-
gps_gl2zhat_fine • Show schema
{'CPlabel': '42G5', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 7], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[0, 17, 11, 6], [0, 19, 11, 22], [0, 55, 71, 82], [0, 71, 55, 44], [0, 73, 67, 48], [0, 79, 79, 0], [0, 83, 43, 68], [43, 0, 0, 1], [43, 42, 42, 43], [83, 0, 42, 83], [83, 42, 0, 83]], 'cm_discriminants': [], 'coarse_class': '42.96.5.a', 'coarse_class_num': 1, 'coarse_index': 96, 'coarse_label': '42.96.5.a.1', 'coarse_level': 42, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 8]], 'cusp_widths': [[1, 1], [2, 1], [3, 1], [6, 1], [7, 1], [14, 1], [21, 1], [42, 1]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': None, 'factorization': ['7.8.0.a.1', '12.24.0-6.a.1.6'], 'fine_num': 47, 'generators': [[7, 60, 58, 65], [27, 80, 40, 53], [36, 37, 23, 22], [41, 28, 78, 61], [52, 59, 55, 42], [59, 24, 32, 79]], 'genus': 5, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 192, '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], [7, 1, 1], [7, 7, 1], [12, 2, 1], [12, 4, 1], [12, 6, 1], [12, 12, 1], [14, 1, 1], [14, 2, 1], [14, 7, 1], [14, 14, 1], [21, 1, 1], [21, 3, 1], [21, 7, 1], [21, 21, 1], [28, 2, 1], [28, 4, 1], [28, 14, 1], [28, 28, 1], [42, 1, 1], [42, 2, 1], [42, 3, 1], [42, 6, 1], [42, 7, 1], [42, 14, 1], [42, 21, 1], [42, 42, 1], [84, 2, 1], [84, 4, 1], [84, 6, 1], [84, 12, 1], [84, 14, 1], [84, 28, 1], [84, 42, 1], [84, 84, 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], [7, 3, 1], [7, 21, 1], [12, 4, 1], [12, 8, 1], [12, 12, 1], [12, 24, 1], [14, 3, 1], [14, 6, 1], [14, 21, 1], [14, 42, 1], [21, 6, 1], [21, 18, 1], [21, 42, 1], [21, 126, 1], [28, 12, 1], [28, 24, 1], [28, 84, 1], [28, 168, 1], [42, 6, 1], [42, 12, 1], [42, 18, 1], [42, 36, 1], [42, 42, 1], [42, 84, 1], [42, 126, 1], [42, 252, 1], [84, 24, 1], [84, 48, 1], [84, 72, 1], [84, 144, 1], [84, 168, 1], [84, 336, 1], [84, 504, 1], [84, 1008, 1]], 'label': '84.192.5-42.a.1.47', 'lattice_labels': None, 'lattice_x': None, 'level': 84, 'level_is_squarefree': False, 'level_radical': 42, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': None, 'num_known_degree1_noncusp_points': None, 'num_known_degree1_points': None, '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], [7, 6, 1], [7, 42, 1], [12, 8, 1], [12, 16, 1], [12, 24, 1], [12, 48, 1], [14, 6, 1], [14, 12, 1], [14, 42, 1], [14, 84, 1], [21, 12, 1], [21, 36, 1], [21, 84, 1], [21, 252, 1], [28, 24, 1], [28, 48, 1], [28, 168, 1], [28, 336, 1], [42, 12, 1], [42, 24, 1], [42, 36, 1], [42, 72, 1], [42, 84, 1], [42, 168, 1], [42, 252, 1], [42, 504, 1], [84, 48, 1], [84, 96, 1], [84, 144, 1], [84, 288, 1], [84, 336, 1], [84, 672, 1], [84, 1008, 1], [84, 2016, 1]], 'parents': ['12.24.0-6.a.1.6'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 96, 'psl2label': '42.96.5.a.1', 'psl2level': 42, 'q_gonality': None, 'q_gonality_bounds': [3, 5], 'qbar_gonality': None, 'qbar_gonality_bounds': [3, 5], 'rank': None, 'rational_cusps': 8, 'reductions': ['2.3.0.a.1', '2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '7.8.0.a.1', '12.24.0-6.a.1.6', '14.24.1.a.1', '14.24.1.a.1', '21.32.1.a.1', '42.96.5.a.1'], 'scalar_label': '3.2.1', 'simple': False, 'sl2label': '42.96.5.a.1', 'sl2level': 84, 'squarefree': None, 'trace_hash': None, 'traces': None} -
gps_gl2zhat_fine • Show schema
{'CPlabel': '42G5', 'Glabel': None, 'RSZBlabel': '42.96.5.1', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 7], 'canonical_conjugator': [12, 29, 29, 41], 'canonical_generators': [[0, 1, 41, 16], [0, 5, 5, 0], [0, 11, 17, 36], [0, 13, 29, 40], [0, 17, 11, 6], [0, 19, 11, 22], [0, 29, 13, 2]], 'cm_discriminants': [], 'coarse_class': '42.96.5.a', 'coarse_class_num': 1, 'coarse_index': 96, 'coarse_label': '42.96.5.a.1', 'coarse_level': 42, 'coarse_num': 1, 'conductor': [[2, 3], [3, 3], [7, 5]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 8]], 'cusp_widths': [[1, 1], [2, 1], [3, 1], [6, 1], [7, 1], [14, 1], [21, 1], [42, 1]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1, 1, 1], 'factorization': ['2.3.0.a.1', '3.4.0.a.1', '7.8.0.a.1'], 'fine_num': 0, 'generators': [[1, 35, 0, 37], [5, 14, 0, 37], [13, 22, 0, 31], [25, 16, 0, 17], [41, 39, 0, 31]], 'genus': 5, 'genus_minus_rank': 5, 'has_obstruction': -1, 'index': 96, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [7, 1, 1], [7, 7, 1], [14, 1, 1], [14, 2, 1], [14, 7, 1], [14, 14, 1], [21, 1, 1], [21, 3, 1], [21, 7, 1], [21, 21, 1], [42, 1, 1], [42, 2, 1], [42, 3, 1], [42, 6, 1], [42, 7, 1], [42, 14, 1], [42, 21, 1], [42, 42, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [7, 3, 1], [7, 21, 1], [14, 3, 1], [14, 6, 1], [14, 21, 1], [14, 42, 1], [21, 6, 1], [21, 18, 1], [21, 42, 1], [21, 126, 1], [42, 6, 1], [42, 12, 1], [42, 18, 1], [42, 36, 1], [42, 42, 1], [42, 84, 1], [42, 126, 1], [42, 252, 1]], 'label': '42.96.5.a.1', 'lattice_labels': None, 'lattice_x': None, 'level': 42, 'level_is_squarefree': True, 'level_radical': 42, 'log_conductor': {'__RealLiteral__': 0, 'data': '15.10482915296073152796', 'prec': 77}, 'models': 1, 'mults': [2, 2, 1], 'name': 'X0(42)', 'newforms': ['14.2.a.a', '21.2.a.a', '42.2.a.a'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, '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, 2, 1], [3, 6, 1], [6, 2, 1], [6, 4, 1], [6, 6, 1], [6, 12, 1], [7, 6, 1], [7, 42, 1], [14, 6, 1], [14, 12, 1], [14, 42, 1], [14, 84, 1], [21, 12, 1], [21, 36, 1], [21, 84, 1], [21, 252, 1], [42, 12, 1], [42, 24, 1], [42, 36, 1], [42, 72, 1], [42, 84, 1], [42, 168, 1], [42, 252, 1], [42, 504, 1]], 'parents': ['6.12.0.a.1', '14.24.1.a.1', '21.32.1.a.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': False, 'psl2index': 96, 'psl2label': '42.96.5.a.1', 'psl2level': 42, 'q_gonality': None, 'q_gonality_bounds': [3, 5], 'qbar_gonality': None, 'qbar_gonality_bounds': [3, 5], 'rank': 0, 'rational_cusps': 8, 'reductions': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '7.8.0.a.1', '14.24.1.a.1', '21.32.1.a.1'], 'scalar_label': '1.1.1', 'simple': False, 'sl2label': '42.96.5.a.1', 'sl2level': 42, 'squarefree': False, 'trace_hash': 2243786701239819527, 'traces': [-3, -3, -6, -1, 4, -6, 2, 8, 8, -18, -8, 6, 10, 4, -24, 30, 16, 18, 4, 8, 2, -16, -40, -46, 2, 26, 16, 44, -34, -30, -32, 24, 34, 56, -18, 24, -22, -4, -48, -22, -44, -30, 32, 34, -2, 96, 20, 32, 24, -30, -46, 96, -14, -88, 58, 8, 10, 0, 14, -30, -80, 106, 40, -104, 42, -42, 4, 18, -92, -38, 26, 8, 48, 30, -28, 56, 22, 10, -78, -38, -48, 62, 0, -94, -56, 44, 10, 10, 26, 64, 88, -120, -40, 28, -44, 72, 58, 42, -16, 38, 12, 6, 112, 26, 68, 106, -56, -6, 72, 66, 80, -90, -22, -32, -104, 2, 64, -80, -18, -52, -38, 122, -78, -36, -56, 94, -90, -72, 0, -110, 28, 72, -96, -10, -22, 18, 74, -168, -70, 106, 48, 126, -88, -132, 114, 64, 82, -22, 136, -128, 46, -102, 4, -80, 92, 48, 168, 82, 66, 2, 140, -30, 152, 0, -54, -48, -80, -22]} -
modcurve_models • Show schema
{'dont_display': False, 'equation': ['x^2-x*w+x*t+y*t', 'x^2+x*z-z^2+2*x*w-2*z*w-w^2+y*t', 'x^2+y^2+2*y*z+z^2+2*y*w+2*z*w-y*t-z*t'], 'modcurve': '42.96.5.a.1', 'model_type': 0, 'number_variables': 5, 'smooth': True, 'upload_id': None} -
modcurve_modelmaps • Show schema
{'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['-1101204000*y*z^2*w^9+769937616*x*y*w^10-2473473600*y*z*w^10-2076263568*z^2*w^10+1805178224*x*w^11-1312033824*y*w^11-4363352352*z*w^11-2226851984*w^12+3375732240*y*z^2*w^8*t-7481495504*x*y*w^9*t+5059358928*y*z*w^9*t-2224674576*z^2*w^9*t+637202672*x*w^10*t+4332162928*y*w^10*t-2866362624*z*w^10*t+1573843584*w^11*t+40513615200*y*z^2*w^7*t^2-41986389168*x*y*w^8*t^2+90289768464*y*z*w^8*t^2+71611914960*z^2*w^8*t^2-66658243360*x*w^9*t^2+50922213632*y*w^9*t^2+141552055152*z*w^9*t^2+64696335456*w^10*t^2-84131529840*y*z^2*w^6*t^3+94680843888*x*y*w^7*t^3-184954443408*y*z*w^7*t^3-102846908976*z^2*w^7*t^3+139134320784*x*w^8*t^3-179961485232*y*w^8*t^3-229062506496*z*w^8*t^3-149322391280*w^9*t^3-65404144400*y*z^2*w^5*t^4-64657507936*x*y*w^6*t^4-275538610864*y*z*w^6*t^4-404471962768*z^2*w^6*t^4+283872442144*x*w^7*t^4-138716908928*y*w^7*t^4-728395806992*z*w^7*t^4-189564572464*w^8*t^4+349910930960*y*z^2*w^4*t^5-230210553200*x*y*w^5*t^5+1098616893328*y*z*w^5*t^5+1042142507552*z^2*w^5*t^5-1124585022912*x*w^6*t^5+1174192396032*y*w^6*t^5+2060241092688*z*w^6*t^5+863050363056*w^7*t^5-306811384560*y*z^2*w^3*t^6+444699730512*x*y*w^4*t^6-930701159904*y*z*w^4*t^6-704274317872*z^2*w^4*t^6+1204755984192*x*w^5*t^6-1482336677680*y*w^5*t^6-1486108944816*z*w^5*t^6-876855455296*w^6*t^6+55178056000*y*z^2*w^2*t^7-290351294784*x*y*w^3*t^7-66344877376*y*z*w^3*t^7-226399477392*z^2*w^3*t^7-342853547984*x*w^4*t^7+344197675120*y*w^4*t^7-410738278480*z*w^4*t^7+177772535440*w^5*t^7+32079604400*y*z^2*w*t^8+86979125168*x*y*w^2*t^8+419469380720*y*z*w^2*t^8+490794373216*z^2*w^2*t^8-285842029152*x*w^3*t^8+606409820608*y*w^3*t^8+1057266016096*z*w^3*t^8+221840899680*w^4*t^8-10173090480*y*z^2*t^9-10629427568*x*y*w*t^9-178987210096*y*z*w*t^9-208058806640*z^2*w*t^9+265598679184*x*w^2*t^9-498748197968*y*w^2*t^9-495548508720*z*w^2*t^9-135234251696*w^3*t^9-126594064*x*y*t^10+21875600944*y*z*t^10+27703743328*z^2*t^10-83137846432*x*w*t^10+140392458576*y*w*t^10+78803719088*z*w*t^10+21413254944*w^2*t^10+9492339776*x*t^11-13658082080*y*t^11-1737168448*z*t^11-240*w*t^11+16*t^12', '-4448*y*z^2*w^8*t+17536*x*y*w^9*t-8768*y*z*w^9*t+3152*z^2*w^9*t-12352*x*w^10*t-4320*y*w^10*t+6176*z*w^10*t+3024*w^11*t+59552*y*z^2*w^7*t^2-246848*x*y*w^8*t^2+129072*y*z*w^8*t^2-55600*z^2*w^8*t^2+247232*x*w^9*t^2+74672*y*w^9*t^2-103616*z*w^9*t^2-55504*w^10*t^2-132640*y*z^2*w^6*t^3+627936*x*y*w^7*t^3-386464*y*z*w^7*t^3+268176*z^2*w^7*t^3-1524176*x*w^8*t^3-375024*y*w^8*t^3+459440*z*w^8*t^3+288992*w^9*t^3-799216*y*z^2*w^5*t^4+3643248*x*y*w^6*t^4-1642000*y*z*w^6*t^4+5936*z^2*w^6*t^4+1846592*x*w^7*t^4-19280*y*w^7*t^4+182112*z*w^7*t^4-8896*w^8*t^4+2680744*y*z^2*w^4*t^5-15969488*x*y*w^5*t^5+8393512*y*z*w^5*t^5-2555496*z^2*w^5*t^5+11289696*x*w^6*t^5+4655040*y*w^6*t^5-4204664*z*w^6*t^5-3263024*w^7*t^5-509900*y*z^2*w^3*t^6+9835120*x*y*w^4*t^6-4802860*y*z*w^4*t^6+5910668*z^2*w^4*t^6-33941088*x*w^5*t^6-10263984*y*w^5*t^6+6877964*z*w^5*t^6+6473072*w^6*t^6-618744*y*z^2*w^2*t^7+9024300*x*y*w^3*t^7-11762024*y*z*w^3*t^7-10781672*z^2*w^3*t^7+29636740*x*w^4*t^7+2007608*y*w^4*t^7-13971664*z*w^4*t^7-4031968*w^5*t^7-1133694*y*z^2*w*t^8-1489758*x*y*w^2*t^8+12120974*y*z*w^2*t^8+14161908*z^2*w^2*t^8-10137902*x*w^3*t^8+17107190*y*w^3*t^8+27609696*z*w^3*t^8+3293846*w^4*t^8+559595*y*z^2*t^9-3110813*x*y*w*t^9-6953923*y*z*w*t^9-9022495*z^2*w*t^9+1087587*x*w^2*t^9-22679769*y*w^2*t^9-22311507*z*w^2*t^9-2425095*w^3*t^9+745595*x*y*t^10+2100788*y*z*t^10+2217743*z^2*t^10-518593*x*w*t^10+9341088*y*w*t^10+7258392*z*w*t^10+673864*w^2*t^10+176194*x*t^11-1199368*y*t^11-701698*z*t^11'], 'degree': 96, 'domain_label': '42.96.5.a.1', 'domain_model_type': 0, 'dont_display': False, 'factored': False, 'leading_coefficients': None, 'upload_id': None} -
modcurve_points • Show schema
-
id: 1708669
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': -12, 'conductor_norm': None, 'coordinates': None, 'curve_genus': 5, 'curve_index': 96, 'curve_label': '42.96.5.a.1', 'curve_level': 42, 'curve_name': 'X0(42)', 'cusp': False, 'degree': 2, 'isolated': 4, 'j_field': '1.1.1.1', 'j_height': 10.8967393255464, 'jinv': '54000', 'jorig': None, 'quo_info': None, 'residue_field': '2.0.3.1', 'upload_id': None} -
id: 1708673
{'Elabel': None, 'ainvs': None, 'cardinality': None, 'cm': -3, 'conductor_norm': None, 'coordinates': None, 'curve_genus': 5, 'curve_index': 96, 'curve_label': '42.96.5.a.1', 'curve_level': 42, 'curve_name': 'X0(42)', 'cusp': False, 'degree': 2, 'isolated': 4, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': '0', 'jorig': None, 'quo_info': None, 'residue_field': '2.0.3.1', 'upload_id': None} -
id: 1787866
{'Elabel': None, 'ainvs': None, 'cardinality': 8, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['0:0:-1:1:1', '1/3:-1/6:-1/6:5/6:1', '0:1:-1:1:0', '1:-2:1:1:0', '-1/3:1/6:1/6:1/6:1', '1:1:-2:1:0', '0:-1:-1:1:0', '0:0:0:0:1']}, 'curve_genus': 5, 'curve_index': 96, 'curve_label': '42.96.5.a.1', 'curve_level': 42, 'curve_name': 'X0(42)', '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: 1708669
Modular curve data - 84.192.5-42.a.1.47