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ec_curvedata • Show schema
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{'Ciso': '21840y', 'Clabel': '21840y4', 'Cnumber': 4, 'abc_quality': 0.9673135241680412, 'absD': 1504386634383360, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 520, 'ainvs': [0, -1, 0, -171816, 27405936], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 21840, 'degree': 147456, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7864702271880005765753374052', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [136948444639063849, 367281893160], 'lmfdb_iso': '21840.e', 'lmfdb_label': '21840.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -10739, -428218], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.4', '20.12.0-4.c.1.2', '40.24.0-40.v.1.2', '104.24.0.?', '520.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 5], [3, 4, 7280], [5, 6, 4368], [7, 8, 3120], [13, 14, 1680]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0933230466280552671581052837', 'prec': 100}, 'szpiro_ratio': 4.781679888709658, '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, -1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 2, 0, 8, 0], 'aplist': [0, -1, -1, -1, 0, -1, 2, 8, 4, 6, 8, -6, 2, 12, 0, 10, 8, -2, 4, -8, 6, 0, 4, -6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 21840, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '21840.e', 'trace_hash': 526543172940502764}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.028073184279501653852551370032', 'prec': 107}, 'conductor': 21840, 'gens': [], 'heights': [], 'lmfdb_label': '21840.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.47879347349223099243279265465', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9151738939689239697311706186180718981', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[249, 0, 1]], 'xcoord_integral_points': [249]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '7': [0, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '21840.e1'}
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ec_torsion_growth • Show schema
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id: 1109449
{'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [2, 2]}
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id: 1109451
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [4]}
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id: 1109450
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '21840.e1', 'torsion': [4]}
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id: 1109452
{'degree': 4, 'field': [4, 0, -6, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [2, 4]}
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id: 1109456
{'degree': 8, 'field': [-48, 0, 181, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [6]}
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id: 1109455
{'degree': 8, 'field': [1225, 0, -380, 0, -4, 0, 4, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [8]}
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id: 1109454
{'degree': 8, 'field': [6241, 0, -7233, 0, 1084, 0, -57, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [8]}
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id: 1109453
{'degree': 8, 'field': [236196, 0, 11792, 0, -956, 0, 8, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [2, 4]}
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id: 1109461
{'degree': 16, 'field': [5444, 54820, -38078, -15730, -28555, 21288, 30586, -32872, 8750, -10, -438, 344, -118, 0, 20, -8, 1], 'lmfdb_label': '21840.e1', 'torsion': [12]}
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id: 1109458
{'degree': 16, 'field': [6561, 0, -14580, 0, 22032, 0, -14760, 0, 6823, 0, -1640, 0, 272, 0, -20, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [2, 8]}
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id: 1109462
{'degree': 16, 'field': [54756, 0, -54756, 0, 13689, 0, -51488, 0, 14276, 0, -278, 0, 64, 0, -16, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [12]}
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id: 1109459
{'degree': 16, 'field': [224676, 2402232, 2814464, -21000848, 3524821, 14472614, -3332983, -3294394, 754822, 353198, -75987, -19622, 3886, 546, -99, -6, 1], 'lmfdb_label': '21840.e1', 'torsion': [2, 8]}
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id: 1109460
{'degree': 16, 'field': [87647044, 0, -47197556, 0, 30887545, 0, -7509408, 0, 829140, 0, -56598, 0, 2752, 0, -80, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [2, 6]}
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id: 1109457
{'degree': 16, 'field': [3603000625, 0, 0, 0, 0, 0, 0, 0, 2040850, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '21840.e1', 'torsion': [4, 4]}
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ec_localdata • Show schema
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id: 497999
{'conductor': 21840, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '21840.e1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 498000
{'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '21840.e1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 498001
{'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21840.e1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 498002
{'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21840.e1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 498003
{'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '21840.e1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1810140
{'adelic_gens': [[41, 8, 164, 33], [513, 8, 512, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [216, 3, 5, 2], [328, 73, 187, 174], [7, 6, 514, 515], [317, 324, 278, 59]], 'adelic_image': '520.48.0.?', 'conductor': 21840, 'lmfdb_label': '21840.e1', 'prime': 0}
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id: 101053
{'conductor': 21840, 'elladic_image': '8.12.0.8', 'lmfdb_label': '21840.e1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 21840.e does not appear in ec_padic