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ec_curvedata • Show schema
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{'Ciso': '22080dc', 'Clabel': '22080dc1', 'Cnumber': 1, 'abc_quality': 0.9760884218335485, 'absD': 2228268662784000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2760, 'ainvs': [0, 1, 0, 29215, -1200225], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 22080, 'degree': 153600, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6328474741218918852652189327', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 62, 'isogeny_degrees': [1, 2, 4], 'jinv': [10519294081031, 8500170375], 'lmfdb_iso': '22080.ck', 'lmfdb_label': '22080.ck4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 456, 2401], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.1', '30.6.0.a.1', '40.12.0-4.c.1.1', '60.12.0.g.1', '120.24.0.?', '184.12.0.?', '552.24.0.?', '920.24.0.?', '2760.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.37888332042953503601150728787', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.59312670328197392113937075051', 'prec': 103}, 'szpiro_ratio': 4.245057658937504, '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, 1, 0, -4, 0, 1, 0, 4, 0, -6, 0, 1, 0, -2, 0, -4, 0], 'aplist': [0, 1, 1, -4, 4, -6, -2, -4, 1, 10, 8, -2, 2, -8, 0, 6, 0, -6, 8, 4, 10, -16, -12, -10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 22080, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '22080.ck', 'trace_hash': 1355938349911716841}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.038170399412252690744816521012', 'prec': 107}, 'conductor': 22080, 'gens': [[85, 1380, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.37888332042953503601150728787', 'prec': 103}], 'lmfdb_label': '22080.ck4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25623227976959174836241052922', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.8249282176199498909378119875108805450', 'prec': 130}, 'tamagawa_product': 240, 'torsion_generators': [[39, 0, 1]], 'xcoord_integral_points': [39, 85, 295, 775, 2293]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [2, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '22080.ck4'}
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ec_torsion_growth • Show schema
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id: 1123874
{'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [4]}
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id: 1123873
{'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '22080.ck4', 'torsion': [2, 2]}
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id: 1123875
{'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [4]}
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id: 1123876
{'degree': 4, 'field': [16, 0, 2, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [2, 4]}
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id: 1123880
{'degree': 8, 'field': [-1200, 0, -2008, 0, 120, 0, 0, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [6]}
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id: 1123879
{'degree': 8, 'field': [1, 0, 24, 0, 31, 0, 24, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [8]}
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id: 1123877
{'degree': 8, 'field': [256, 0, -136, 0, 81, 0, -16, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [2, 4]}
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id: 1123878
{'degree': 8, 'field': [4624, 0, -1816, 0, 192, 0, -22, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [8]}
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id: 1123881
{'degree': 16, 'field': [256, 0, 0, 0, 16, 0, 0, 0, 216, 0, 0, 0, 1, 0, 0, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [4, 4]}
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id: 1123885
{'degree': 16, 'field': [518400, 0, -1042944, 0, 381952, 0, -110112, 0, 28224, 0, 808, 0, -12, 0, -12, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [12]}
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id: 1123882
{'degree': 16, 'field': [1104601, 0, -1246744, 0, 280822, 0, -9460, 0, 32791, 0, 1220, 0, 22, 0, -4, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [2, 8]}
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id: 1123886
{'degree': 16, 'field': [3385600, 0, 2708480, 0, 541696, 0, -84000, 0, -27840, 0, 2472, 0, 100, 0, 20, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [12]}
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id: 1123883
{'degree': 16, 'field': [5688225, 0, 2956500, 0, 1260270, 0, 346320, 0, 64531, 0, 8016, 0, 686, 0, 36, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [2, 8]}
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id: 1123884
{'degree': 16, 'field': [47775744, 0, 8626176, 0, 2746368, 0, 359424, 0, 75600, 0, 3432, 0, 504, 0, 0, 0, 1], 'lmfdb_label': '22080.ck4', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 504675
{'conductor': 22080, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '22080.ck4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 504676
{'conductor': 22080, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '22080.ck4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
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id: 504677
{'conductor': 22080, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '22080.ck4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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id: 504678
{'conductor': 22080, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '22080.ck4', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1811758
{'adelic_gens': [[1844, 1, 943, 6], [1, 0, 8, 1], [1, 8, 0, 1], [2216, 3, 5, 2], [1, 4, 4, 17], [7, 6, 2754, 2755], [341, 342, 1022, 2405], [1031, 1032, 2402, 1025], [1201, 8, 2044, 33], [2753, 8, 2752, 9]], 'adelic_image': '2760.48.0.?', 'conductor': 22080, 'lmfdb_label': '22080.ck4', 'prime': 0}
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id: 102275
{'conductor': 22080, 'elladic_image': '4.6.0.1', 'lmfdb_label': '22080.ck4', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 1038944
{'lmfdb_iso': '22080.ck', 'p': 7, 'prec': 20, 'unit': 7567347541963733, 'val': 1}
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id: 1038950
{'lmfdb_iso': '22080.ck', 'p': 11, 'prec': 20, 'unit': 55509473740152203671, 'val': 1}
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id: 1038948
{'lmfdb_iso': '22080.ck', 'p': 13, 'prec': 20, 'unit': 1328701630380141327456, 'val': 1}
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id: 1038951
{'lmfdb_iso': '22080.ck', 'p': 17, 'prec': 20, 'unit': 185276349621896355435900, 'val': 1}
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id: 1038952
{'lmfdb_iso': '22080.ck', 'p': 19, 'prec': 20, 'unit': 701486907798344888758698, 'val': 1}
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id: 1038947
{'lmfdb_iso': '22080.ck', 'p': 29, 'prec': 20, 'unit': 3479590343932215695797740322, 'val': 1}
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id: 1038958
{'lmfdb_iso': '22080.ck', 'p': 31, 'prec': 20, 'unit': 40863470604668773358605708, 'val': 1}
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id: 1038943
{'lmfdb_iso': '22080.ck', 'p': 37, 'prec': 20, 'unit': 565398038076976900802624529271, 'val': 1}
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id: 1038945
{'lmfdb_iso': '22080.ck', 'p': 41, 'prec': 20, 'unit': 722635715834668220842652006712, 'val': 1}
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id: 1038946
{'lmfdb_iso': '22080.ck', 'p': 43, 'prec': 20, 'unit': 10400239704545876139356275318502, 'val': 1}
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id: 1038953
{'lmfdb_iso': '22080.ck', 'p': 53, 'prec': 20, 'unit': 366890681847288882847313903714802, 'val': 1}
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id: 1038957
{'lmfdb_iso': '22080.ck', 'p': 61, 'prec': 20, 'unit': 4249504540097808354436256354850429, 'val': 1}
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id: 1038942
{'lmfdb_iso': '22080.ck', 'p': 67, 'prec': 20, 'unit': 4648444369224990591111389399875606, 'val': 1}
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id: 1038956
{'lmfdb_iso': '22080.ck', 'p': 71, 'prec': 20, 'unit': 21007104088641804274697522898070629, 'val': 1}
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id: 1038954
{'lmfdb_iso': '22080.ck', 'p': 73, 'prec': 20, 'unit': 145473566773643180651338244555463301, 'val': 1}
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id: 1038949
{'lmfdb_iso': '22080.ck', 'p': 79, 'prec': 20, 'unit': 246794330127496055080933310866033962, 'val': 1}
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id: 1038941
{'lmfdb_iso': '22080.ck', 'p': 83, 'prec': 20, 'unit': 1516090952359602060139058772378118773, 'val': 1}
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id: 1038955
{'lmfdb_iso': '22080.ck', 'p': 89, 'prec': 20, 'unit': 1469773287274265271509687838831494168, 'val': 1}
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id: 1038940
{'lmfdb_iso': '22080.ck', 'p': 97, 'prec': 20, 'unit': 6927309052435446124081253912418294267, 'val': 1}