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ec_curvedata • Show schema
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{'Ciso': '28322bi', 'Clabel': '28322bi2', 'Cnumber': 2, 'abc_quality': 1.0533569673638747, 'absD': 793042169743898606, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 168, 'ainvs': [1, 1, 1, 42188, -42698013], 'analytic_rank': 0, 'bad_primes': [2, 7, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 28322, 'degree': 435456, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1139986751388195091031037432', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 18, 'isogeny_degrees': [1, 3], 'jinv': [845095823, 80707214], 'lmfdb_iso': '28322.s', 'lmfdb_label': '28322.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 861, 124607], 'min_quad_twist_disc': -7, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '21.8.0-3.a.1.2', '24.8.0-3.a.1.5', '56.2.0.b.1', '168.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.19663915259242416313391583219', 'prec': 103}, 'szpiro_ratio': 4.746992831754884, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, -1, 1, -3, -1, 0, 1, -2, -3, 0, -1, -5, 0, 3, 1, 0, -2, 4, -3], 'aplist': [1, -1, -3, 0, 0, -5, 0, 4, 3, 6, -2, -4, -6, -4, -6, -12, -12, 1, 8, -9, 16, 8, 3, -6, 10], 'class_deg': 3, 'class_size': 2, 'conductor': 28322, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '28322.s', 'trace_hash': 2208809083394166180}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.014581563090749542273378385451', 'prec': 107}, 'conductor': 28322, 'gens': [], 'heights': [], 'lmfdb_label': '28322.s2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.13442883935703785467156852875', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.80657303614222712802941117248644395655', 'prec': 133}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [4, 0], '3': [4, 0], '5': [0, 0], '7': 'a', '11': [0, 0, 0], '13': [0, 0], '17': 'a', '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '28322.s2'}
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ec_torsion_growth • Show schema
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id: 1420693
{'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '28322.s2', 'torsion': [3]}
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id: 1420694
{'degree': 3, 'field': [22, 6, -1, 1], 'lmfdb_label': '28322.s2', 'torsion': [2]}
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id: 1420697
{'degree': 6, 'field': [121, -1067, 138, -45, -4, -1, 1], 'lmfdb_label': '28322.s2', 'torsion': [6]}
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id: 1420696
{'degree': 6, 'field': [1334, -318, -84, 55, 9, -3, 1], 'lmfdb_label': '28322.s2', 'torsion': [3]}
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id: 1420695
{'degree': 6, 'field': [2192, -2144, 608, -24, 55, -2, 1], 'lmfdb_label': '28322.s2', 'torsion': [2, 2]}
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id: 1420698
{'degree': 12, 'field': [3728, 800, -5496, 576, 2710, -1332, -153, 316, -107, 12, 13, -4, 1], 'lmfdb_label': '28322.s2', 'torsion': [4]}
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id: 1420700
{'degree': 12, 'field': [577648, -441920, -124176, 97696, -5116, -4560, 7444, -480, 827, -88, 60, -4, 1], 'lmfdb_label': '28322.s2', 'torsion': [2, 6]}
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id: 1420699
{'degree': 12, 'field': [988036, 292236, -32844, 196308, 29268, -17994, 8351, 285, -282, 135, 0, -3, 1], 'lmfdb_label': '28322.s2', 'torsion': [3, 3]}
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id: 1420701
{'degree': 18, 'field': [-32418725, 10218858, 59868600, -26104537, -18312339, -818862, 4910114, 3069519, -1145862, -463813, -16203, 82959, 13205, -12189, 453, 494, -39, -9, 1], 'lmfdb_label': '28322.s2', 'torsion': [9]}
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id: 1420702
{'degree': 18, 'field': [1404928, 0, 0, 0, 0, 0, 15940, 0, 0, 0, 0, 0, 404, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '28322.s2', 'torsion': [6]}
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ec_localdata • Show schema
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id: 657034
{'conductor': 28322, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '28322.s2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 657035
{'conductor': 28322, 'conductor_valuation': 2, 'discriminant_valuation': 15, 'j_denominator_valuation': 9, 'kodaira_symbol': -13, 'lmfdb_label': '28322.s2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 657036
{'conductor': 28322, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '28322.s2', 'prime': 17, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
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ec_galrep • Show schema
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id: 1853327
{'adelic_gens': [[122, 51, 31, 91], [127, 6, 0, 1], [95, 162, 117, 149], [1, 0, 6, 1], [4, 3, 9, 7], [163, 6, 162, 7], [3, 4, 8, 11], [85, 6, 87, 19], [1, 6, 0, 1]], 'adelic_image': '168.16.0.?', 'conductor': 28322, 'lmfdb_label': '28322.s2', 'prime': 0}
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id: 128175
{'conductor': 28322, 'elladic_image': '3.4.0.1', 'lmfdb_label': '28322.s2', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 28322.s does not appear in ec_padic