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{'Lvalue': {'__RealLiteral__': 0, 'data': '2.1056856366902993881518569538570464891', 'prec': 130}, 'abs_disc': 8, 'ainvs': '1,1;-1,-1;1,1;-376,132;2353,-1908', 'analytic_rank': 0, 'bad_primes': ['(w)', '(-2*w+1)', '(2*w+1)'], 'base_change': [], 'class_deg': 36, 'class_label': '2.2.8.1-686.1-d', 'class_size': 12, 'cm': 0, 'cm_type': 0, 'conductor_ideal': '(7*w+28)', 'conductor_label': '686.1', 'conductor_norm': 686, 'conductor_norm_factors': [2, 7], 'degree': 2, 'disc': '(-8953*w+64148)', 'equation': '{y}^2+\\left(a+1\\right){x}{y}+\\left(a+1\\right){y}={x}^{3}+\\left(-a-1\\right){x}^{2}+\\left(132a-376\\right){x}-1908a+2353', 'field_label': '2.2.8.1', 'galois_images': ['2B', '3B'], 'gens': [], 'heights': [], 'iso_label': 'd', 'iso_nlabel': 3, 'isodeg': [1, 2, 3, 4, 6, 9, 12, 18, 36], 'isogeny_matrix': [[1, 9, 3, 36, 6, 12, 4, 18, 12, 2, 36, 4], [9, 1, 3, 4, 6, 12, 36, 2, 12, 18, 4, 36], [3, 3, 1, 12, 2, 4, 12, 6, 4, 6, 12, 12], [36, 4, 12, 1, 6, 12, 36, 2, 3, 18, 4, 9], [6, 6, 2, 6, 1, 2, 6, 3, 2, 3, 6, 6], [12, 12, 4, 12, 2, 1, 3, 6, 4, 6, 3, 12], [4, 36, 12, 36, 6, 3, 1, 18, 12, 2, 9, 4], [18, 2, 6, 2, 3, 6, 18, 1, 6, 9, 2, 18], [12, 12, 4, 3, 2, 4, 12, 6, 1, 6, 12, 3], [2, 18, 6, 18, 3, 6, 2, 9, 6, 1, 18, 2], [36, 4, 12, 4, 6, 3, 9, 2, 12, 18, 1, 36], [4, 36, 12, 9, 6, 12, 4, 18, 3, 2, 36, 1]], 'jinv': '2070934198465000/2401,-2928743223192875/4802', 'label': '2.2.8.1-686.1-d4', 'local_data': [{'p': '(w)', 'cp': 1, 'kod': 5, 'red': 1, 'normp': 2, 'rootno': -1, 'ord_cond': 1, 'ord_disc': 1, 'ord_den_j': 1}, {'p': '(-2*w+1)', 'cp': 1, 'kod': 5, 'red': -1, 'normp': 7, 'rootno': 1, 'ord_cond': 1, 'ord_disc': 1, 'ord_den_j': 1}, {'p': '(2*w+1)', 'cp': 4, 'kod': -8, 'red': 0, 'normp': 7, 'rootno': -1, 'ord_cond': 2, 'ord_disc': 10, 'ord_den_j': 4}], 'minD': '(-8953*w+64148)', 'n_bad_primes': 3, 'ngens': 0, 'non_min_p': [], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'normdisc': 3954653486, 'number': 4, 'omega': {'__RealLiteral__': 0, 'data': '5.9557783710032941478932809253009259746', 'prec': 130}, 'potential_good_reduction': False, 'q_curve': True, 'rank': 0, 'rank_bounds': [0, 0], 'reducible_primes': [2, 3], 'reg': 1, 'root_analytic_conductor': 1.2934944687685523, 'semistable': False, 'sha': 1, 'short_class_label': '686.1-d', 'short_label': '686.1-d4', 'signature': [2, 0], 'tamagawa_product': 4, 'torsion_gens': ['[[57/4,1/2],[-65/8,-63/8],[1,0]]'], 'torsion_order': 2, 'torsion_primes': [2], 'torsion_structure': [2], 'trace_hash': 788073117808483933}