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ec_curvedata • Show schema
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{'Ciso': '5200n', 'Clabel': '5200n1', 'Cnumber': 1, 'abc_quality': 0.9356398193134444, 'absD': 1064960000000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 1040, 'ainvs': [0, 0, 0, -2675, 19250], 'analytic_rank': 0, 'bad_primes': [2, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 5200, 'degree': 4608, 'elladic_images': ['16.24.0.15'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0005059862994014547658495980', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [33076161, 16640], 'lmfdb_iso': '5200.r', 'lmfdb_label': '5200.r4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -7, -1], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.o.1', '16.24.0.i.1', '20.12.0-4.c.1.1', '40.24.0-8.o.1.3', '52.12.0-4.c.1.1', '80.48.0.?', '104.24.0.?', '130.6.0.?', '208.48.0.?', '260.24.0.?', '520.96.0.?', '1040.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 325], [5, 18, 208], [13, 14, 400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.49736015047759404195176219007', 'prec': 107}, 'szpiro_ratio': 4.124241464273742, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -1, 0, 0, 0, -2, 0, 8, 0], 'aplist': [0, 0, 0, 0, 0, -1, -2, 8, -4, -2, 4, -6, 10, 0, 8, -6, -8, -2, 4, 12, -10, 8, 12, 10, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 5200, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '5200.r', 'trace_hash': 187173536368573774}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.13519839691261250475033685891', 'prec': 103}, 'conductor': 5200, 'gens': [], 'heights': [], 'lmfdb_label': '5200.r4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.77282584139185895188752797665', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5456516827837179037750559532992484781', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-55, 0, 1]], 'xcoord_integral_points': [-55]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '5': 'a', '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '5200.r4'}
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ec_torsion_growth • Show schema
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id: 272140
{'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '5200.r4', 'torsion': [2, 2]}
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id: 272141
{'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '5200.r4', 'torsion': [4]}
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id: 272142
{'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '5200.r4', 'torsion': [4]}
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id: 272143
{'degree': 4, 'field': [4, 0, 9, 0, 1], 'lmfdb_label': '5200.r4', 'torsion': [2, 4]}
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id: 272145
{'degree': 8, 'field': [1, -4, 7, -4, 0, 2, 3, -2, 1], 'lmfdb_label': '5200.r4', 'torsion': [8]}
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id: 272146
{'degree': 8, 'field': [256, 0, 1488, 0, 424, 0, 37, 0, 1], 'lmfdb_label': '5200.r4', 'torsion': [2, 8]}
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id: 272144
{'degree': 8, 'field': [3771, 1044, -1168, 252, -135, 8, 2, -4, 1], 'lmfdb_label': '5200.r4', 'torsion': [2, 4]}
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id: 272147
{'degree': 8, 'field': [14064, -20616, 5190, -2448, 240, -78, 12, 0, 1], 'lmfdb_label': '5200.r4', 'torsion': [6]}
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id: 272148
{'degree': 16, 'field': [1, 0, 0, 0, -126, 0, 0, 0, 5011, 0, 0, 0, -126, 0, 0, 0, 1], 'lmfdb_label': '5200.r4', 'torsion': [4, 4]}
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id: 272150
{'degree': 16, 'field': [1, 4, 7, 4, -3, -16, -2, 0, 14, 0, -2, 16, -3, -4, 7, -4, 1], 'lmfdb_label': '5200.r4', 'torsion': [16]}
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id: 272149
{'degree': 16, 'field': [196, 0, -552, 0, 657, 0, -492, 0, 288, 0, -106, 0, 28, 0, -4, 0, 1], 'lmfdb_label': '5200.r4', 'torsion': [2, 8]}
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id: 272151
{'degree': 16, 'field': [256, 1152, 1888, 1712, 1268, -204, 1678, 1130, 209, -100, 328, -22, 11, -12, 16, -6, 1], 'lmfdb_label': '5200.r4', 'torsion': [16]}
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id: 272152
{'degree': 16, 'field': [2304, 0, -30204, 0, 23040, 0, -2232, 0, -15315, 0, 1068, 0, -438, 0, 0, 0, 1], 'lmfdb_label': '5200.r4', 'torsion': [2, 6]}
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id: 272153
{'degree': 16, 'field': [544056, -1179768, 1823484, -1500360, 1333950, -852726, 563109, -291888, 144730, -57020, 21205, -6152, 1723, -350, 70, -8, 1], 'lmfdb_label': '5200.r4', 'torsion': [12]}
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id: 272154
{'degree': 16, 'field': [42981136, 0, 20259104, 0, 2311612, 0, 674717, 0, 181570, 0, -1987, 0, 277, 0, 26, 0, 1], 'lmfdb_label': '5200.r4', 'torsion': [12]}
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ec_localdata • Show schema
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id: 101382
{'conductor': 5200, 'conductor_valuation': 4, 'discriminant_valuation': 20, 'j_denominator_valuation': 8, 'kodaira_symbol': -16, 'lmfdb_label': '5200.r4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 101383
{'conductor': 5200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '5200.r4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 101384
{'conductor': 5200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5200.r4', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1698006
{'adelic_gens': [[15, 166, 754, 995], [574, 3, 173, 20], [1039, 504, 642, 1], [1, 16, 0, 1], [1025, 16, 1024, 17], [1, 8, 8, 65], [1, 16, 268, 389], [1, 0, 16, 1], [824, 1031, 809, 1014]], 'adelic_image': '1040.192.3.?', 'conductor': 5200, 'lmfdb_label': '5200.r4', 'prime': 0}
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id: 25912
{'conductor': 5200, 'elladic_image': '16.24.0.15', 'lmfdb_label': '5200.r4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 5200.r does not appear in ec_padic
