{"torsion_structure": [2], "ainvs": "0,1;1,-1;0,1;-2086,422;-55139,11275", "cm": 0, "torsion_gens": ["[[-79/4,19/4],[-361/8,7],[1,0]]"], "number": 3, "rank": 1, "field_label": "2.2.77.1", "galois_images": ["2B", "3B.1.2"], "conductor_norm": 7, "abs_disc": 77, "iso_nlabel": 1, "rank_bounds": [1, 1], "conductor_ideal": "(w+3)", "base_change": [], "local_data": [{"p": "(w+3)", "cp": 2, "kod": 6, "red": 1, "normp": 7, "rootno": -1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 1, "minD": "(7)", "label": "2.2.77.1-7.1-b3", "jinv": "36477727932544988,-52244506558836009/7", "conductor_label": "7.1", "class_deg": 6, "reg": {"__RealLiteral__": 0, "data": "10.115230811604091552528878829854674447", "prec": 130}, "class_size": 4, "class_label": "2.2.77.1-7.1-b", "iso_label": "b", "degree": 2, "non_min_p": [], "q_curve": false, "short_label": "7.1-b3", "short_class_label": "7.1-b", "isogeny_matrix": [[1, 2, 6, 3], [2, 1, 3, 6], [6, 3, 1, 2], [3, 6, 2, 1]], "torsion_order": 2, "equation": "{y}^2+a{x}{y}+a{y}={x}^{3}+\\left(-a+1\\right){x}^{2}+\\left(422a-2086\\right){x}+11275a-55139", "gens": ["[[-5346756443/237468100,38361243/9498724],[-140091664842003/3659383421000,16028167371023/1829691710500],[1,0]]"], "ngens": 1, "signature": [2, 0], "trace_hash": 720967202769497461, "heights": [{"__RealLiteral__": 0, "data": "10.115230811604091552528878829854674447", "prec": 130}], "isodeg": [1, 2, 3, 6], "omega": {"__RealLiteral__": 0, "data": "1.5351391385085707690194001046655983370", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(w+3)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.7696125053512826426664371217499189712", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2, 3], "semistable": true, "disc": "(7)", "normdisc": 49, "conductor_norm_factors": [7], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 1.2754352805782216, "cm_type": 0}