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ec_nfcurves • Show schema
{'Lvalue': {'__RealLiteral__': 0, 'data': '2.81038060887703', 'prec': 54}, 'abs_disc': 725, 'ainvs': '1,-2,-1,1;0,3,0,-1;0,1,0,0;1,1,-1,0;0,0,0,0', 'analytic_rank': 1, 'bad_primes': ['(-w^3-3*w^2+8)'], 'base_change': [], 'class_deg': 2, 'class_label': '4.4.725.1-3169.1-b', 'class_size': 2, 'cm': 0, 'cm_type': 0, 'conductor_ideal': '(-w^3-3*w^2+8)', 'conductor_label': '3169.1', 'conductor_norm': 3169, 'conductor_norm_factors': [3169], 'degree': 4, 'disc': '(-5*w^3+7*w^2+12*w-1)', 'equation': '{y}^2+\\left(a^{3}-a^{2}-2a+1\\right){x}{y}+a{y}={x}^{3}+\\left(-a^{3}+3a\\right){x}^{2}+\\left(-a^{2}+a+1\\right){x}', 'field_label': '4.4.725.1', 'galois_images': ['2B'], 'gens': ['[[1,-2,-1,1],[0,-1,0,0],[1,0,0,0]]'], 'heights': [{'__RealLiteral__': 0, 'data': '0.038571329856688113857415227617945202064', 'prec': 137}], 'iso_label': 'b', 'iso_nlabel': 1, 'isodeg': [1, 2], 'isogeny_matrix': [[1, 2], [2, 1]], 'jinv': '6495478/3169,3082469/3169,5992969/3169,2653932/3169', 'label': '4.4.725.1-3169.1-b2', 'local_data': [{'p': '(-w^3-3*w^2+8)', 'cp': 1, 'kod': 5, 'red': 1, 'normp': 3169, 'rootno': -1, 'ord_cond': 1, 'ord_disc': 1, 'ord_den_j': 1}], 'minD': '(-w^3-3*w^2+8)', 'n_bad_primes': 1, 'ngens': 1, 'non_min_p': [], 'nonmax_primes': [2], 'nonmax_rad': 2, 'normdisc': 3169, 'number': 2, 'omega': {'__RealLiteral__': 0, 'data': '1961.8668588572914538766656715505601345', 'prec': 130}, 'potential_good_reduction': False, 'q_curve': False, 'rank': 1, 'rank_bounds': [1, 1], 'reducible_primes': [2], 'reg': {'__RealLiteral__': 0, 'data': '0.038571329856688113857415227617945202064', 'prec': 137}, 'root_analytic_conductor': 6.590567868708442, 'semistable': True, 'sha': 1, 'short_class_label': '3169.1-b', 'short_label': '3169.1-b2', 'signature': [4, 0], 'tamagawa_product': 1, 'torsion_gens': ['[[-1,-1,1,0],[0,-1,0,0],[1,0,0,0]]'], 'torsion_order': 2, 'torsion_primes': [2], 'torsion_structure': [2], 'trace_hash': 2257271811634391025}
Elliptic curve data - 4.4.725.1-3169.1-b2