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ec_curvedata • Show schema
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{'Ciso': '2205k', 'Clabel': '2205k1', 'Cnumber': 1, 'abc_quality': 0.9665903421508077, 'absD': 9005442705, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [1, -1, 1, -1112, 13794], 'analytic_rank': 0, 'bad_primes': [3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 2205, 'degree': 1536, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.66315187887454291105801751191', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [1771561, 105], 'lmfdb_iso': '2205.b', 'lmfdb_label': '2205.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -3, 1], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '40.24.0-40.ba.1.13', '168.24.0.?', '210.6.0.?', '420.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.85910933998716858719228147827', 'prec': 107}, 'szpiro_ratio': 4.241680752282244, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, -1, 1, 0, 0, 3, 0, -1, 0, 0, 6, 0, 0, -1, 2, 0, 8, -1], 'aplist': [-1, 0, 1, 0, 0, 6, 2, 8, -8, 2, -4, -2, -6, 4, 8, -10, 4, 2, 4, 12, 2, 8, -4, -6, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 2205, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '2205.b', 'trace_hash': 1109683623272241717}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.26545664222698599330144358638', 'prec': 103}, 'conductor': 2205, 'gens': [], 'heights': [], 'lmfdb_label': '2205.b3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2795104421583822886471140628', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2795104421583822886471140628052350840', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[44, 198, 1]], 'xcoord_integral_points': [23, 44]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '2205.b3'}
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ec_torsion_growth • Show schema
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id: 112320
{'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '2205.b3', 'torsion': [2, 4]}
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id: 112321
{'degree': 4, 'field': [4, 10, -9, -2, 1], 'lmfdb_label': '2205.b3', 'torsion': [8]}
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id: 112325
{'degree': 8, 'field': [1, -4, 4, -17, 11, -17, 4, -4, 1], 'lmfdb_label': '2205.b3', 'torsion': [12]}
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id: 112323
{'degree': 8, 'field': [1, 0, -17, 0, 48, 0, -17, 0, 1], 'lmfdb_label': '2205.b3', 'torsion': [2, 8]}
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id: 112324
{'degree': 8, 'field': [1, 0, 9, 0, -4, 0, 9, 0, 1], 'lmfdb_label': '2205.b3', 'torsion': [2, 8]}
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id: 112322
{'degree': 8, 'field': [37636, 0, 7669, 0, 831, 0, 79, 0, 1], 'lmfdb_label': '2205.b3', 'torsion': [4, 4]}
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id: 112326
{'degree': 16, 'field': [-269, 5500, 5070, -15904, -3703, 10584, 574, -1220, -804, -1688, 2212, -336, -490, 224, -12, -8, 1], 'lmfdb_label': '2205.b3', 'torsion': [16]}
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id: 112327
{'degree': 16, 'field': [9, 0, 363, 0, -740, 0, 726, 0, 30, 0, -121, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '2205.b3', 'torsion': [2, 12]}
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ec_localdata • Show schema
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id: 36998
{'conductor': 2205, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '2205.b3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 36999
{'conductor': 2205, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2205.b3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 37000
{'conductor': 2205, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '2205.b3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1678314
{'adelic_gens': [[833, 8, 832, 9], [1, 0, 8, 1], [113, 108, 110, 527], [1, 8, 0, 1], [1, 4, 4, 17], [592, 837, 475, 838], [508, 1, 191, 6], [7, 6, 834, 835], [739, 738, 538, 115], [272, 837, 275, 838]], 'adelic_image': '840.48.0.?', 'conductor': 2205, 'lmfdb_label': '2205.b3', 'prime': 0}
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id: 10862
{'conductor': 2205, 'elladic_image': '4.12.0.7', 'lmfdb_label': '2205.b3', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 2205.b does not appear in ec_padic