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ec_curvedata • Show schema
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{'Ciso': '259896cs', 'Clabel': '259896cs2', 'Cnumber': 2, 'abc_quality': 0.9332211540954428, 'absD': 778764849408, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [0, 1, 0, -40196, -3115008], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 259896, 'degree': 737280, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3117843198766988053394356329', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 70, 'isogeny_degrees': [1, 2], 'jinv': [238481570896, 25857], 'lmfdb_iso': '259896.cs', 'lmfdb_label': '259896.cs1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -820, 9316], 'min_quad_twist_disc': -7, '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': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.2047498443211678053814168503', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.12326887502425472015806215313', 'prec': 107}, 'szpiro_ratio': 3.4823602788721337, '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, 0, 0, 1, 0, -2, 0, 1, 0, 4, 0, -1, 0, 0, 0], 'aplist': [0, 1, 4, 0, -2, 1, -1, 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': 259896, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '259896.cs', 'trace_hash': 2079503221156880505}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.072543518665165131622444140227', 'prec': 107}, 'conductor': 259896, 'gens': [[15808, 1987440, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.2047498443211678053814168503', 'prec': 100}], 'lmfdb_label': '259896.cs1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.33717531381498945189482466603', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '14.039305296700058001423878955618939363', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-117, 0, 1]], 'xcoord_integral_points': [-117, 15808]}
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lmfdb_label 259896.cs1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 11143405
{'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '259896.cs1', 'torsion': [2, 2]}
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id: 11143406
{'degree': 4, 'field': [833, 0, 63, 0, 1], 'lmfdb_label': '259896.cs1', 'torsion': [4]}
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id: 11143408
{'degree': 8, 'field': [38416, 0, 23324, 0, 3773, 0, 119, 0, 1], 'lmfdb_label': '259896.cs1', 'torsion': [2, 4]}
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id: 11143407
{'degree': 8, 'field': [382159, 48928, -47816, -2096, 729, 380, -122, -4, 1], 'lmfdb_label': '259896.cs1', 'torsion': [2, 4]}
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id: 11143409
{'degree': 8, 'field': [14565278, 11029900, 3119222, 195834, -17664, -5238, -302, -4, 1], 'lmfdb_label': '259896.cs1', 'torsion': [6]}
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id: 11143410
{'degree': 16, 'field': [370899703924, 726707620752, 562963335752, 141321333968, 37712075832, 1922973776, 879645904, -91795208, 21916410, -5879440, 773132, -138020, 11548, -1708, 142, -4, 1], 'lmfdb_label': '259896.cs1', 'torsion': [8]}
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id: 11143411
{'degree': 16, 'field': [2727633901196, -3058329264040, 4694019273376, -1576327520904, 113941381588, -30040662872, 1687896988, -155389984, -99764592, 10708508, -1725544, 207460, -19240, 876, 104, -4, 1], 'lmfdb_label': '259896.cs1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 6442416
{'conductor': 259896, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '259896.cs1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 6442417
{'conductor': 259896, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '259896.cs1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 6442418
{'conductor': 259896, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '259896.cs1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 6442419
{'conductor': 259896, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '259896.cs1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 6442420
{'conductor': 259896, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '259896.cs1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 3310591
{'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': 259896, 'lmfdb_label': '259896.cs1', 'prime': 0}
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id: 933335
{'conductor': 259896, 'elladic_image': '2.3.0.1', 'lmfdb_label': '259896.cs1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 259896.cs does not appear in ec_padic