{"torsion_structure": [2, 2], "ainvs": "0,1,0,0;-1,-1,0,0;0,0,0,0;-24,20,-5,0;-35,64,-35,7", "cm": 0, "torsion_gens": ["[[-2,2,0,0],[0,1,-1,0],[1,0,0,0]]", "[[6,-2,0,0],[0,-3,1,0],[1,0,0,0]]"], "number": 3, "rank": 0, "field_label": "4.4.1125.1", "galois_images": ["2Cs"], "conductor_norm": 31, "abs_disc": 1125, "iso_nlabel": 1, "rank_bounds": [0, 0], "conductor_ideal": "(-2*w^3-2*w^2+6*w+3)", "base_change": [], "local_data": [{"p": "(-2*w^3-2*w^2+6*w+3)", "cp": 2, "kod": 12, "red": -1, "normp": 31, "rootno": 1, "ord_cond": 1, "ord_disc": 8, "ord_den_j": 8}], "analytic_rank": 0, "minD": "(-255*w^3-278*w^2+684*w-520)", "label": "4.4.1125.1-31.3-b3", "jinv": "-5628354043368086906140/852891037441,-19636479236469948927748/852891037441,32551084210297485030913/852891037441,-11010764002907552479232/852891037441", "conductor_label": "31.3", "class_deg": 8, "reg": 1, "class_size": 6, "isogeny_degrees": [1, 2, 4], "class_label": "4.4.1125.1-31.3-b", "iso_label": "b", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "31.3-b3", "short_class_label": "31.3-b", "isogeny_matrix": [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], "torsion_order": 4, "non-surjective_primes": [2], "equation": "{y}^2+a{x}{y}={x}^{3}+\\left(-a-1\\right){x}^{2}+\\left(-5a^{2}+20a-24\\right){x}+7a^{3}-35a^{2}+64a-35", "gens": [], "ngens": 0, "signature": [4, 0], "trace_hash": 1168144009904954139, "heights": [], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "47.3508490162373", "prec": 54}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(-2*w^3-2*w^2+6*w+3)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.705864781284238", "prec": 57}, "sha": 4, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2], "semistable": true, "disc": "(255*w^3+278*w^2-684*w+520)", "normdisc": 852891037441}