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ec_curvedata • Show schema
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{'Ciso': '36822i', 'Clabel': '36822i5', 'Cnumber': 5, 'abc_quality': 1.036242441540377, 'absD': 5907251780174709378, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 5168, 'ainvs': [1, 1, 0, -593491, 211044199], 'analytic_rank': 1, 'bad_primes': [2, 3, 17, 19], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 36822, 'degree': 884736, 'elladic_images': ['8.48.0.224'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3192977752246924842423407726', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-491411892194497, 125563633938], 'lmfdb_iso': '36822.e', 'lmfdb_label': '36822.e3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1644, -30942], 'min_quad_twist_disc': -19, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0.m.2', '76.12.0.?', '152.96.0.?', '272.96.1.?', '5168.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.66861399107055033725235850742', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.84707828564147225423782705666', 'prec': 103}, 'szpiro_ratio': 4.932602245445719, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, -1, 1, -2, 1, 0, -1, 1, 2, -4, -1, 2, 0, 2, 1, 1, -1, 0, -2], 'aplist': [-1, -1, -2, 0, -4, 2, 1, 0, 0, 10, -8, 2, -10, 12, 0, -6, -12, -10, 12, 0, 10, 8, 4, 6, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 36822, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '36822.e', 'trace_hash': 869768459210792631}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0096712709058920045336937787698', 'prec': 110}, 'conductor': 36822, 'gens': [[625, 8893, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.66861399107055033725235850742', 'prec': 103}], 'lmfdb_label': '36822.e3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.22792036965624663519621564981', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4382519680342115165566917164466951848', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-3637, 3637, 2]], 'xcoord_integral_points': [-259, 319, 625]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [5, 1], '3': [1, 0], '5': [3, 0], '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': [2, 0], '19': 'a', '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 3, 0]}, 'iwp0': 0, 'lmfdb_label': '36822.e3'}
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ec_torsion_growth • Show schema
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id: 1822205
{'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [4]}
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id: 1822204
{'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [2, 2]}
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id: 1822206
{'degree': 2, 'field': [38, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [4]}
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id: 1822209
{'degree': 4, 'field': [25, 0, -9, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [8]}
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id: 1822208
{'degree': 4, 'field': [81, 0, -20, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [8]}
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id: 1822207
{'degree': 4, 'field': [81, 0, 20, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [2, 4]}
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id: 1822213
{'degree': 8, 'field': [-138598, 10189, 36749, -12395, 2129, -293, 91, -1, 1], 'lmfdb_label': '36822.e3', 'torsion': [6]}
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id: 1822211
{'degree': 8, 'field': [391, -1508, 1622, -248, 175, -64, 26, -4, 1], 'lmfdb_label': '36822.e3', 'torsion': [8]}
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id: 1822212
{'degree': 8, 'field': [625, 0, 0, 0, 31, 0, 0, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [2, 8]}
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id: 1822210
{'degree': 8, 'field': [1507, 508, -322, -392, 247, -64, 26, -4, 1], 'lmfdb_label': '36822.e3', 'torsion': [2, 4]}
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id: 1822216
{'degree': 16, 'field': [-79556175, -686572200, -430999704, 269439696, 160813944, -48747096, -28410408, 3589920, 2948830, -123768, -188456, 3024, 7512, -72, -152, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [16]}
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id: 1822217
{'degree': 16, 'field': [88357, 265912, -119506, -451096, 680376, -722164, 568270, -351392, 184053, -76860, 28858, -8344, 2240, -420, 80, -8, 1], 'lmfdb_label': '36822.e3', 'torsion': [16]}
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id: 1822214
{'degree': 16, 'field': [161449, 56456, -88720, -12696, 281504, -577928, 660760, -516768, 285265, -122712, 44140, -11896, 3014, -504, 92, -8, 1], 'lmfdb_label': '36822.e3', 'torsion': [4, 8]}
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id: 1822215
{'degree': 16, 'field': [385747, -544504, 1035284, -1151808, 1045310, -692888, 468664, -249384, 124567, -49848, 18928, -5656, 1610, -336, 68, -8, 1], 'lmfdb_label': '36822.e3', 'torsion': [2, 8]}
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id: 1822219
{'degree': 16, 'field': [749956, 0, -619331, 0, -14174, 0, -40557, 0, 21987, 0, -5673, 0, 667, 0, -38, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [12]}
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id: 1822220
{'degree': 16, 'field': [34668544, 0, 75249304, 0, 26950084, 0, 5175000, 0, 618204, 0, 48852, 0, 2488, 0, 76, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [12]}
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id: 1822218
{'degree': 16, 'field': [16751607184, 0, 9860108368, 0, 85002340, 0, -6357984, 0, 971376, 0, 8724, 0, -1076, 0, 4, 0, 1], 'lmfdb_label': '36822.e3', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 868114
{'conductor': 36822, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '36822.e3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 868115
{'conductor': 36822, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '36822.e3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 868116
{'conductor': 36822, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '36822.e3', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
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id: 868117
{'conductor': 36822, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '36822.e3', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1910123
{'adelic_gens': [[4865, 2736, 4104, 1217], [815, 0, 0, 5167], [1, 16, 0, 1], [5153, 16, 5152, 17], [628, 4693, 3287, 4770], [1198, 4693, 1881, 4770], [15, 2, 5070, 5155], [1, 0, 16, 1], [5, 4, 5164, 5165]], 'adelic_image': '5168.192.1.?', 'conductor': 36822, 'lmfdb_label': '36822.e3', 'prime': 0}
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id: 162896
{'conductor': 36822, 'elladic_image': '8.48.0.224', 'lmfdb_label': '36822.e3', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 1813392
{'lmfdb_iso': '36822.e', 'p': 5, 'prec': 20, 'unit': 3579908849363, 'val': 2}
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id: 1813378
{'lmfdb_iso': '36822.e', 'p': 11, 'prec': 20, 'unit': 54931861997953858419, 'val': 1}
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id: 1813384
{'lmfdb_iso': '36822.e', 'p': 13, 'prec': 20, 'unit': 165450060722517979615, 'val': 1}
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id: 1813383
{'lmfdb_iso': '36822.e', 'p': 29, 'prec': 20, 'unit': 3590467130177445835471889567, 'val': 1}
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id: 1813380
{'lmfdb_iso': '36822.e', 'p': 31, 'prec': 20, 'unit': 6888011341471445418779541006, 'val': 1}
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id: 1813379
{'lmfdb_iso': '36822.e', 'p': 37, 'prec': 20, 'unit': 352063087456145756749893439124, 'val': 1}
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id: 1813381
{'lmfdb_iso': '36822.e', 'p': 41, 'prec': 20, 'unit': 2129411325574932948920369178546, 'val': 1}
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id: 1813382
{'lmfdb_iso': '36822.e', 'p': 43, 'prec': 20, 'unit': 909697616670721292543869289680, 'val': 1}
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id: 1813387
{'lmfdb_iso': '36822.e', 'p': 53, 'prec': 20, 'unit': 315652996005384358143232095221915, 'val': 1}
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id: 1813390
{'lmfdb_iso': '36822.e', 'p': 59, 'prec': 20, 'unit': 3157968290126377189252523889449398, 'val': 1}
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id: 1813391
{'lmfdb_iso': '36822.e', 'p': 61, 'prec': 20, 'unit': 807934184944203746412344232133544, 'val': 1}
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id: 1813377
{'lmfdb_iso': '36822.e', 'p': 67, 'prec': 20, 'unit': 6402858874433092271549775813041092, 'val': 1}
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id: 1813388
{'lmfdb_iso': '36822.e', 'p': 73, 'prec': 20, 'unit': 77597450699312771580235613425140938, 'val': 1}
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id: 1813385
{'lmfdb_iso': '36822.e', 'p': 79, 'prec': 20, 'unit': 37828841638265364320563580366779163, 'val': 1}
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id: 1813386
{'lmfdb_iso': '36822.e', 'p': 83, 'prec': 20, 'unit': 2467201612708038115950849377814578135, 'val': 1}
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id: 1813389
{'lmfdb_iso': '36822.e', 'p': 89, 'prec': 20, 'unit': 8280767368329926134523849897960010366, 'val': 1}
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id: 1813376
{'lmfdb_iso': '36822.e', 'p': 97, 'prec': 20, 'unit': 25855956715738653542882122821264706565, 'val': 1}