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ec_curvedata • Show schema
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{'Ciso': '9747a', 'Clabel': '9747a1', 'Cnumber': 1, 'absD': 1270238787, 'ainvs': [0, 0, 1, 0, -1715], 'analytic_rank': 0, 'bad_primes': [3, 19], 'class_deg': 27, 'class_size': 4, 'cm': -3, 'conductor': 9747, 'degree': 2106, 'elladic_images': ['27.972.55.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.42575513332220973786345582932', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 3, 9], 'jinv': [0, 1], 'lmfdb_iso': '9747.f', 'lmfdb_label': '9747.f3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 0], 'min_quad_twist_disc': -19, 'modell_images': ['3Cs'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 3.0939654887344443, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, -5, 0, 0, 4, 0, 0, 0, 0], 'aplist': [0, 0, 0, -1, 0, -5, 0, 0, 0, 0, 4, -11, 0, 8, 0, 0, 0, -1, -5, 0, -7, -17, 0, 0, 19], 'class_deg': 27, 'class_size': 4, 'conductor': 9747, 'isogeny_matrix': [[1, 27, 9, 3], [27, 1, 3, 9], [9, 3, 1, 3], [3, 9, 3, 1]], 'lmfdb_iso': '9747.f', 'trace_hash': 845470507183729647}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.42676990863487866530770015897', 'prec': 103}, 'conductor': 9747, 'gens': [], 'heights': [], 'lmfdb_label': '9747.f3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.70199105639940910915592388802', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.70199105639940910915592388801839131254', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [0, 5, 0], '3': 'a', '5': [0, 0, 0], '7': [0, 0], '11': [0, 0, 0], '13': [0, 0], '17': [0, 0, 0], '19': 'a', '23': [0, 0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '9747.f3'}
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ec_torsion_growth • Show schema
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id: 505941
{'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '9747.f3', 'torsion': [3]}
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id: 505942
{'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '9747.f3', 'torsion': [3]}
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id: 505943
{'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '9747.f3', 'torsion': [2]}
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id: 505944
{'degree': 4, 'field': [25, -5, -4, -1, 1], 'lmfdb_label': '9747.f3', 'torsion': [3, 3]}
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id: 505947
{'degree': 6, 'field': [-192, -144, 12, -9, 21, -3, 1], 'lmfdb_label': '9747.f3', 'torsion': [6]}
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id: 505945
{'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '9747.f3', 'torsion': [2, 2]}
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id: 505948
{'degree': 6, 'field': [157, -129, 84, -27, 18, -3, 1], 'lmfdb_label': '9747.f3', 'torsion': [6]}
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id: 505946
{'degree': 6, 'field': [323, -114, 87, -17, 12, -3, 1], 'lmfdb_label': '9747.f3', 'torsion': [9]}
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id: 505949
{'degree': 12, 'field': [-422274, -401760, -323676, 35484, 33186, 32784, -4728, -3804, 78, 138, 18, -6, 1], 'lmfdb_label': '9747.f3', 'torsion': [4]}
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id: 505952
{'degree': 12, 'field': [6388, 3540, 6168, 3028, 5334, 516, 2291, -12, 417, -4, 33, 0, 1], 'lmfdb_label': '9747.f3', 'torsion': [6, 6]}
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id: 505950
{'degree': 12, 'field': [15625, 0, 0, -1750, 0, 0, 71, 0, 0, -14, 0, 0, 1], 'lmfdb_label': '9747.f3', 'torsion': [3, 9]}
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id: 505951
{'degree': 12, 'field': [531061, 731742, 513870, 148783, -21882, -29334, -6093, 1461, 483, -17, -15, -3, 1], 'lmfdb_label': '9747.f3', 'torsion': [7]}
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id: 505953
{'degree': 18, 'field': [-5735339, 0, 0, -5656137, 0, 0, 786705, 0, 0, 43855, 0, 0, -2757, 0, 0, -51, 0, 0, 1], 'lmfdb_label': '9747.f3', 'torsion': [9]}
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id: 505954
{'degree': 18, 'field': [38809, 269322, 534951, -88971, 1289631, -642153, 1117095, -468645, 475011, -156528, 114072, -28581, 16179, -2901, 1323, -150, 57, -3, 1], 'lmfdb_label': '9747.f3', 'torsion': [18]}
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ec_localdata • Show schema
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id: 205434
{'conductor': 9747, 'conductor_valuation': 3, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '9747.f3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 205435
{'conductor': 9747, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '9747.f3', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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{'conductor': 9747, 'elladic_image': '27.972.55.16', 'lmfdb_label': '9747.f3', 'modell_image': '3Cs', 'prime': 3}
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lmfdb_iso 9747.f does not appear in ec_padic