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ec_nfcurves • Show schema
{'Lvalue': {'__RealLiteral__': 0, 'data': '1.15236323498953', 'prec': 54}, 'abs_disc': 2225, 'ainvs': '0,-3/2,-1/2,1/2;3,1,-1,0;-2,0,1,0;21,5/2,-51/2,17/2;76,-3/2,-189/2,67/2', 'analytic_rank': 0, 'bad_primes': ['(1/2*w^3-3/2*w^2-1/2*w+4)'], 'base_change': [], 'class_deg': 8, 'class_label': '4.4.2225.1-19.1-a', 'class_size': 6, 'cm': 0, 'cm_type': 0, 'conductor_ideal': '(1/2*w^3-3/2*w^2-1/2*w+4)', 'conductor_label': '19.1', 'conductor_norm': 19, 'conductor_norm_factors': [19], 'degree': 4, 'disc': '(13/2*w^3-31/2*w^2-29/2*w+47)', 'equation': '{y}^2+\\left(\\frac{1}{2}a^{3}-\\frac{1}{2}a^{2}-\\frac{3}{2}a\\right){x}{y}+\\left(a^{2}-2\\right){y}={x}^{3}+\\left(-a^{2}+a+3\\right){x}^{2}+\\left(\\frac{17}{2}a^{3}-\\frac{51}{2}a^{2}+\\frac{5}{2}a+21\\right){x}+\\frac{67}{2}a^{3}-\\frac{189}{2}a^{2}-\\frac{3}{2}a+76', 'field_label': '4.4.2225.1', 'galois_images': ['2Cs'], 'gens': [], 'heights': [], 'iso_label': 'a', 'iso_nlabel': 0, 'isodeg': [1, 2, 4], 'isogeny_matrix': [[1, 8, 4, 2, 8, 4], [8, 1, 2, 4, 4, 8], [4, 2, 1, 2, 2, 4], [2, 4, 2, 1, 4, 2], [8, 4, 2, 4, 1, 8], [4, 8, 4, 2, 8, 1]], 'jinv': '16630098173/130321,26352219634/130321,2678496927/130321,-6593184883/130321', 'label': '4.4.2225.1-19.1-a3', 'local_data': [{'p': '(1/2*w^3-3/2*w^2-1/2*w+4)', 'cp': 2, 'kod': 8, 'red': -1, 'normp': 19, 'rootno': 1, 'ord_cond': 1, 'ord_disc': 4, 'ord_den_j': 4}], 'minD': '(8*w^3-3*w^2-38*w+3)', 'n_bad_primes': 1, 'ngens': 0, 'non_min_p': [], 'nonmax_primes': [2], 'nonmax_rad': 2, 'normdisc': 130321, 'number': 3, 'omega': {'__RealLiteral__': 0, 'data': '434.85492064667811289629217138118454955', 'prec': 130}, 'potential_good_reduction': False, 'q_curve': False, 'rank': 0, 'rank_bounds': [0, 0], 'reducible_primes': [2], 'reg': 1, 'root_analytic_conductor': 6.090427269067156, 'semistable': True, 'sha': 1, 'short_class_label': '19.1-a', 'short_label': '19.1-a3', 'signature': [4, 0], 'tamagawa_product': 2, 'torsion_gens': ['[[2,-2,-2,1],[1,-1/2,-3/2,1/2],[1,0,0,0]]', '[[-1/4,1/8,-7/8,3/8],[15/8,-5/8,-13/8,1/2],[1,0,0,0]]'], 'torsion_order': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2], 'trace_hash': 926341335723613385}
Elliptic curve data - 4.4.2225.1-19.1-a3