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ec_curvedata • Show schema
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{'Ciso': '180336de', 'Clabel': '180336de2', 'Cnumber': 2, 'abc_quality': 0.9332211540954428, 'absD': 159776031138048, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [0, -1, 0, -237076, -44347232], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 180336, 'degree': 1179648, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7554359173771501929115265701', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 43, 'isogeny_degrees': [1, 2], 'jinv': [238481570896, 25857], 'lmfdb_iso': '180336.br', 'lmfdb_label': '180336.br1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -820, 9316], 'min_quad_twist_disc': -68, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '34.6.0.a.1', '52.6.0.c.1', '884.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.5690595779855065245421484171', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.12326887502425472015806215314', 'prec': 107}, 'szpiro_ratio': 4.027407977222894, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -1, 0, 4, 0, 2, 0, 1, 0, -2, 0, -1, 0, -4, 0, 0, 0, 0, 0], 'aplist': [0, -1, 4, 2, -2, -1, 0, 0, 0, 6, 2, -4, -8, -4, 4, 2, -4, -6, 8, -6, -4, 12, 0, 2, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 180336, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '180336.br', 'trace_hash': 1684932678416838337}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.029870860626832701256300528329', 'prec': 107}, 'conductor': 180336, 'gens': [[49501, 10639824, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '5.5690595779855065245421484171', 'prec': 100}], 'lmfdb_label': '180336.br1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.21636167238645142322719084514', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.6394483513018366669309287036530553485', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-283, 0, 1]], 'xcoord_integral_points': [-283]}
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lmfdb_label 180336.br1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 7982633
{'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '180336.br1', 'torsion': [2, 2]}
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id: 7982634
{'degree': 4, 'field': [4, -2, 1, -1, 1], 'lmfdb_label': '180336.br1', 'torsion': [4]}
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id: 7982637
{'degree': 8, 'field': [-70227, 0, -15300, 0, -918, 0, 0, 0, 1], 'lmfdb_label': '180336.br1', 'torsion': [6]}
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id: 7982636
{'degree': 8, 'field': [-191, -360, 28, 38, -91, 58, -12, -2, 1], 'lmfdb_label': '180336.br1', 'torsion': [2, 4]}
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id: 7982635
{'degree': 8, 'field': [17, -34, 123, -2, -38, -4, 1, 0, 1], 'lmfdb_label': '180336.br1', 'torsion': [2, 4]}
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id: 7982638
{'degree': 16, 'field': [457060347, 47245272, 315354782, -36230356, 102089509, -19775800, 18572960, -3516740, 2025398, -316000, 133408, -15620, 5185, -400, 110, -4, 1], 'lmfdb_label': '180336.br1', 'torsion': [8]}
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id: 7982639
{'degree': 16, 'field': [1009714176, 0, -168377088, 0, -29137856, 0, 7719168, 0, -450411, 0, 76, 0, 258, 0, 0, 0, 1], 'lmfdb_label': '180336.br1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 4465222
{'conductor': 180336, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '180336.br1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 4465223
{'conductor': 180336, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '180336.br1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 4465224
{'conductor': 180336, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '180336.br1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 4465225
{'conductor': 180336, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '180336.br1', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2825049
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [881, 4, 880, 5], [210, 1, 779, 0], [613, 4, 342, 9], [665, 222, 220, 663]], 'adelic_image': '884.12.0.?', 'conductor': 180336, 'lmfdb_label': '180336.br1', 'prime': 0}
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id: 676801
{'conductor': 180336, 'elladic_image': '2.3.0.1', 'lmfdb_label': '180336.br1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 180336.br does not appear in ec_padic