{"torsion_structure": [6], "ainvs": "0,-3,1/3,1/3;-2,-3,1/3,1/3;-3,-1,1,0;1,25,-44/3,-26/3;-36,-120,84,47", "cm": 0, "torsion_gens": ["[[1,0,1/3,1/3],[3,0,0,0],[1,0,0,0]]"], "number": 2, "rank": 0, "field_label": "4.4.19821.1", "galois_images": ["2B", "3B.1.1"], "conductor_norm": 21, "abs_disc": 19821, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(-1/3*w^3-1/3*w^2+4*w-1)", "base_change": [], "local_data": [{"p": "(-1/3*w^3-1/3*w^2+3*w+2)", "cp": 4, "kod": 8, "red": 1, "normp": 3, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}, {"p": "(-1/3*w^3-1/3*w^2+2*w)", "cp": 6, "kod": 10, "red": 1, "normp": 7, "rootno": -1, "ord_cond": 1, "ord_disc": 6, "ord_den_j": 6}], "analytic_rank": 0, "minD": "(-7/3*w^3-46/3*w^2+20*w+86)", "label": "4.4.19821.1-21.1-a2", "jinv": "-31682015546507/1058841,-67381326805957/352947,42308209276609/352947,74079408535072/1058841", "conductor_label": "21.1", "class_deg": 6, "reg": 1, "class_size": 4, "class_label": "4.4.19821.1-21.1-a", "iso_label": "a", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "21.1-a2", "short_class_label": "21.1-a", "isogeny_matrix": [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], "torsion_order": 6, "equation": "{y}^2+\\left(\\frac{1}{3}a^{3}+\\frac{1}{3}a^{2}-3a\\right){x}{y}+\\left(a^{2}-a-3\\right){y}={x}^{3}+\\left(\\frac{1}{3}a^{3}+\\frac{1}{3}a^{2}-3a-2\\right){x}^{2}+\\left(-\\frac{26}{3}a^{3}-\\frac{44}{3}a^{2}+25a+1\\right){x}+47a^{3}+84a^{2}-120a-36", "gens": [], "ngens": 0, "signature": [4, 0], "trace_hash": 717926711534010101, "heights": [], "isodeg": [1, 2, 3, 6], "omega": {"__RealLiteral__": 0, "data": "693.80853289965479005901279715235314063", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 24, "bad_primes": ["(-1/3*w^3-1/3*w^2+3*w+2)", "(-1/3*w^3-1/3*w^2+2*w)"], "Lvalue": {"__RealLiteral__": 0, "data": "3.28537990874532", "prec": 54}, "sha": 1, "torsion_primes": [2, 3], "n_bad_primes": 2, "reducible_primes": [2, 3], "semistable": true, "disc": "(-7/3*w^3-46/3*w^2+20*w+86)", "normdisc": -9529569, "conductor_norm_factors": [3, 7], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 18.40681918345954, "cm_type": 0}