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ec_curvedata • Show schema
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{'Ciso': '2112bd', 'Clabel': '2112bd1', 'Cnumber': 1, 'abc_quality': 1.073399617726021, 'absD': 717527973888, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 1320, 'ainvs': [0, 1, 0, -2881, -44353], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 2112, 'degree': 3840, 'elladic_images': ['8.6.0.4', '5.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.98285508101941543494074416967', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 29, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [10091699281, 2737152], 'lmfdb_iso': '2112.bd', 'lmfdb_label': '2112.bd3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -45, 81], 'min_quad_twist_disc': -8, 'modell_images': ['2B', '5B.4.1'], 'modm_images': ['2.3.0.a.1', '5.12.0.a.1', '8.6.0.d.1', '10.36.0.a.2', '20.72.0-10.a.2.11', '40.144.1-40.t.2.12', '66.6.0.a.1', '264.12.0.?', '330.72.1.?', '660.144.1.?', '1320.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.056865689820502529185104012517', 'prec': 110}, 'szpiro_ratio': 4.638774161524989, '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, 1, 0, -4, 0, 4, 0, -2, 0, 0, 0], 'aplist': [0, 1, 4, 2, 1, -4, -2, 0, 6, -10, 8, 2, 2, 4, 2, -4, 0, 8, -12, -2, -6, -10, 4, 10, -2], 'class_deg': 10, 'class_size': 4, 'conductor': 2112, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '2112.bd', 'trace_hash': 548676465511683384}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.14005638855967499531871242018', 'prec': 103}, 'conductor': 2112, 'gens': [], 'heights': [], 'lmfdb_label': '2112.bd3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.66487808510934423351031659377', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3243904255467211675515829688463677508', 'prec': 130}, 'tamagawa_product': 20, 'torsion_generators': [[-17, 0, 1]], 'xcoord_integral_points': [-17]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 0], '5': [2, 0], '11': [1, 0]}, 'iwp0': 7, 'lmfdb_label': '2112.bd3'}
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ec_torsion_growth • Show schema
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id: 107376
{'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '2112.bd3', 'torsion': [2, 2]}
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id: 107377
{'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '2112.bd3', 'torsion': [10]}
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id: 107378
{'degree': 4, 'field': [2, 0, 1, -2, 1], 'lmfdb_label': '2112.bd3', 'torsion': [20]}
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id: 107379
{'degree': 4, 'field': [102, 12, -11, -2, 1], 'lmfdb_label': '2112.bd3', 'torsion': [2, 10]}
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id: 107381
{'degree': 8, 'field': [-1284, 1236, 93, -186, 139, -8, -21, -2, 1], 'lmfdb_label': '2112.bd3', 'torsion': [2, 4]}
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id: 107382
{'degree': 8, 'field': [-12, 0, -1390, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '2112.bd3', 'torsion': [6]}
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id: 107380
{'degree': 8, 'field': [256, 128, 16, 32, 42, -8, 1, -2, 1], 'lmfdb_label': '2112.bd3', 'torsion': [2, 20]}
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id: 107384
{'degree': 16, 'field': [1024, 0, 2176, 0, -28736, 0, 122272, 0, 79216, 0, -13544, 0, -236, 0, -2, 0, 1], 'lmfdb_label': '2112.bd3', 'torsion': [2, 6]}
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id: 107383
{'degree': 16, 'field': [1188, -3168, 5280, -4224, 1500, 1632, -2648, 2416, -1299, 88, 340, -312, 214, -104, 36, -8, 1], 'lmfdb_label': '2112.bd3', 'torsion': [40]}
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id: 107386
{'degree': 16, 'field': [43308, -54216, 75780, -54300, 57570, -44296, 30317, -18808, 12392, -6586, 3053, -1316, 553, -182, 46, -8, 1], 'lmfdb_label': '2112.bd3', 'torsion': [30]}
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id: 107385
{'degree': 16, 'field': [224832, -328320, 331680, -183936, 50164, 19608, -21072, 8444, -399, 84, 336, -132, 126, -4, 0, 0, 1], 'lmfdb_label': '2112.bd3', 'torsion': [2, 20]}
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id: 107387
{'degree': 20, 'field': [1848320, 0, 1172480, 0, 358656, 0, -52480, 0, -55296, 0, -75360, 0, -24144, 0, -4960, 0, -516, 0, -10, 0, 1], 'lmfdb_label': '2112.bd3', 'torsion': [10]}
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ec_localdata • Show schema
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id: 35073
{'conductor': 2112, 'conductor_valuation': 6, 'discriminant_valuation': 28, 'j_denominator_valuation': 10, 'kodaira_symbol': -22, 'lmfdb_label': '2112.bd3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 35074
{'conductor': 2112, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '2112.bd3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
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id: 35075
{'conductor': 2112, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2112.bd3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1677667
{'adelic_gens': [[1301, 20, 1300, 21], [659, 1300, 1310, 1119], [1, 20, 0, 1], [896, 5, 1275, 1306], [736, 5, 75, 1306], [329, 1300, 0, 1319], [1, 10, 10, 101], [531, 20, 1300, 1187], [11, 16, 1080, 971], [1, 0, 20, 1]], 'adelic_image': '1320.288.5.?', 'conductor': 2112, 'lmfdb_label': '2112.bd3', 'prime': 0}
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id: 10311
{'conductor': 2112, 'elladic_image': '8.6.0.4', 'lmfdb_label': '2112.bd3', 'modell_image': '2B', 'prime': 2}
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id: 10312
{'conductor': 2112, 'elladic_image': '5.12.0.1', 'lmfdb_label': '2112.bd3', 'modell_image': '5B.4.1', 'prime': 5}
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lmfdb_iso 2112.bd does not appear in ec_padic