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gps_gl2zhat_fine • Show schema
{'CPlabel': '12I0', 'Glabel': '48.51', 'RSZBlabel': '12.96.0.52', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [1, 9, 1, 4], 'canonical_generators': [[1, 2, 4, 9], [1, 6, 4, 11], [3, 2, 4, 5], [3, 2, 10, 11], [7, 8, 10, 3], [11, 10, 8, 9]], 'cm_discriminants': [], 'coarse_class': '12.48.0.a', 'coarse_class_num': 1, 'coarse_index': 48, 'coarse_label': '12.48.0.a.2', 'coarse_level': 12, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 3]], 'cusp_widths': [[2, 4], [4, 1], [6, 4], [12, 1]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 9, 'generators': [[5, 2, 6, 11], [5, 10, 0, 1], [7, 0, 0, 11], [7, 0, 6, 11]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 96, 'isogeny_orbits': [[2, 1, 3], [3, 1, 1], [3, 3, 1], [4, 2, 3], [6, 1, 3], [6, 3, 3], [12, 2, 3], [12, 6, 3]], 'kummer_orbits': [[2, 1, 3], [3, 1, 1], [3, 3, 1], [4, 2, 3], [6, 1, 3], [6, 3, 3], [12, 4, 3], [12, 6, 2], [12, 12, 2]], 'label': '12.96.0-12.a.2.9', 'lattice_labels': None, 'lattice_x': None, 'level': 12, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 17, 'num_known_degree1_noncusp_points': 17, 'num_known_degree1_points': 18, 'obstructions': None, 'orbits': [[2, 1, 3], [3, 2, 1], [3, 6, 1], [4, 4, 3], [6, 2, 3], [6, 6, 3], [12, 4, 2], [12, 8, 2], [12, 12, 2], [12, 24, 2]], 'parents': ['12.48.0-6.a.1.3', '12.48.0-6.a.1.6'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 48, 'psl2label': '12.48.0.a.1', 'psl2level': 12, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.6.0.a.1', '2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1'], 'scalar_label': '12.4.1', 'simple': None, 'sl2label': '12.96.0-12.a.1.1', 'sl2level': 12, 'squarefree': None, 'trace_hash': 0, 'traces': None} -
gps_gl2zhat_fine • Show schema
{'CPlabel': '12I0', 'Glabel': '96.230', 'RSZBlabel': '12.48.0.21', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [7, 11, 7, 4], 'canonical_generators': [[1, 2, 4, 3], [1, 2, 4, 9], [1, 6, 4, 11], [3, 2, 4, 5], [3, 2, 10, 11], [5, 4, 2, 9]], 'cm_discriminants': [], 'coarse_class': '12.48.0.a', 'coarse_class_num': 1, 'coarse_index': 48, 'coarse_label': '12.48.0.a.2', 'coarse_level': 12, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 3]], 'cusp_widths': [[2, 4], [4, 1], [6, 4], [12, 1]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[1, 4, 6, 11], [5, 10, 6, 11], [11, 0, 0, 1], [11, 2, 0, 11], [11, 6, 0, 1]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 3], [3, 1, 1], [3, 3, 1], [4, 2, 3], [6, 1, 3], [6, 3, 3], [12, 2, 3], [12, 6, 3]], 'kummer_orbits': [[2, 1, 3], [3, 1, 1], [3, 3, 1], [4, 2, 3], [6, 1, 3], [6, 3, 3], [12, 4, 3], [12, 6, 2], [12, 12, 2]], 'label': '12.48.0.a.2', 'lattice_labels': ['1.1.0.a.1', '2.2.0.a.1', '2.3.0.a.1', '2.6.0.a.1', '3.4.0.a.1', '6.8.0.a.1', '6.12.0.a.1', '6.24.0.a.1', '12.48.0.a.2'], 'lattice_x': [5936, 2829, 8526, 2829, 6335, 1076, 6335, 3267, 3267], 'level': 12, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': None, 'models': 1, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 17, 'num_known_degree1_noncusp_points': 17, 'num_known_degree1_points': 18, 'obstructions': [], 'orbits': [[2, 1, 3], [3, 2, 1], [3, 6, 1], [4, 4, 3], [6, 2, 3], [6, 6, 3], [12, 8, 3], [12, 12, 2], [12, 24, 2]], 'parents': ['6.24.0.a.1'], 'parents_conj': [[1, 0, 0, 1]], 'pointless': False, 'power': None, 'psl2index': 48, 'psl2label': '12.48.0.a.1', 'psl2level': 12, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.6.0.a.1', '2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1'], 'scalar_label': '12.2.1', 'simple': None, 'sl2label': '12.48.0.a.1', 'sl2level': 12, 'squarefree': None, 'trace_hash': 0, 'traces': []} - modcurve 12.48.0.a.2 does not appear in modcurve_models
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modcurve_modelmaps • Show schema
{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['(x+2*y)^48*(x^4+2*x^3*y+6*x^2*y^2+8*x*y^3+4*y^4)^3*(x^12+6*x^11*y+246*x^10*y^2+1400*x^9*y^3+3960*x^8*y^4+6696*x^7*y^5+7224*x^6*y^6+5184*x^5*y^7+2880*x^4*y^8+1760*x^3*y^9+1056*x^2*y^10+384*x*y^11+64*y^12)^3', 'y^2*x^4*(x+y)^2*(x+2*y)^60*(x^2-2*x*y-2*y^2)^6*(x^2+x*y+y^2)^6*(x^2+2*x*y+2*y^2)^2'], 'degree': 48, 'domain_label': '12.48.0.a.2', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': None, 'upload_id': None} -
modcurve_points • Show schema
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id: 1848148
{'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['-2:1', '-1:1', '0:1', '1:0']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, '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: 996
{'Elabel': '30.a6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 30, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 20.3702917065417, 'jinv': '702595369/72900', 'jorig': '702595369/72900', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 3632
{'Elabel': '210.b2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 41.6035148014809, 'jinv': '1169975873419524361/108425318400', 'jorig': '1169975873419524361/108425318400', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 25602
{'Elabel': '2730.o6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 2730, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 44.7058360023511, 'jinv': '26031421522845051769/5797789779600', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 25939
{'Elabel': '2730.bd2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 2730, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 55.8232590197564, 'jinv': '1752803993935029634719121/4599740941532100', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 35349
{'Elabel': '4290.bb2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 4290, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 52.7900324068928, 'jinv': '84415028961834287121601/30783551683856400', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 49610
{'Elabel': '6630.v2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 6630, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 71.122749666903, 'jinv': '7730680381889320597382223137569/441370202660156250000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 150202
{'Elabel': '30030.bt4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 30030, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 61.5520213790483, 'jinv': '539142086340577084766074129/309580507925165039062500', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 183821
{'Elabel': '39270.bg5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 39270, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 60.0732886864045, 'jinv': '122884692280581205924284889/439106354595306090000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 226661
{'Elabel': '51870.bd6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 51870, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 65.132716529065, 'jinv': '19354385182631020519933543609/1297852417956067777440000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 262191
{'Elabel': '62790.bu4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 62790, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 77.0404376340035, 'jinv': '2872347286043717137884962530087201/890114999660918118510786090000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 370162
{'Elabel': '99330.bg4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 99330, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 79.561371719164, 'jinv': '35732607610705316025359129586549001/466066466565993496219484160000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 404921
{'Elabel': '111930.x7', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 111930, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 69.1587262323392, 'jinv': '1084558988896508932654216096729/147930812860191365916147600', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 442963
{'Elabel': '125970.w2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 125970, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 68.4592904634442, 'jinv': '538880022089281144229433470281/247731924436944317684121600', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 491560
{'Elabel': '144690.u6', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 144690, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 78.6386416761613, 'jinv': '14201301386688072974887643602001929/643473293344889428102500', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 549637
{'Elabel': '167790.bx2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 167790, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 86.3015017969832, 'jinv': '30218020423746445491048161330249640961/2483613169007730825212985600', 'jorig': '30218020423746445491048161330249640961/2483613169007730825212985600', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 798195
{'Elabel': '274170.ck2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 274170, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 80.3861046774085, 'jinv': '81515778978451355139317145508643761/458987832550501978522500', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None} -
id: 805848
{'Elabel': '278070.s3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 278070, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '12.48.0.a.2', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 71.6592900894521, 'jinv': '13220085470315564319698413588681/184165747140990752952422400', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
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id: 1848148
Modular curve data - 12.96.0-12.a.2.9