# Data for modular curve with label 168.192.1-56.by.1.2, downloaded from the LMFDB on 03 June 2024.
{"label": "168.192.1-56.by.1.2", "coarse_level": 56, "coarse_index": 96, "genus": 1, "coarse_label": "56.96.1.by.1", "coarse_class": "56.96.1.by", "coarse_class_num": 51, "coarse_num": 1, "level": 168, "index": 192, "fine_num": 2, "contains_negative_one": false, "determinant_label": "1.1.1", "scalar_label": "8.4.1", "generators": [[49, 76, 128, 133], [55, 36, 94, 19], [127, 80, 130, 105], [143, 52, 12, 155]], "canonical_generators": [[1, 0, 56, 1], [1, 0, 84, 1], [1, 0, 120, 1], [1, 56, 0, 1], [1, 60, 120, 91], [1, 120, 0, 1], [1, 120, 18, 49], [41, 0, 84, 41], [55, 0, 0, 167], [57, 56, 112, 113], [121, 120, 48, 49], [161, 108, 48, 83], [167, 48, 108, 161]], "parents": ["24.96.0-8.i.1.2", "168.96.0-8.i.1.8", "168.96.0-56.i.2.3", "168.96.0-56.i.2.9", "168.96.0-56.j.1.2", "168.96.0-56.j.1.9", "168.96.0-56.x.1.3", "168.96.0-56.x.1.13", "168.96.1-56.bi.1.7", "168.96.1-56.bi.1.9", "168.96.1-56.bj.2.7", "168.96.1-56.bj.2.11", "168.96.1-56.bs.1.3", "168.96.1-56.bs.1.4"], "parents_conj": null, "reductions": ["1.1.0.a.1", "1.1.0.a.1", "1.1.0.a.1", "2.6.0.a.1", "2.6.0.a.1", "2.6.0.a.1", "2.6.0.a.1", "4.12.0.b.1", "4.12.0.b.1", "8.48.0.i.1", "24.96.0-8.i.1.2", "28.24.0.c.1", "28.24.0.c.1", "56.96.1.by.1"], "factorization": [], "orbits": [[2, 1, 3], [3, 8, 1], [4, 2, 2], [4, 4, 2], [6, 8, 3], [7, 48, 1], [8, 4, 2], [8, 8, 3], [8, 16, 1], [12, 16, 2], [12, 32, 2], [14, 48, 3], [21, 384, 1], [24, 32, 2], [24, 64, 3], [24, 128, 1], [28, 96, 2], [28, 192, 2], [42, 384, 3], [56, 192, 2], [56, 384, 3], [56, 768, 1], [84, 768, 2], [84, 1536, 2], [168, 1536, 2], [168, 3072, 3], [168, 6144, 1]], "kummer_orbits": [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [7, 24, 1], [8, 2, 2], [8, 4, 3], [8, 8, 1], [12, 8, 2], [12, 16, 2], [14, 24, 3], [21, 192, 1], [24, 16, 2], [24, 32, 3], [24, 64, 1], [28, 48, 2], [28, 96, 2], [42, 192, 3], [56, 96, 2], [56, 192, 3], [56, 384, 1], [84, 384, 2], [84, 768, 2], [168, 768, 2], [168, 1536, 3], [168, 3072, 1]], "isogeny_orbits": [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [7, 8, 1], [8, 2, 2], [8, 4, 2], [12, 4, 2], [12, 8, 2], [14, 8, 3], [21, 32, 1], [24, 8, 2], [24, 16, 2], [28, 8, 2], [28, 16, 2], [42, 32, 3], [56, 16, 2], [56, 32, 2], [84, 32, 2], [84, 64, 2], [168, 64, 2], [168, 128, 2]], "psl2index": 96, "nu2": 0, "nu3": 0, "cusps": 16, "psl2level": 8, "sl2level": 8, "rational_cusps": 0, "cusp_orbits": [[2, 4], [4, 2]], "cusp_widths": [[4, 8], [8, 8]], "psl2label": "8.96.1.a.1", "sl2label": "8.96.1.a.1", "CPlabel": "8K1", "Slabel": null, "SZlabel": null, "RZBlabel": null, "RSZBlabel": null, "Glabel": null, "name": null, "rank": null, "genus_minus_rank": null, "newforms": ["3136.2.a.m"], "dims": [1], "mults": [1], "traces": [0, 0, -2, 0, 0, 6, -2, 0, 0, 10, 0, 2, -10, 0, 0, -14, 0, -10, 0, 0, 6, 0, 0, -10, -18, -2, 0, 0, -6, -14, 0, 0, -22, 0, -14, 0, 22, 0, 0, -26, 0, -18, 0, -14, 2, 0, 0, 0, 0, 30, 26, 0, 30, 0, -2, 0, -26, 0, 18, 10, 0, -34, 0, 0, -26, -22, 0, 18, 0, -10, -34, 0, 0, -14, 0, 0, 34, 38, 2, 6, 0, -30, 0, -34, 0, 0, -14, 42, 38, 0, 0, 0, 0, 0, 0, 0, -10, 22, 0, 42, 0, -38, 0, 26, 0, -2, 0, 46, 0, -10, 0, 34, -38, 0, 0, 50, 0, 0, 26, 0, -50, -46, -2, 0, 0, 10, -30, 0, 0, 54, 0, 0, 0, 18, 38, -50, -34, 0, 22, 10, 0, 50, 0, 0, 54, 0, 46, -58, 0, 0, 58, -50, 0, 0, 0, 0, 0, 46, 38, -58, 0, 26, 0, 0, -62, 0, 0, 62], "trace_hash": null, "simple": true, "squarefree": true, "power": true, "conductor": null, "log_conductor": null, "q_gonality": null, "q_gonality_bounds": [2, 96], "qbar_gonality": 2, "qbar_gonality_bounds": [2, 2], "bad_primes": [2, 3, 7], "num_bad_primes": 3, "level_radical": 42, "level_is_squarefree": false, "cm_discriminants": [], "obstructions": [], "pointless": null, "num_known_degree1_points": null, "lattice_labels": null, "lattice_x": null, "curve_label": null, "canonical_conjugator": [1, 0, 0, 1], "has_obstruction": -1, "num_known_degree1_noncusp_points": null, "num_known_degree1_noncm_points": null, "models": null, "all_degree1_points_known": null, "coarse_parents": ["8.48.0.i.1", "56.48.0.i.2", "56.48.0.j.1", "56.48.0.x.1", "56.48.1.bi.1", "56.48.1.bj.2", "56.48.1.bs.1"]}