# Data for modular curve with label 35.3360.117-35.a.1.7, downloaded from the LMFDB on 01 June 2024.
{"label": "35.3360.117-35.a.1.7", "coarse_level": 35, "coarse_index": 1680, "genus": 117, "coarse_label": "35.1680.117.a.1", "coarse_class": "35.1680.117.a", "coarse_class_num": 1, "coarse_num": 1, "level": 35, "index": 3360, "fine_num": 7, "contains_negative_one": false, "determinant_label": "1.1.1", "scalar_label": "5.4.1", "generators": [[14, 12, 30, 21], [26, 5, 5, 16], [28, 18, 25, 1]], "canonical_generators": [[0, 8, 26, 18], [0, 18, 1, 28], [0, 23, 31, 8], [0, 33, 11, 13], [1, 5, 25, 21], [1, 20, 30, 6], [21, 5, 25, 6]], "parents": ["5.120.0-5.a.1.2", "35.672.21-35.a.1.6", "35.672.21-35.a.2.2"], "parents_conj": null, "reductions": ["5.120.0-5.a.1.2", "7.28.0.a.1"], "factorization": ["5.120.0-5.a.1.2", "7.28.0.a.1"], "orbits": [[5, 1, 4], [5, 4, 5], [7, 12, 1], [7, 36, 1], [35, 12, 4], [35, 36, 4], [35, 48, 5], [35, 144, 5]], "kummer_orbits": [[5, 1, 2], [5, 2, 1], [5, 4, 2], [7, 6, 1], [7, 18, 1], [35, 12, 2], [35, 24, 1], [35, 36, 2], [35, 48, 2], [35, 72, 1], [35, 144, 2]], "isogeny_orbits": [[5, 1, 2], [5, 4, 1], [7, 2, 1], [7, 6, 1], [35, 2, 2], [35, 6, 2], [35, 8, 1], [35, 24, 1]], "psl2index": 1680, "nu2": 0, "nu3": 0, "cusps": 48, "psl2level": 35, "sl2level": 35, "rational_cusps": 2, "cusp_orbits": [[1, 2], [2, 1], [3, 2], [4, 2], [6, 1], [12, 2]], "cusp_widths": [[35, 48]], "psl2label": "35.1680.117.a.1", "sl2label": "35.3360.117-35.a.1.1", "CPlabel": null, "Slabel": null, "SZlabel": null, "RZBlabel": null, "RSZBlabel": "35.3360.117.1", "Glabel": "288.699", "name": null, "rank": 19, "genus_minus_rank": 98, "newforms": ["35.2.a.a", "35.2.a.b", "35.2.b.a", "175.2.a.a", "175.2.a.b", "175.2.a.c", "175.2.a.d", "175.2.a.e", "175.2.a.f", "175.2.b.a", "175.2.b.b", "175.2.b.c", "245.2.a.e", "245.2.a.f", "245.2.a.h", "245.2.b.c", "245.2.b.e", "245.2.b.f", "1225.2.a.ba", "1225.2.a.bb", "1225.2.a.bc", "1225.2.a.d", "1225.2.a.f", "1225.2.a.k", "1225.2.a.l", "1225.2.a.p", "1225.2.a.r", "1225.2.a.v", "1225.2.a.x", "1225.2.a.y", "1225.2.b.g", "1225.2.b.i", "1225.2.b.j", "1225.2.b.l", "1225.2.b.n"], "dims": [1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 4, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 6, 8], "mults": [2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], "traces": [1, 2, 2, -1, 0, 6, 2, -16, 14, -34, -60, 6, -6, 18, 8, 2, -56, 30, 6, 24, -2, -36, 22, -30, 2, 90, 10, 46, 34, -38, 8, -120, 2, -8, -70, 0, 50, 8, 54, -38, -4, -186, 120, -58, 6, -16, 84, -16, 52, 78, -50, -224, 150, 24, 66, -14, -6, -180, -14, -6, -20, -46, -58, 300, -34, -42, -360, 74, 42, 46, -42, -72, -2, -10, 48, 22, -90, 38, 390, 14, -108, -426, 180, -22, -88, 42, 14, -90, 114, 14, 38, -96, 52, -36, 176, 98, -2, -150, 128, 30, -14, -6, 38, 58, -420, -38, -72, -42, -152, 54, -26, 94, 114, 8, -216, -270, 36, 2, 38, -8, 450, 74, -2, -18, -120, 354, 94, -124, 2, -74, 120, 66, 660, -6, 630, 66, 54, -74, 10, -270, 264, -150, -38, 130, 182, -228, -18, -66, 28, -46, 162, 114, 176, 58, 42, 684, 4, 158, 38, -690, -194, -26, -146, -720, 82, 34, -300, -14], "trace_hash": 503539924622311096, "simple": false, "squarefree": false, "power": false, "conductor": [[5, 192], [7, 205]], "log_conductor": {"__RealLiteral__": 0, "data": "707.92365974368649946994", "prec": 80}, "q_gonality": null, "q_gonality_bounds": [17, 28], "qbar_gonality": null, "qbar_gonality_bounds": [17, 28], "bad_primes": [5, 7], "num_bad_primes": 2, "level_radical": 35, "level_is_squarefree": true, "cm_discriminants": [], "obstructions": [], "pointless": false, "num_known_degree1_points": 0, "lattice_labels": null, "lattice_x": null, "curve_label": null, "canonical_conjugator": [8, 0, 6, 1], "has_obstruction": -1, "num_known_degree1_noncusp_points": 0, "num_known_degree1_noncm_points": 0, "models": null, "all_degree1_points_known": null, "coarse_parents": ["5.60.0.a.1", "35.336.21.a.1", "35.336.21.a.2", "35.840.57.d.1"]}