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ec_nfcurves • Show schema
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{'Lvalue': {'__RealLiteral__': 0, 'data': '1.94518480872993', 'prec': 54}, 'abs_disc': 2304, 'ainvs': '1,1,0,0;-2,0,1,0;-1,0,1,0;1,16,-40,16;-42,-16,249,-119', 'analytic_rank': 1, 'bad_primes': ['(w^3-4*w+1)', '(w^2-2)'], 'base_change': ['24a3', '144b4', '192c4', '576i4', '2.2.12.1-24.1-a6', '2.2.12.1-768.1-l6', '2.2.24.1-24.1-b5', '2.2.24.1-48.1-a5', '2.2.8.1-72.1-a6', '2.2.8.1-1296.1-b6'], 'class_deg': 32, 'class_label': '4.4.2304.1-72.1-b', 'class_size': 10, 'cm': 0, 'cm_type': 0, 'conductor_ideal': '(-w^3+w^2+5*w-5)', 'conductor_label': '72.1', 'conductor_norm': 72, 'conductor_norm_factors': [2, 3], 'degree': 4, 'disc': '(6)', 'equation': '{y}^2+\\left(a+1\\right){x}{y}+\\left(a^{2}-1\\right){y}={x}^{3}+\\left(a^{2}-2\\right){x}^{2}+\\left(16a^{3}-40a^{2}+16a+1\\right){x}-119a^{3}+249a^{2}-16a-42', 'field_label': '4.4.2304.1', 'galois_images': ['2Cs'], 'gens': ['[[-5,1,26,-13],[-100,52,372,-193],[1,0,0,0]]'], 'heights': [{'__RealLiteral__': 0, 'data': '0.53963693233858955721845168328714855890', 'prec': 133}], 'iso_label': 'b', 'iso_nlabel': 1, 'isodeg': [1, 2, 4, 8, 16], 'isogeny_matrix': [[1, 16, 8, 4, 8, 2, 16, 4, 32, 32], [16, 1, 8, 4, 2, 8, 4, 16, 8, 8], [8, 8, 1, 2, 4, 4, 8, 8, 16, 16], [4, 4, 2, 1, 2, 2, 4, 4, 8, 8], [8, 2, 4, 2, 1, 4, 2, 8, 4, 4], [2, 8, 4, 2, 4, 1, 8, 2, 16, 16], [16, 4, 8, 4, 2, 8, 1, 16, 2, 2], [4, 16, 8, 4, 8, 2, 16, 1, 32, 32], [32, 8, 16, 8, 4, 16, 2, 32, 1, 4], [32, 8, 16, 8, 4, 16, 2, 32, 4, 1]], 'jinv': '28756228/3,0,0,0', 'label': '4.4.2304.1-72.1-b6', 'local_data': [{'p': '(w^3-4*w+1)', 'cp': 2, 'kod': 3, 'red': 0, 'normp': 2, 'rootno': 1, 'ord_cond': 3, 'ord_disc': 4, 'ord_den_j': 0}, {'p': '(w^2-2)', 'cp': 2, 'kod': 6, 'red': 1, 'normp': 9, 'rootno': -1, 'ord_cond': 1, 'ord_disc': 2, 'ord_den_j': 2}], 'minD': '(6)', 'n_bad_primes': 2, 'ngens': 1, 'non_min_p': [], 'nonmax_primes': [2], 'nonmax_rad': 2, 'normdisc': 1296, 'number': 6, 'omega': {'__RealLiteral__': 0, 'data': '2768.3463521122585759457130131342742444', 'prec': 130}, 'potential_good_reduction': False, 'q_curve': True, 'rank': 1, 'rank_bounds': [1, 1], 'reducible_primes': [2], 'reg': {'__RealLiteral__': 0, 'data': '0.53963693233858955721845168328714855890', 'prec': 133}, 'root_analytic_conductor': 7.3205945289283045, 'semistable': False, 'sha': 1, 'short_class_label': '72.1-b', 'short_label': '72.1-b6', 'signature': [4, 0], 'tamagawa_product': 4, 'torsion_gens': ['[[3,-3,-4,2],[0,0,-1,1],[1,0,0,0]]', '[[4,-8,3,0],[-7,21,-17,4],[1,0,0,0]]'], 'torsion_order': 16, 'torsion_primes': [2], 'torsion_structure': [2, 8], 'trace_hash': 405768818576626520}