{"torsion_structure": [], "ainvs": "0,0;1,1;0,1;-37314,7700;3292065,-834775", "cm": 0, "torsion_gens": [], "number": 2, "rank": 1, "field_label": "2.2.53.1", "galois_images": ["7B.6.3"], "conductor_norm": 49, "abs_disc": 53, "iso_nlabel": 0, "rank_bounds": [1, 1], "conductor_ideal": "(2*w+1)", "base_change": [], "local_data": [{"p": "(-w+3)", "cp": 2, "kod": -5, "red": 0, "normp": 7, "rootno": -1, "ord_cond": 2, "ord_disc": 7, "ord_den_j": 1}], "analytic_rank": 1, "minD": "(-w-907)", "label": "2.2.53.1-49.3-a2", "jinv": "-808691822475743232/7,195338235078135808/7", "conductor_label": "49.3", "class_deg": 7, "reg": {"__RealLiteral__": 0, "data": "4.1956504423692845760429277676729381697", "prec": 130}, "class_size": 2, "class_label": "2.2.53.1-49.3-a", "iso_label": "a", "degree": 2, "non_min_p": [], "q_curve": false, "short_label": "49.3-a2", "short_class_label": "49.3-a", "isogeny_matrix": [[1, 7], [7, 1]], "torsion_order": 1, "equation": "{y}^2+a{y}={x}^{3}+\\left(a+1\\right){x}^{2}+\\left(7700a-37314\\right){x}-834775a+3292065", "gens": ["[[5168493/82418,-4261197/164836],[164369/66923416,-16745041/33461708],[1,0]]"], "ngens": 1, "signature": [2, 0], "trace_hash": 525143244515473219, "heights": [{"__RealLiteral__": 0, "data": "4.1956504423692845760429277676729381697", "prec": 130}], "isodeg": [1, 7], "omega": {"__RealLiteral__": 0, "data": "1.0687645857255591820172420411006653990", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(-w+3)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.4637884180790739340499993630567958570", "prec": 130}, "sha": 1, "torsion_primes": [], "n_bad_primes": 1, "reducible_primes": [7], "semistable": false, "disc": "(w+907)", "normdisc": -823543, "conductor_norm_factors": [7], "nonmax_primes": [7], "nonmax_rad": 7, "root_analytic_conductor": 1.7211768982267637, "cm_type": 0}