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ec_nfcurves • Show schema
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{'Lvalue': {'__RealLiteral__': 0, 'data': '3.28537990874532', 'prec': 54}, 'abs_disc': 19821, 'ainvs': '1,1,0,0;3,0,-1,0;-3,3,2/3,-1/3;-21,-75,1/3,28/3;-103,-292,4,37', 'analytic_rank': 0, 'bad_primes': ['(-1/3*w^3-1/3*w^2+3*w+2)', '(-1/3*w^3-1/3*w^2+2*w)'], 'base_change': [], 'class_deg': 6, 'class_label': '4.4.19821.1-21.1-a', 'class_size': 4, 'cm': 0, 'cm_type': 0, 'conductor_ideal': '(-1/3*w^3-1/3*w^2+4*w-1)', 'conductor_label': '21.1', 'conductor_norm': 21, 'conductor_norm_factors': [3, 7], 'degree': 4, 'disc': '(7/3*w^3-8/3*w^2-20*w+13)', 'equation': '{y}^2+\\left(a+1\\right){x}{y}+\\left(-\\frac{1}{3}a^{3}+\\frac{2}{3}a^{2}+3a-3\\right){y}={x}^{3}+\\left(-a^{2}+3\\right){x}^{2}+\\left(\\frac{28}{3}a^{3}+\\frac{1}{3}a^{2}-75a-21\\right){x}+37a^{3}+4a^{2}-292a-103', 'field_label': '4.4.19821.1', 'galois_images': ['2B', '3B.1.2'], 'gens': [], 'heights': [], 'iso_label': 'a', 'iso_nlabel': 0, 'isodeg': [1, 2, 3, 6], 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'jinv': '-4497131/189,-2609822/63,5279251/63,-3858185/189', 'label': '4.4.19821.1-21.1-a3', 'local_data': [{'p': '(-1/3*w^3-1/3*w^2+3*w+2)', 'cp': 6, 'kod': 10, 'red': 1, 'normp': 3, 'rootno': -1, 'ord_cond': 1, 'ord_disc': 6, 'ord_den_j': 6}, {'p': '(-1/3*w^3-1/3*w^2+2*w)', 'cp': 1, 'kod': 5, 'red': 1, 'normp': 7, 'rootno': -1, 'ord_cond': 1, 'ord_disc': 1, 'ord_den_j': 1}], 'minD': '(7/3*w^3-8/3*w^2-20*w+13)', 'n_bad_primes': 2, 'ngens': 0, 'non_min_p': [], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'normdisc': -5103, 'number': 3, 'omega': {'__RealLiteral__': 0, 'data': '308.35934795540212891511679873437917362', 'prec': 130}, 'potential_good_reduction': False, 'q_curve': False, 'rank': 0, 'rank_bounds': [0, 0], 'reducible_primes': [2, 3], 'reg': 1, 'root_analytic_conductor': 18.40681918345954, 'semistable': True, 'sha': 1, 'short_class_label': '21.1-a', 'short_label': '21.1-a3', 'signature': [4, 0], 'tamagawa_product': 6, 'torsion_gens': ['[[-2,-3,1/3,1/3],[3,2,-1/3,-1/3],[1,0,0,0]]'], 'torsion_order': 2, 'torsion_primes': [2], 'torsion_structure': [2], 'trace_hash': 717926711534010101}