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ec_curvedata • Show schema
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{'Ciso': '34a', 'Clabel': '34a1', 'Cnumber': 1, 'abc_quality': 0.9000957170016773, 'absD': 1088, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 408, 'ainvs': [1, 0, 0, -3, 1], 'analytic_rank': 0, 'bad_primes': [2, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 34, 'degree': 2, 'elladic_images': ['8.6.0.1', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.71639233654846198665198817793', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [3048625, 1088], 'lmfdb_iso': '34.a', 'lmfdb_label': '34.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3, 1], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '6.24.0-6.a.1.4', '8.6.0.c.1', '24.48.0-24.bw.1.15', '34.6.0.a.1', '102.48.0.?', '136.12.0.?', '408.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.71639233654846198665198817793', 'prec': 107}, 'szpiro_ratio': 4.233883950049846, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, -2, 1, 0, -2, -4, 1, 1, 0, 6, -2, 2, -4, 0, 1, -1, 1, -4, 0], 'aplist': [1, -2, 0, -4, 6, 2, -1, -4, 0, 0, -4, -4, 6, 8, 0, -6, 0, -4, 8, 0, 2, 8, 0, -6, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 34, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '34.a', 'trace_hash': 2246807206681965941}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '4.1903517198537857224752071975', 'prec': 100}, 'conductor': 34, 'gens': [], 'heights': [], 'lmfdb_label': '34.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '4.4956633263137035532067468518', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.74927722105228392553445780862768318112', 'prec': 133}, 'tamagawa_product': 6, 'torsion_generators': [[0, 1, 1]], 'xcoord_integral_points': [-2, 0, 2]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 0], '3': [2, 0], '17': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '34.a4'}
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ec_torsion_growth • Show schema
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id: 932
{'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '34.a4', 'torsion': [2, 6]}
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id: 933
{'degree': 4, 'field': [2, -4, 5, -2, 1], 'lmfdb_label': '34.a4', 'torsion': [12]}
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id: 934
{'degree': 6, 'field': [12, 0, -11, 0, 1, 0, 1], 'lmfdb_label': '34.a4', 'torsion': [3, 6]}
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id: 935
{'degree': 8, 'field': [-16, -8, 6, 8, 15, -2, -6, -2, 1], 'lmfdb_label': '34.a4', 'torsion': [2, 12]}
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id: 936
{'degree': 8, 'field': [8, -8, 9, -2, 3, 20, 3, -2, 1], 'lmfdb_label': '34.a4', 'torsion': [2, 12]}
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id: 937
{'degree': 9, 'field': [-32, -48, 24, 20, 0, 6, -5, 3, -3, 1], 'lmfdb_label': '34.a4', 'torsion': [18]}
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id: 938
{'degree': 12, 'field': [16, -56, 120, -178, 175, 3, -65, 12, 12, -2, 1, -3, 1], 'lmfdb_label': '34.a4', 'torsion': [6, 6]}
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id: 939
{'degree': 16, 'field': [32, -64, 144, -240, 450, -752, 896, -880, 1079, -1152, 600, 48, -190, 56, 12, -8, 1], 'lmfdb_label': '34.a4', 'torsion': [24]}
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id: 940
{'degree': 18, 'field': [1024, 1536, -13824, 16576, -960, -13536, 13216, -192, -6120, 3412, -108, -840, 460, -96, -36, 43, -9, -3, 1], 'lmfdb_label': '34.a4', 'torsion': [2, 18]}
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ec_localdata • Show schema
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id: 120
{'conductor': 34, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '34.a4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
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id: 121
{'conductor': 34, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '34.a4', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1665948
{'adelic_gens': [[27, 88, 398, 77], [370, 3, 21, 400], [397, 12, 396, 13], [1, 0, 12, 1], [11, 2, 358, 399], [1, 6, 6, 37], [281, 2, 126, 13], [1, 12, 0, 1], [205, 12, 6, 73]], 'adelic_image': '408.96.1.?', 'conductor': 34, 'lmfdb_label': '34.a4', 'prime': 0}
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id: 81
{'conductor': 34, 'elladic_image': '8.6.0.1', 'lmfdb_label': '34.a4', 'modell_image': '2B', 'prime': 2}
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id: 82
{'conductor': 34, 'elladic_image': '3.8.0.1', 'lmfdb_label': '34.a4', 'modell_image': '3B.1.1', 'prime': 3}
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lmfdb_iso 34.a does not appear in ec_padic