# Data for modular curve with label 72.144.4-36.m.1.2, downloaded from the LMFDB on 11 June 2024.
{"label": "72.144.4-36.m.1.2", "coarse_level": 36, "coarse_index": 72, "genus": 4, "coarse_label": "36.72.4.m.1", "coarse_class": "36.72.4.m", "coarse_class_num": 13, "coarse_num": 1, "level": 72, "index": 144, "fine_num": 2, "contains_negative_one": false, "determinant_label": "1.1.1", "scalar_label": "3.2.1", "generators": [[7, 48, 58, 65], [14, 13, 3, 4], [35, 30, 44, 1], [62, 13, 27, 22]], "canonical_generators": [[0, 1, 7, 0], [0, 1, 17, 10], [0, 11, 17, 12], [1, 0, 36, 1], [1, 2, 4, 9], [1, 8, 10, 9], [1, 36, 0, 1], [35, 0, 0, 71], [37, 36, 36, 37], [53, 54, 54, 53], [71, 0, 54, 71], [71, 54, 0, 71]], "parents": ["24.48.0-12.h.1.6", "72.72.2-18.d.1.1", "72.72.2-18.d.1.4"], "parents_conj": null, "reductions": ["2.3.0.a.1", "2.3.0.a.1", "2.3.0.a.1", "3.4.0.a.1", "6.12.0.a.1", "9.12.0.b.1", "12.24.0.h.1", "18.36.2.d.1", "24.48.0-12.h.1.6", "36.72.4.m.1"], "factorization": [], "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], [8, 16, 1], [8, 32, 1], [9, 18, 1], [9, 54, 1], [12, 8, 1], [12, 16, 1], [12, 24, 1], [12, 48, 1], [18, 18, 1], [18, 36, 1], [18, 54, 1], [18, 108, 1], [24, 32, 1], [24, 64, 1], [24, 96, 1], [24, 192, 1], [36, 72, 1], [36, 144, 1], [36, 216, 1], [36, 432, 1], [72, 288, 1], [72, 576, 1], [72, 864, 1], [72, 1728, 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], [8, 8, 1], [8, 16, 1], [9, 9, 1], [9, 27, 1], [12, 4, 1], [12, 8, 1], [12, 12, 1], [12, 24, 1], [18, 9, 1], [18, 18, 1], [18, 27, 1], [18, 54, 1], [24, 16, 1], [24, 32, 1], [24, 48, 1], [24, 96, 1], [36, 36, 1], [36, 72, 1], [36, 108, 1], [36, 216, 1], [72, 144, 1], [72, 288, 1], [72, 432, 1], [72, 864, 1]], "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], [8, 4, 1], [8, 8, 1], [9, 3, 1], [9, 9, 1], [12, 2, 1], [12, 4, 1], [12, 6, 1], [12, 12, 1], [18, 3, 1], [18, 6, 1], [18, 9, 1], [18, 18, 1], [24, 4, 1], [24, 8, 1], [24, 12, 1], [24, 24, 1], [36, 6, 1], [36, 12, 1], [36, 18, 1], [36, 36, 1], [72, 12, 1], [72, 24, 1], [72, 36, 1], [72, 72, 1]], "psl2index": 72, "nu2": 0, "nu3": 0, "cusps": 6, "psl2level": 18, "sl2level": 36, "rational_cusps": 2, "cusp_orbits": [[1, 2], [2, 2]], "cusp_widths": [[6, 3], [18, 3]], "psl2label": "18.72.4.b.1", "sl2label": "18.72.4.b.1", "CPlabel": "18C4", "Slabel": null, "SZlabel": null, "RZBlabel": null, "RSZBlabel": null, "Glabel": null, "name": null, "rank": null, "genus_minus_rank": null, "newforms": ["54.2.a.a", "54.2.a.b", "432.2.a.b", "432.2.a.g"], "dims": null, "mults": null, "traces": [0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 32, 0, 0, -28, 0, 0, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, -64, 0, 20, 0, 0, 0, 0, 0, 56, 0, 0, -40, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -76, 0, 0, -88, 0, -40, 0, 0, 0, 128, 0, 0, 0, 80, 0, 92, 0, 32, 0, 116, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 152, 0, 0, 0, 140, 0, -136, 0, 0, 0, 0, 0, 0, 0, 0, 56, -76, 0, 0, 0, 0, 176, 0, 0, -88, 0, 0, 0, 8, 0, -124, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -40, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, -112], "trace_hash": null, "simple": false, "squarefree": null, "power": null, "conductor": null, "log_conductor": null, "q_gonality": null, "q_gonality_bounds": [3, 4], "qbar_gonality": null, "qbar_gonality_bounds": [3, 4], "bad_primes": [2, 3], "num_bad_primes": 2, "level_radical": 6, "level_is_squarefree": false, "cm_discriminants": [], "obstructions": [], "pointless": false, "num_known_degree1_points": null, "lattice_labels": null, "lattice_x": null, "curve_label": null, "canonical_conjugator": [1, 0, 0, 1], "has_obstruction": 0, "num_known_degree1_noncusp_points": null, "num_known_degree1_noncm_points": null, "models": null, "all_degree1_points_known": null, "coarse_parents": ["12.24.0.h.1", "18.36.2.d.1", "36.24.0.c.1"]}