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ec_curvedata • Show schema
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{'Ciso': '134640eq', 'Clabel': '134640eq2', 'Cnumber': 2, 'abc_quality': 0.8867500256108677, 'absD': 710687352038400, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2040, 'ainvs': [0, 0, 0, -50043, -4113542], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 134640, 'degree': 720896, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6076725122926563410529821621', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [18566337396964, 952031025], 'lmfdb_iso': '134640.f', 'lmfdb_label': '134640.f3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -5560, -150500], 'min_quad_twist_disc': 12, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0-2.a.1.1', '20.12.0-2.a.1.1', '60.24.0-60.b.1.2', '136.12.0.?', '408.24.0.?', '680.24.0.?', '2040.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 17, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.95712151416244813830696670005', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.48074371749198040417433277576', 'prec': 103}, 'szpiro_ratio': 3.7319368262996506, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, -1, 0, -4, 0, 0, 0, 1, 0, 2, 0, 0, 0, -1, 0, 4, 0], 'aplist': [0, 0, -1, -4, 1, 2, -1, 4, -8, -6, 8, -2, 2, 8, 0, -14, -8, -2, 8, 12, -2, 0, -12, 14, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 134640, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '134640.f', 'trace_hash': 1732444702116436622}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.040141481636033486815091098425', 'prec': 107}, 'conductor': 134640, 'gens': [[389, 5940, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.95712151416244813830696670005', 'prec': 103}], 'lmfdb_label': '134640.f3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.32021782498168257761189668711', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9037979121323814475568238312254825418', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[-106, 0, 1], [257, 0, 1]], 'xcoord_integral_points': [-151, -139, -117, -106, 257, 378, 389, 1379, 1481, 1093349]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '134640.f3'}
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ec_torsion_growth • Show schema
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id: 6103155
{'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '134640.f3', 'torsion': [2, 4]}
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id: 6103154
{'degree': 4, 'field': [289, 0, -68, 0, 1], 'lmfdb_label': '134640.f3', 'torsion': [2, 4]}
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id: 6103156
{'degree': 4, 'field': [9409, 0, 214, 0, 1], 'lmfdb_label': '134640.f3', 'torsion': [2, 4]}
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id: 6103157
{'degree': 8, 'field': [-3885132, 0, 163020, 0, 3528, 0, -112, 0, 1], 'lmfdb_label': '134640.f3', 'torsion': [2, 6]}
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id: 6103158
{'degree': 16, 'field': [6810801444, 367154856, -392205348, 44438952, -7800758, -18038280, 7231470, -1027564, 231653, 23000, -10870, 3524, -648, 0, 20, -8, 1], 'lmfdb_label': '134640.f3', 'torsion': [4, 4]}
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id: 6103159
{'degree': 16, 'field': [6975757441, 0, -6565418768, 0, -2396718616, 0, -108243216, 0, 40576178, 0, -374544, 0, -28696, 0, -272, 0, 1], 'lmfdb_label': '134640.f3', 'torsion': [2, 8]}
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id: 6103160
{'degree': 16, 'field': [9001455376, -3214778384, -1423962904, -947817048, 576129632, 159675716, -26519018, -23204058, 2154571, 545412, 157537, 28126, 1112, -948, -19, -4, 1], 'lmfdb_label': '134640.f3', 'torsion': [2, 8]}
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id: 6103161
{'degree': 16, 'field': [8702033906241, 0, 1997684498088, 0, 229004957268, 0, -2361456024, 0, 211306150, 0, -447784, 0, 11988, 0, -232, 0, 1], 'lmfdb_label': '134640.f3', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 3322481
{'conductor': 134640, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '134640.f3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 3322482
{'conductor': 134640, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '134640.f3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 3322483
{'conductor': 134640, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '134640.f3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 3322484
{'conductor': 134640, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '134640.f3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 3322485
{'conductor': 134640, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '134640.f3', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 2540181
{'adelic_gens': [[1, 0, 4, 1], [679, 2036, 1358, 2031], [1529, 2036, 1018, 2031], [1, 4, 0, 1], [723, 2, 1558, 2039], [817, 4, 1634, 9], [2037, 4, 2036, 5], [1023, 2, 2038, 2039]], 'adelic_image': '2040.48.0.?', 'conductor': 134640, 'lmfdb_label': '134640.f3', 'prime': 0}
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id: 522299
{'conductor': 134640, 'elladic_image': '2.6.0.1', 'lmfdb_label': '134640.f3', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 134640.f does not appear in ec_padic