{"torsion_structure": [4], "ainvs": "1,1;1,1;0,0;-18375,-6945;1313891,496604", "cm": 0, "torsion_gens": ["[[43,16],[-280,-106],[1,0]]"], "number": 5, "rank": 1, "field_label": "2.2.28.1", "galois_images": ["2B"], "conductor_norm": 648, "abs_disc": 28, "iso_nlabel": 5, "rank_bounds": [1, 1], "conductor_ideal": "(18*w+54)", "base_change": ["3528.d2", "144.b2"], "local_data": [{"p": "(w+3)", "cp": 4, "kod": -5, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 3, "ord_disc": 8, "ord_den_j": 0}, {"p": "(-w+2)", "cp": 4, "kod": -5, "red": 0, "normp": 3, "rootno": -1, "ord_cond": 2, "ord_disc": 7, "ord_den_j": 1}, {"p": "(-w-2)", "cp": 4, "kod": -5, "red": 0, "normp": 3, "rootno": -1, "ord_cond": 2, "ord_disc": 7, "ord_den_j": 1}], "analytic_rank": 1, "minD": "(34992)", "label": "2.2.28.1-648.1-f5", "jinv": "28756228/3,0", "conductor_label": "648.1", "class_deg": 8, "reg": {"__RealLiteral__": 0, "data": "0.20471928891868969715110070467212167158", "prec": 133}, "class_size": 6, "class_label": "2.2.28.1-648.1-f", "iso_label": "f", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "648.1-f5", "short_class_label": "648.1-f", "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": 4, "equation": "{y}^2+\\left(a+1\\right){x}{y}={x}^{3}+\\left(a+1\\right){x}^{2}+\\left(-6945a-18375\\right){x}+496604a+1313891", "gens": ["[[-68,-26],[-1018,-385],[1,0]]"], "ngens": 1, "signature": [2, 0], "trace_hash": 1330896836457473296, "heights": [{"__RealLiteral__": 0, "data": "0.20471928891868969715110070467212167158", "prec": 133}], "isodeg": [1, 2, 4, 8], "omega": {"__RealLiteral__": 0, "data": "12.401492634428814718752155867842209557", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 64, "bad_primes": ["(w+3)", "(-w+2)", "(-w-2)"], "Lvalue": {"__RealLiteral__": 0, "data": "3.8383422403053732066954961709488466164", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 3, "reducible_primes": [2], "semistable": false, "disc": "(34992)", "normdisc": 1224440064, "conductor_norm_factors": [2, 3], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 2.3856752259206853, "cm_type": 0}