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ec_curvedata • Show schema
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{'Ciso': '8470ba', 'Clabel': '8470ba1', 'Cnumber': 1, 'abc_quality': 1.019093873411884, 'absD': 312892253470720, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 440, 'ainvs': [1, -1, 1, -3532, 855759], 'analytic_rank': 0, 'bad_primes': [2, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 8470, 'degree': 30720, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4611941763729379789035366883', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 4], 'jinv': [-2749884201, 176619520], 'lmfdb_iso': '8470.z', 'lmfdb_label': '8470.z4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -29, -635], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '40.24.0-40.z.1.13', '88.24.0.?', '110.6.0.?', '220.24.0.?', '440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, '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': '0.26224653997375270687256489932', 'prec': 103}, 'szpiro_ratio': 4.515621323457783, '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, -1, 1, -3, 1, 0, 0, 6, -1, 0, 1, 2, -3, 4, 1], 'aplist': [1, 0, 1, -1, 0, 6, 2, 4, -4, -6, 0, -2, 6, 4, 4, -2, 12, 2, -8, -8, 10, 8, 12, 10, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 8470, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '8470.z', 'trace_hash': 1284131491870043763}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.053805028332854495471513857955', 'prec': 107}, 'conductor': 8470, 'gens': [], 'heights': [], 'lmfdb_label': '8470.z4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.44947334307635948303224896625', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5957867446108758642579917299872846759', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[69, 933, 1]], 'xcoord_integral_points': [-107, 69]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 0], '5': [1, 0], '7': [0, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '8470.z4'}
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ec_torsion_growth • Show schema
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id: 443996
{'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '8470.z4', 'torsion': [2, 4]}
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id: 443997
{'degree': 4, 'field': [-2, -6, 7, -2, 1], 'lmfdb_label': '8470.z4', 'torsion': [8]}
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id: 444001
{'degree': 8, 'field': [-1920, 12480, 2880, 4128, 216, -84, -48, 0, 1], 'lmfdb_label': '8470.z4', 'torsion': [12]}
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id: 444000
{'degree': 8, 'field': [784, 344, 390, -110, -39, 22, 12, -4, 1], 'lmfdb_label': '8470.z4', 'torsion': [2, 8]}
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id: 443999
{'degree': 8, 'field': [5041, 0, 579, 0, 136, 0, 19, 0, 1], 'lmfdb_label': '8470.z4', 'torsion': [2, 8]}
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id: 443998
{'degree': 8, 'field': [8976016, 0, 569009, 0, 14291, 0, 179, 0, 1], 'lmfdb_label': '8470.z4', 'torsion': [4, 4]}
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id: 444002
{'degree': 16, 'field': [1472768, -1179904, -1636800, -1660736, -3934216, -1557424, 110352, -223520, -86470, 47468, -15922, 2364, 543, -232, 72, -8, 1], 'lmfdb_label': '8470.z4', 'torsion': [16]}
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id: 444003
{'degree': 16, 'field': [8410120, 7744780, -618370, -1032555, 2581670, -681685, 436339, -116994, 30265, 24450, -1508, 289, 488, -105, 35, -4, 1], 'lmfdb_label': '8470.z4', 'torsion': [2, 12]}
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ec_localdata • Show schema
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id: 176912
{'conductor': 8470, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '8470.z4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
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id: 176913
{'conductor': 8470, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8470.z4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 176914
{'conductor': 8470, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8470.z4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 176915
{'conductor': 8470, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '8470.z4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1720112
{'adelic_gens': [[268, 1, 111, 6], [169, 168, 398, 175], [1, 0, 8, 1], [433, 8, 432, 9], [1, 8, 0, 1], [1, 4, 4, 17], [72, 437, 155, 438], [7, 6, 434, 435], [59, 58, 178, 395]], 'adelic_image': '440.48.0.?', 'conductor': 8470, 'lmfdb_label': '8470.z4', 'prime': 0}
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id: 41648
{'conductor': 8470, 'elladic_image': '4.12.0.7', 'lmfdb_label': '8470.z4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 8470.z does not appear in ec_padic