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gps_gl2zhat_fine • Show schema
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{'CPlabel': '20D1', 'Glabel': None, 'RSZBlabel': '40.72.1.160', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [11, 0, 25, 31], 'canonical_generators': [[0, 1, 9, 2], [0, 3, 1, 2], [0, 3, 7, 6], [0, 3, 13, 10], [0, 3, 17, 6], [0, 29, 31, 38], [0, 31, 29, 22], [0, 39, 21, 38], [19, 0, 0, 39], [21, 20, 20, 21], [39, 0, 20, 39], [39, 20, 0, 39]], 'cm_discriminants': [], 'coarse_class': '20.36.1.b', 'coarse_class_num': 2, 'coarse_index': 36, 'coarse_label': '20.36.1.b.1', 'coarse_level': 20, 'coarse_num': 1, 'conductor': [[2, 4], [5, 1]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 2]], 'cusp_widths': [[1, 2], [4, 1], [5, 2], [20, 1]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 9, 'generators': [[3, 39, 10, 27], [5, 14, 24, 25], [7, 16, 4, 19], [27, 16, 38, 5], [29, 38, 26, 31]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 72, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 1, 1], [5, 5, 1], [8, 4, 1], [8, 8, 1], [10, 1, 1], [10, 2, 1], [10, 5, 1], [10, 10, 1], [20, 2, 1], [20, 4, 1], [20, 10, 1], [20, 20, 1], [40, 4, 1], [40, 8, 1], [40, 20, 1], [40, 40, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 2, 1], [5, 10, 1], [8, 8, 1], [8, 16, 1], [10, 2, 1], [10, 4, 1], [10, 10, 1], [10, 20, 1], [20, 8, 1], [20, 16, 1], [20, 40, 1], [20, 80, 1], [40, 32, 1], [40, 64, 1], [40, 160, 1], [40, 320, 1]], 'label': '40.72.1-20.b.1.9', 'lattice_labels': None, 'lattice_x': None, 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '4.38202663467388161227', '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], [4, 4, 1], [4, 8, 1], [5, 4, 1], [5, 20, 1], [8, 16, 1], [8, 32, 1], [10, 4, 1], [10, 8, 1], [10, 20, 1], [10, 40, 1], [20, 16, 1], [20, 32, 1], [20, 80, 1], [20, 160, 1], [40, 64, 1], [40, 128, 1], [40, 320, 1], [40, 640, 1]], 'parents': ['40.12.0-4.b.1.3'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 36, 'psl2label': '20.36.1.a.1', 'psl2level': 20, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 2, 'reductions': ['2.3.0.a.1', '4.6.0.b.1', '4.6.0.b.1', '5.6.0.a.1', '10.18.0.a.1', '20.36.1.b.1'], 'scalar_label': '4.2.1', 'simple': True, 'sl2label': '40.72.1-20.a.1.2', 'sl2level': 40, 'squarefree': True, 'trace_hash': 203926327671425217, 'traces': None}
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gps_gl2zhat_fine • Show schema
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{'CPlabel': '20D1', 'Glabel': '1280.1098157', 'RSZBlabel': '20.36.1.3', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [1, 11, 18, 19], 'canonical_generators': [[0, 1, 9, 2], [0, 1, 19, 2], [0, 3, 1, 2], [0, 3, 7, 6], [0, 3, 13, 10], [0, 3, 17, 6], [0, 9, 11, 18], [0, 11, 9, 2]], 'cm_discriminants': [], 'coarse_class': '20.36.1.b', 'coarse_class_num': 2, 'coarse_index': 36, 'coarse_label': '20.36.1.b.1', 'coarse_level': 20, 'coarse_num': 1, 'conductor': [[2, 4], [5, 1]], 'contains_negative_one': True, 'curve_label': '80.b4', 'cusp_orbits': [[1, 2], [2, 2]], 'cusp_widths': [[1, 2], [4, 1], [5, 2], [20, 1]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['4.6.0.b.1', '5.6.0.a.1'], 'fine_num': 0, 'generators': [[1, 16, 9, 13], [7, 4, 13, 3], [11, 6, 3, 19], [17, 0, 3, 9]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 36, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 1, 1], [5, 5, 1], [10, 1, 1], [10, 2, 1], [10, 5, 1], [10, 10, 1], [20, 2, 1], [20, 4, 1], [20, 10, 1], [20, 20, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [4, 2, 1], [4, 4, 1], [5, 2, 1], [5, 10, 1], [10, 2, 1], [10, 4, 1], [10, 10, 1], [10, 20, 1], [20, 8, 1], [20, 16, 1], [20, 40, 1], [20, 80, 1]], 'label': '20.36.1.b.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.b.1', '5.6.0.a.1', '10.18.0.a.1', '20.36.1.b.1'], 'lattice_x': [3750, 5544, 8533, 2011, 4728, 6630], 'level': 20, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': {'__RealLiteral__': 0, 'data': '4.38202663467388161227', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['80.2.a.b'], '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], [4, 4, 1], [4, 8, 1], [5, 4, 1], [5, 20, 1], [10, 4, 1], [10, 8, 1], [10, 20, 1], [10, 40, 1], [20, 16, 1], [20, 32, 1], [20, 80, 1], [20, 160, 1]], 'parents': ['4.6.0.b.1', '10.18.0.a.1'], 'parents_conj': [[14, 1, 9, 7], [14, 13, 9, 19]], 'pointless': False, 'power': True, 'psl2index': 36, 'psl2label': '20.36.1.a.1', 'psl2level': 20, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 2, 'reductions': ['2.3.0.a.1', '4.6.0.b.1', '5.6.0.a.1', '10.18.0.a.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '20.36.1.a.1', 'sl2level': 20, 'squarefree': True, 'trace_hash': 203926327671425217, 'traces': [0, 2, -1, -2, 0, 2, -6, 4, -6, 6, 4, 2, 6, 10, 6, -6, -12, 2, -2, 12, 2, -8, -6, -6, 2, 6, -14, 6, 2, -6, -2, 0, 18, 4, -6, -20, -22, 10, -18, -6, 12, -10, 12, 26, 18, -8, 16, 10, 6, 14, -6, 24, 14, 0, -6, 18, 18, -20, 26, 6, -14, -30, -2, -12, -22, -6, -8, 2, 30, -10, 18, -24, 22, 26, 28, -6, -6, 2, -30, -34, -36, 26, -36, 2, -8, -6, 6, 26, 30, -14, 30, 24, -26, 0, 4, 18, 6, -6, -14, 14, -26, -30, 18, 30, -8, -22, 6, 18, 0, -10, 22, 2, -6, -20, 28, -18, -14, -42, 42, -36, -22, -46, 18, 42, -8, -30, -34, 24, 46, -22, -20, -6, 4, -22, 42, 2, -30, -26, 42, -6, 16, -54, -38, 30, 2, 48, 50, 18, 4, -6, 26, -18, -14, -18, 46, -12, 16, -42, -22, -18, -18, -6, 22, 24, 18, 18, 4, 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': '20.36.1.b.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': ['18*x^2*y^10+231870*x^2*y^8*z^2+160411560*x^2*y^6*z^4+2836033434*x^2*y^4*z^6+5360733242*x^2*y^2*z^8+5211922921*x^2*z^10+819*x*y^10*z+2126268*x*y^8*z^3+512947965*x*y^6*z^5-122871624*x*y^4*z^7+6960980885*x*y^2*z^9-7562391552*x*z^11+y^12+10983*y^10*z^2+23771328*y^8*z^4+1733869315*y^6*z^6+10433358193*y^4*z^8+23727088765*y^2*z^10+32868046756*z^12', 'z*(50*x^2*y^8*z+2918*x^2*y^6*z^3-104248*x^2*y^4*z^5-958112*x^2*y^2*z^7-515968*x^2*z^9+x*y^10-320*x*y^8*z^2+15859*x*y^6*z^4+333620*x*y^4*z^6+39632*x*y^2*z^8-4376384*x*z^10+15*y^10*z-1205*y^8*z^3-33613*y^6*z^5+80052*y^4*z^7+2000144*y^2*z^9+4892352*z^11)'], 'degree': 36, 'domain_label': '20.36.1.b.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': None, 'upload_id': None}
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modcurve_points • Show schema
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id: 1715357
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['1:0:1', '0:1:0']}, 'curve_genus': 1, 'curve_index': 36, 'curve_label': '20.36.1.b.1', 'curve_level': 20, '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}
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id: 1715358
{'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-4,0:0,-10:1,0', '0,0:0,-2:1,0']}, 'curve_genus': 1, 'curve_index': 36, 'curve_label': '20.36.1.b.1', 'curve_level': 20, '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': '2.0.4.1', 'upload_id': None}