{"torsion_structure": [4], "ainvs": "1,1;-1,-1;1,1;39,17;143,126", "cm": 0, "torsion_gens": ["[[7,0],[-10,-23],[1,0]]"], "number": 3, "rank": 0, "field_label": "2.2.8.1", "galois_images": ["2B", "3Cs"], "conductor_norm": 686, "abs_disc": 8, "iso_nlabel": 3, "rank_bounds": [0, 0], "conductor_ideal": "(7*w+28)", "base_change": [], "local_data": [{"p": "(w)", "cp": 12, "kod": 16, "red": 1, "normp": 2, "rootno": -1, "ord_cond": 1, "ord_disc": 12, "ord_den_j": 12}, {"p": "(-2*w+1)", "cp": 1, "kod": 7, "red": -1, "normp": 7, "rootno": 1, "ord_cond": 1, "ord_disc": 3, "ord_den_j": 3}, {"p": "(2*w+1)", "cp": 4, "kod": -7, "red": 0, "normp": 7, "rootno": -1, "ord_cond": 2, "ord_disc": 9, "ord_den_j": 3}], "analytic_rank": 0, "minD": "(5817280*w-3314752)", "label": "2.2.8.1-686.1-d3", "jinv": "9938375/21952,0", "conductor_label": "686.1", "class_deg": 36, "reg": 1, "class_size": 12, "class_label": "2.2.8.1-686.1-d", "iso_label": "d", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "686.1-d3", "short_class_label": "686.1-d", "isogeny_matrix": [[1, 9, 3, 36, 6, 12, 4, 18, 12, 2, 36, 4], [9, 1, 3, 4, 6, 12, 36, 2, 12, 18, 4, 36], [3, 3, 1, 12, 2, 4, 12, 6, 4, 6, 12, 12], [36, 4, 12, 1, 6, 12, 36, 2, 3, 18, 4, 9], [6, 6, 2, 6, 1, 2, 6, 3, 2, 3, 6, 6], [12, 12, 4, 12, 2, 1, 3, 6, 4, 6, 3, 12], [4, 36, 12, 36, 6, 3, 1, 18, 12, 2, 9, 4], [18, 2, 6, 2, 3, 6, 18, 1, 6, 9, 2, 18], [12, 12, 4, 3, 2, 4, 12, 6, 1, 6, 12, 3], [2, 18, 6, 18, 3, 6, 2, 9, 6, 1, 18, 2], [36, 4, 12, 4, 6, 3, 9, 2, 12, 18, 1, 36], [4, 36, 12, 9, 6, 12, 4, 18, 3, 2, 36, 1]], "torsion_order": 4, "equation": "{y}^2+\\left(a+1\\right){x}{y}+\\left(a+1\\right){y}={x}^{3}+\\left(-a-1\\right){x}^{2}+\\left(17a+39\\right){x}+126a+143", "gens": [], "ngens": 0, "signature": [2, 0], "trace_hash": 788073117808483933, "heights": [], "isodeg": [1, 2, 3, 4, 6, 12], "omega": {"__RealLiteral__": 0, "data": "1.9852594570010980492977603084336419915", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 48, "bad_primes": ["(w)", "(-2*w+1)", "(2*w+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.1056856366902993881518569538570464891", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 3, "reducible_primes": [2, 3], "semistable": false, "disc": "(-5817280*w+3314752)", "normdisc": 56693912375296, "conductor_norm_factors": [2, 7], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 1.2934944687685523, "cm_type": 0}