{"torsion_structure": [2, 4], "ainvs": "1,1;-1,1;1,1;-771,292;11915,-4503", "cm": 0, "torsion_gens": ["[[9,-4],[9,-3],[1,0]]", "[[1,-1],[-65,25],[1,0]]"], "number": 4, "rank": 0, "field_label": "2.2.28.1", "galois_images": ["2Cs"], "conductor_norm": 72, "abs_disc": 28, "iso_nlabel": 3, "rank_bounds": [0, 0], "conductor_ideal": "(6*w+18)", "base_change": ["1176.i3", "48.a3"], "local_data": [{"p": "(w+3)", "cp": 2, "kod": -5, "red": 0, "normp": 2, "rootno": 1, "ord_cond": 3, "ord_disc": 8, "ord_den_j": 0}, {"p": "(-w+2)", "cp": 4, "kod": 8, "red": 1, "normp": 3, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}, {"p": "(-w-2)", "cp": 4, "kod": 8, "red": 1, "normp": 3, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}], "analytic_rank": 0, "minD": "(1296)", "label": "2.2.28.1-72.1-d4", "jinv": "1556068/81,0", "conductor_label": "72.1", "class_deg": 8, "reg": 1, "class_size": 6, "class_label": "2.2.28.1-72.1-d", "iso_label": "d", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "72.1-d4", "short_class_label": "72.1-d", "isogeny_matrix": [[1, 8, 4, 2, 8, 4], [8, 1, 2, 4, 4, 8], [4, 2, 1, 2, 2, 4], [2, 4, 2, 1, 4, 2], [8, 4, 2, 4, 1, 8], [4, 8, 4, 2, 8, 1]], "torsion_order": 8, "equation": "{y}^2+\\left(a+1\\right){x}{y}+\\left(a+1\\right){y}={x}^{3}+\\left(a-1\\right){x}^{2}+\\left(292a-771\\right){x}-4503a+11915", "gens": [], "ngens": 0, "signature": [2, 0], "trace_hash": 775133903492172839, "heights": [], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "22.734034070006347604148590511773734758", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 32, "bad_primes": ["(w+3)", "(-w+2)", "(-w-2)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.1481643016609415941808358326468364517", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 3, "reducible_primes": [2], "semistable": false, "disc": "(1296)", "normdisc": 1679616, "conductor_norm_factors": [2, 3], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 1.3773702338843288, "cm_type": 0}