*x*y^18*z+1104*x*y^17*z^2-11256*x*y^16*z^3-179088*x*y^15*z^4+4206645*x*y^14*z^5-4892508*x*y^13*z^6-558507488*x*y^12*z^7+6296584752*x*y^11*z^8-31984123140*x*y^10*z^9+143865810592*x*y^9*z^10-940892663100*x*y^8*z^11+4093361403528*x*y^7*z^12-11459434632751*x*y^6*z^13+54116794688700*x*y^5*z^14-154918400876424*x*y^4*z^15+205069924433920*x*y^3*z^16-1337414159674413*x*y^2*z^17-3851755662082048*x*z^19-y^20+92*y^19*z-3751*y^18*z^2+90832*y^17*z^3-1435992*y^16*z^4+14904456*y^15*z^5-95890979*y^14*z^6+355234060*y^13*z^7-1318659676*y^12*z^8+13337497332*y^11*z^9-93057880540*y^10*z^10+344878976160*y^9*z^11-1517760503142*y^8*z^12+7831841864180*y^7*z^13-19504002535899*y^6*z^14+60762966629636*y^5*z^15-237763963224665*y^4*z^16+136712833644752*y^3*z^17-1355245848604091*y^2*z^18-2567837446836764*z^20)', '12*x^2*y^22-2561*x^2*y^20*z^2+182896*x^2*y^18*z^4+387882*x^2*y^16*z^6-1015428912*x^2*y^14*z^8+36210315435*x^2*y^12*z^10+3388653456360*x^2*y^10*z^12-105467029420318*x^2*y^8*z^14-7385426436654324*x^2*y^6*z^16-127749987690690027*x^2*y^4*z^18-893607185213181280*x^2*y^2*z^20-2218611123791166013*x^2*z^22-42*x*y^22*z+3810*x*y^20*z^3+92378*x*y^18*z^5+2302992*x*y^16*z^7-4535297352*x*y^14*z^9+289224461982*x*y^12*z^11+10075944029550*x*y^10*z^13-642872749839864*x*y^8*z^15-29949279572534562*x*y^6*z^17-448729386849568722*x*y^4*z^19-2865706083783071553*x*y^2*z^21-6655833303041441792*x*z^23-y^24+358*y^22*z^2-41669*y^20*z^4+3870230*y^18*z^6-254058972*y^16*z^8-2077810344*y^14*z^10+1163457082655*y^12*z^12-5106390518758*y^10*z^14-2291956414568165*y^8*z^16-58442153031889442*y^6*z^18-598305851844701719*y^4*z^20-2711635915506578239*y^2*z^22-4437222179637696268*z^24'], 'degree': 48, 'domain_label': '12.48.1.o.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^14*3^3', '1'], 'upload_id': None}
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modcurve_points • Show schema
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id: 1320
{'Elabel': '27.a3', 'ainvs': None, 'cardinality': None, 'cm': -3, 'conductor_norm': 36, 'coordinates': {'5': ['-2:0:1', '-1:0:1', '2:0:1', '0:1:0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '12.48.1.o.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 4, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': '0', 'jorig': '0', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 1709903
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-2,2:-4,2:1,0', '0,-2:2,2:1,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '12.48.1.o.1', 'curve_level': 12, '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': '2.0.3.1', 'upload_id': None}
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id: 1709904
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['2,-2:6,-4:1,0', '2,-2:-6,4:1,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '12.48.1.o.1', 'curve_level': 12, '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': '2.2.12.1', 'upload_id': None}