# Data for modular curve with label 56.504.16-56.b.1.6, downloaded from the LMFDB on 23 May 2024.
{"label": "56.504.16-56.b.1.6", "coarse_level": 56, "coarse_index": 252, "genus": 16, "coarse_label": "56.252.16.b.1", "coarse_class": "56.252.16.b", "coarse_class_num": 2, "coarse_num": 1, "level": 56, "index": 504, "fine_num": 6, "contains_negative_one": false, "determinant_label": "1.1.1", "scalar_label": "4.2.1", "generators": [[15, 28, 14, 27], [17, 12, 12, 25], [29, 46, 52, 15], [41, 6, 36, 13], [41, 54, 40, 43]], "canonical_generators": [[1, 0, 28, 1], [1, 2, 4, 9], [1, 16, 4, 9], [1, 28, 0, 1], [9, 8, 2, 55], [9, 22, 16, 41], [29, 18, 24, 13], [29, 28, 28, 29], [41, 54, 52, 33], [47, 34, 12, 29], [47, 48, 40, 29]], "parents": ["8.24.0-8.b.1.1", "28.252.7-14.a.1.1", "56.252.7-14.a.1.4"], "parents_conj": null, "reductions": ["2.6.0.a.1", "4.12.0-2.a.1.1", "7.21.0.a.1", "8.24.0-8.b.1.1", "14.126.7.a.1", "28.252.7-14.a.1.1"], "factorization": ["7.21.0.a.1", "8.24.0-8.b.1.1"], "orbits": [[2, 1, 3], [4, 2, 2], [4, 4, 2], [7, 48, 1], [8, 8, 2], [8, 16, 2], [14, 48, 3], [28, 96, 2], [28, 192, 2], [56, 384, 2], [56, 768, 2]], "kummer_orbits": [[2, 1, 3], [4, 2, 3], [7, 24, 1], [8, 8, 3], [14, 24, 3], [28, 96, 3], [56, 384, 3]], "isogeny_orbits": [[2, 1, 3], [4, 2, 3], [7, 8, 1], [8, 4, 3], [14, 8, 3], [28, 16, 3], [56, 32, 3]], "psl2index": 252, "nu2": 0, "nu3": 0, "cusps": 12, "psl2level": 28, "sl2level": 28, "rational_cusps": 0, "cusp_orbits": [[3, 2], [6, 1]], "cusp_widths": [[14, 6], [28, 6]], "psl2label": "28.252.16.a.1", "sl2label": "28.504.16-28.a.1.1", "CPlabel": "28C16", "Slabel": null, "SZlabel": null, "RZBlabel": null, "RSZBlabel": "56.504.16.3", "Glabel": null, "name": null, "rank": 0, "genus_minus_rank": 16, "newforms": ["98.2.a.b", "196.2.a.b", "196.2.a.c", "3136.2.a.bc", "3136.2.a.bm", "3136.2.a.bp", "3136.2.a.bs", "3136.2.a.j", "3136.2.a.s"], "dims": [2, 1, 2, 1, 2, 2, 2, 1, 1], "mults": [2, 1, 1, 1, 1, 1, 1, 1, 1], "traces": [4, 4, 2, 0, 12, 4, 4, 4, -6, 20, 6, 18, 0, 0, -6, 10, 36, 2, 68, -16, 12, 10, 32, 28, -16, 10, 10, 52, 10, -56, 48, 28, 36, 32, 34, -58, -6, 124, 32, 34, 140, -12, -6, -84, -44, 22, 48, 0, 12, -30, 116, -32, -36, 40, -28, 38, 26, 10, -22, 144, 28, -12, -48, -26, 76, 34, -52, -48, -172, 4, -44, -54, -42, -62, -216, -6, 122, 34, -12, 68, 16, 52, -10, -48, -6, -92, 40, 228, 36, 96, -20, -10, -42, 104, 28, 16, 2, 60, 4, 66, -200, -102, -12, 124, -84, -4, 16, -44, 6, 16, -6, -166, -80, -76, 48, 204, -48, -58, -14, 272, -22, -160, -30, 188, -68, 52, -46, 10, -48, -30, -324, 64, 10, 4, 36, -32, -54, -92, -60, -204, -112, 34, 166, 0, 26, 48, -12, 12, 52, -150, -78, 40, 144, 58, -268, 48, -6, -52, 8, -6, 44, -152, -224, 124, 308, 54, -42, 10], "trace_hash": 886177292736462918, "simple": false, "squarefree": false, "power": false, "conductor": [[2, 64], [7, 32]], "log_conductor": {"__RealLiteral__": 0, "data": "106.63054432560652556607", "prec": 80}, "q_gonality": null, "q_gonality_bounds": [5, 8], "qbar_gonality": null, "qbar_gonality_bounds": [5, 8], "bad_primes": [2, 7], "num_bad_primes": 2, "level_radical": 14, "level_is_squarefree": false, "cm_discriminants": [], "obstructions": [3, 11, 67], "pointless": true, "num_known_degree1_points": 0, "lattice_labels": null, "lattice_x": null, "curve_label": null, "canonical_conjugator": [37, 16, 35, 43], "has_obstruction": 1, "num_known_degree1_noncusp_points": 0, "num_known_degree1_noncm_points": 0, "models": null, "all_degree1_points_known": null, "coarse_parents": ["8.12.0.b.1", "14.126.7.a.1", "56.126.6.c.1", "56.126.7.d.1"]}