# Data for modular curve with label 40.72.1-20.b.1.9, downloaded from the LMFDB on 05 June 2024.
{"label": "40.72.1-20.b.1.9", "coarse_level": 20, "coarse_index": 36, "genus": 1, "coarse_label": "20.36.1.b.1", "coarse_class": "20.36.1.b", "coarse_class_num": 2, "coarse_num": 1, "level": 40, "index": 72, "fine_num": 9, "contains_negative_one": false, "determinant_label": "1.1.1", "scalar_label": "4.2.1", "generators": [[3, 39, 10, 27], [5, 14, 24, 25], [7, 16, 4, 19], [27, 16, 38, 5], [29, 38, 26, 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]], "parents": ["40.12.0-4.b.1.3"], "parents_conj": null, "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"], "factorization": [], "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]], "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]], "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]], "psl2index": 36, "nu2": 0, "nu3": 0, "cusps": 6, "psl2level": 20, "sl2level": 40, "rational_cusps": 2, "cusp_orbits": [[1, 2], [2, 2]], "cusp_widths": [[1, 2], [4, 1], [5, 2], [20, 1]], "psl2label": "20.36.1.a.1", "sl2label": "40.72.1-20.a.1.2", "CPlabel": "20D1", "Slabel": null, "SZlabel": null, "RZBlabel": null, "RSZBlabel": "40.72.1.160", "Glabel": null, "name": null, "rank": 0, "genus_minus_rank": 1, "newforms": ["80.2.a.b"], "dims": [1], "mults": [1], "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], "trace_hash": 203926327671425217, "simple": true, "squarefree": true, "power": true, "conductor": [[2, 4], [5, 1]], "log_conductor": {"__RealLiteral__": 0, "data": "4.38202663467388161227", "prec": 74}, "q_gonality": 2, "q_gonality_bounds": [2, 2], "qbar_gonality": 2, "qbar_gonality_bounds": [2, 2], "bad_primes": [2, 5], "num_bad_primes": 2, "level_radical": 10, "level_is_squarefree": false, "cm_discriminants": [], "obstructions": [], "pointless": false, "num_known_degree1_points": 1, "lattice_labels": null, "lattice_x": null, "curve_label": null, "canonical_conjugator": [11, 0, 25, 31], "has_obstruction": -1, "num_known_degree1_noncusp_points": 0, "num_known_degree1_noncm_points": 0, "models": null, "all_degree1_points_known": null, "coarse_parents": ["4.6.0.b.1", "10.18.0.a.1"]}