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ec_curvedata • Show schema
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{'Ciso': '22080d', 'Clabel': '22080d2', 'Cnumber': 2, 'abc_quality': 0.9952642288505263, 'absD': 112326082560000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 552, 'ainvs': [0, -1, 0, -441601, 113097985], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 22080, 'degree': 147456, 'elladic_images': ['8.48.0.85'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8461642509124663447853580706', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [36330796409313601, 428490000], 'lmfdb_iso': '22080.k', 'lmfdb_label': '22080.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -6900, 220032], 'min_quad_twist_disc': 8, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.e.2.3', '24.96.0-24.r.2.4', '92.24.0.?', '184.96.0.?', '552.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.1176926613203711285773393411', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.80644348007254838065950988841', 'prec': 103}, 'szpiro_ratio': 5.059580927783543, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -1, 0, -1, 0, 0, 0, 1, 0, -4, 0, 2, 0, 1, 0, -6, 0, -4, 0], 'aplist': [0, -1, -1, 0, -4, 2, -6, -4, -1, 2, 0, 2, 10, 4, 0, -6, 4, 10, 12, -8, 10, -8, 4, 18, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 22080, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '22080.k', 'trace_hash': 688121948255344679}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.024913922335542013502103698119', 'prec': 107}, 'conductor': 22080, 'gens': [[360, 805, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.1176926613203711285773393411', 'prec': 100}], 'lmfdb_label': '22080.k4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.53809608167907354613435293657', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3552364098721892020657720671367871170', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[383, 0, 1], [385, 0, 1]], 'xcoord_integral_points': [-767, 360, 383, 385, 483]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [7, 0], '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '22080.k4'}
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ec_torsion_growth • Show schema
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id: 1121958
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '22080.k4', 'torsion': [2, 4]}
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id: 1121961
{'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '22080.k4', 'torsion': [2, 8]}
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id: 1121960
{'degree': 4, 'field': [18, -16, 17, -2, 1], 'lmfdb_label': '22080.k4', 'torsion': [2, 4]}
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id: 1121959
{'degree': 4, 'field': [121, 0, 24, 0, 1], 'lmfdb_label': '22080.k4', 'torsion': [2, 4]}
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id: 1121964
{'degree': 8, 'field': [-314928, 0, 46494, 0, -1944, 0, 0, 0, 1], 'lmfdb_label': '22080.k4', 'torsion': [2, 6]}
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id: 1121963
{'degree': 8, 'field': [772, -536, 790, -536, 339, -88, 34, -4, 1], 'lmfdb_label': '22080.k4', 'torsion': [2, 8]}
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id: 1121962
{'degree': 8, 'field': [1296, 0, 0, 0, 49, 0, 0, 0, 1], 'lmfdb_label': '22080.k4', 'torsion': [4, 4]}
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id: 1121968
{'degree': 16, 'field': [12996, 0, -22320, 0, -222852, 0, -342240, 0, 63253, 0, 3700, 0, -642, 0, -20, 0, 1], 'lmfdb_label': '22080.k4', 'torsion': [2, 16]}
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id: 1121969
{'degree': 16, 'field': [42248, 114544, -51620, -133368, 78346, 6584, -38183, 33976, -11880, 1546, 221, -76, -139, 42, 14, -8, 1], 'lmfdb_label': '22080.k4', 'torsion': [2, 12]}
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id: 1121965
{'degree': 16, 'field': [156816, 0, 11222928, 0, 1910412, 0, -198012, 0, -7727, 0, 6264, 0, 518, 0, 36, 0, 1], 'lmfdb_label': '22080.k4', 'torsion': [2, 8]}
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id: 1121967
{'degree': 16, 'field': [1679616, 0, 0, 0, -63504, 0, 0, 0, 1105, 0, 0, 0, -49, 0, 0, 0, 1], 'lmfdb_label': '22080.k4', 'torsion': [4, 8]}
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id: 1121966
{'degree': 16, 'field': [6885376, 0, -4130048, 0, 2862564, 0, -355132, 0, 63169, 0, -4432, 0, 222, 0, -20, 0, 1], 'lmfdb_label': '22080.k4', 'torsion': [4, 8]}
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ec_localdata • Show schema
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id: 503911
{'conductor': 22080, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '22080.k4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 503912
{'conductor': 22080, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '22080.k4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 503913
{'conductor': 22080, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '22080.k4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 503914
{'conductor': 22080, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '22080.k4', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1811820
{'adelic_gens': [[127, 2, 462, 547], [185, 4, 0, 1], [5, 4, 548, 549], [1, 0, 8, 1], [3, 418, 548, 133], [271, 412, 412, 275], [545, 8, 544, 9], [1, 8, 0, 1]], 'adelic_image': '552.192.1.?', 'conductor': 22080, 'lmfdb_label': '22080.k4', 'prime': 0}
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id: 102329
{'conductor': 22080, 'elladic_image': '8.48.0.85', 'lmfdb_label': '22080.k4', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 1038313
{'lmfdb_iso': '22080.k', 'p': 11, 'prec': 20, 'unit': 48062758435205633065, 'val': 1}
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id: 1038311
{'lmfdb_iso': '22080.k', 'p': 13, 'prec': 20, 'unit': 1885138451481216492, 'val': 2}
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id: 1038314
{'lmfdb_iso': '22080.k', 'p': 17, 'prec': 20, 'unit': 193335878315622866269548, 'val': 1}
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id: 1038315
{'lmfdb_iso': '22080.k', 'p': 19, 'prec': 20, 'unit': 1926066345138453117953001, 'val': 1}
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id: 1038310
{'lmfdb_iso': '22080.k', 'p': 29, 'prec': 20, 'unit': 4280837722307758771685855950, 'val': 1}
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id: 1038306
{'lmfdb_iso': '22080.k', 'p': 37, 'prec': 20, 'unit': 356494344471106415967105335925, 'val': 1}
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id: 1038308
{'lmfdb_iso': '22080.k', 'p': 41, 'prec': 20, 'unit': 61727465508083833718417647916, 'val': 2}
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id: 1038309
{'lmfdb_iso': '22080.k', 'p': 43, 'prec': 20, 'unit': 1126337753308611780820560020707, 'val': 1}
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id: 1038316
{'lmfdb_iso': '22080.k', 'p': 53, 'prec': 20, 'unit': 472087322781834998964719922119912, 'val': 1}
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id: 1038319
{'lmfdb_iso': '22080.k', 'p': 59, 'prec': 20, 'unit': 2486968692469047762746471392202028, 'val': 1}
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id: 1038320
{'lmfdb_iso': '22080.k', 'p': 61, 'prec': 20, 'unit': 1166020835590848389131561461018807, 'val': 1}
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id: 1038305
{'lmfdb_iso': '22080.k', 'p': 67, 'prec': 20, 'unit': 4154059498710379719392701721160169, 'val': 1}
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id: 1038307
{'lmfdb_iso': '22080.k', 'p': 71, 'prec': 20, 'unit': 126614907847002358230489278394738830, 'val': 1}
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id: 1038317
{'lmfdb_iso': '22080.k', 'p': 73, 'prec': 20, 'unit': 133389920023734442425462022295956616, 'val': 1}
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id: 1038312
{'lmfdb_iso': '22080.k', 'p': 79, 'prec': 20, 'unit': 385762304743502637638711252190790619, 'val': 1}
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id: 1038304
{'lmfdb_iso': '22080.k', 'p': 83, 'prec': 20, 'unit': 1415326267899962117226915046625683116, 'val': 1}
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id: 1038318
{'lmfdb_iso': '22080.k', 'p': 89, 'prec': 20, 'unit': 9057700399122556421434574278895352070, 'val': 1}
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id: 1038303
{'lmfdb_iso': '22080.k', 'p': 97, 'prec': 20, 'unit': 39795948806165646251880268072271940439, 'val': 1}