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ec_curvedata • Show schema
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{'Ciso': '69360cc', 'Clabel': '69360cc3', 'Cnumber': 3, 'abc_quality': 1.0253374473912513, 'absD': 5005166307840000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 4080, 'ainvs': [0, -1, 0, -46336, 1791040], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 69360, 'degree': 327680, 'elladic_images': ['8.48.0.44'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7074762805052095620984029332', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 4], 'jinv': [111284641, 50625], 'lmfdb_iso': '69360.n', 'lmfdb_label': '69360.n5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -10, -10], 'min_quad_twist_disc': -68, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0.b.1', '8.48.0.b.2', '24.96.1.n.1', '40.96.1.s.1', '68.48.0-4.b.1.1', '80.192.5.?', '120.192.5.?', '136.96.0.?', '240.384.13.?', '408.192.1.?', '680.192.1.?', '1360.384.5.?', '2040.384.5.?', '4080.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 19, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '5.3015380425609294227256150325', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.40227757208284378744359649719', 'prec': 107}, 'szpiro_ratio': 3.9332905689834954, '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, 0, 0, -4, 0], 'aplist': [0, -1, -1, 0, -4, -2, 0, -4, 0, 2, 0, 10, -10, -4, -8, -10, 4, 2, -12, -8, -10, 0, -12, -6, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 69360, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '69360.n', 'trace_hash': 1860647470187174535}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.032877966362022486790687393855', 'prec': 107}, 'conductor': 69360, 'gens': [[-96, 2312, 1], [24, 832, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4014431019994695734936844422', 'prec': 100}, {'__RealLiteral__': 0, 'data': '3.9758943972851868255926332588', 'prec': 100}], 'lmfdb_label': '69360.n5', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.38714560505411717238514855374', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.2098686128186840755164073140394883603', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[40, 0, 1], [193, 0, 1]], 'xcoord_integral_points': [-232, -96, -32, 24, 40, 193, 209, 346, 618, 2218, 2641]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': [2, 2, 0], '11': [2, 0], '13': [2, 0], '17': 'a', '19': [2, 0], '23': [2, 2, 0], '29': [2, 0], '31': [2, 2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '69360.n5'}
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ec_torsion_growth • Show schema
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id: 3296563
{'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '69360.n5', 'torsion': [2, 4]}
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id: 3296562
{'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '69360.n5', 'torsion': [2, 4]}
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id: 3296564
{'degree': 4, 'field': [16, 0, 9, 0, 1], 'lmfdb_label': '69360.n5', 'torsion': [4, 4]}
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id: 3296565
{'degree': 4, 'field': [341, -32, 33, -2, 1], 'lmfdb_label': '69360.n5', 'torsion': [2, 8]}
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id: 3296569
{'degree': 8, 'field': [-250563, 0, -34391, 0, -1734, 0, 0, 0, 1], 'lmfdb_label': '69360.n5', 'torsion': [2, 6]}
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id: 3296568
{'degree': 8, 'field': [106, 412, -194, -404, 123, 92, -26, -4, 1], 'lmfdb_label': '69360.n5', 'torsion': [2, 8]}
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id: 3296567
{'degree': 8, 'field': [784, -560, 706, -272, 87, 56, -14, -4, 1], 'lmfdb_label': '69360.n5', 'torsion': [2, 8]}
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id: 3296566
{'degree': 8, 'field': [909, 390, -304, -162, 57, 26, -4, -4, 1], 'lmfdb_label': '69360.n5', 'torsion': [4, 8]}
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id: 3296574
{'degree': 16, 'field': [-31531, 214054, -38258, -273618, -37421, 154820, 28102, -48224, -10158, 10534, 1730, -1552, -166, 168, -4, -8, 1], 'lmfdb_label': '69360.n5', 'torsion': [2, 12]}
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id: 3296571
{'degree': 16, 'field': [15264, 65088, 154080, -358176, 826, 155652, 34482, -53884, -8815, 10604, 1694, -1540, -168, 168, -4, -8, 1], 'lmfdb_label': '69360.n5', 'torsion': [4, 8]}
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id: 3296570
{'degree': 16, 'field': [65536, 0, 0, 0, -12544, 0, 0, 0, 2145, 0, 0, 0, -49, 0, 0, 0, 1], 'lmfdb_label': '69360.n5', 'torsion': [4, 8]}
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id: 3296572
{'degree': 16, 'field': [69579801, 31623408, 34091238, 12661632, 28722268, 14985238, 137124, -156524, 229398, 24728, -3414, 3110, 663, -194, 72, -8, 1], 'lmfdb_label': '69360.n5', 'torsion': [2, 16]}
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id: 3296573
{'degree': 16, 'field': [7831307109, -3629926776, 4368283202, -1562385778, 1001578664, -282120080, 124339327, -27738584, 9204012, -1606836, 417285, -54872, 11299, -1022, 166, -8, 1], 'lmfdb_label': '69360.n5', 'torsion': [2, 12]}
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ec_localdata • Show schema
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id: 1678716
{'conductor': 69360, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '69360.n5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 1678717
{'conductor': 69360, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '69360.n5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1678718
{'conductor': 69360, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '69360.n5', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1678719
{'conductor': 69360, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '69360.n5', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2122812
{'adelic_gens': [[4065, 16, 4064, 17], [441, 3332, 1564, 3399], [1, 16, 0, 1], [341, 2176, 3536, 3537], [1, 8, 0, 1], [1, 16, 8, 129], [3839, 0, 0, 4079], [1, 0, 16, 1], [3605, 3604, 1972, 205], [1361, 3128, 884, 273]], 'adelic_image': '4080.768.13.?', 'conductor': 69360, 'lmfdb_label': '69360.n5', 'prime': 0}
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id: 289235
{'conductor': 69360, 'elladic_image': '8.48.0.44', 'lmfdb_label': '69360.n5', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 3549495
{'lmfdb_iso': '69360.n', 'p': 11, 'prec': 20, 'unit': 31577882277965738468, 'val': 2}
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id: 3549501
{'lmfdb_iso': '69360.n', 'p': 13, 'prec': 20, 'unit': 447446186857056473308, 'val': 2}
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id: 3549503
{'lmfdb_iso': '69360.n', 'p': 19, 'prec': 20, 'unit': 269148614449619696540489, 'val': 2}
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id: 3549500
{'lmfdb_iso': '69360.n', 'p': 29, 'prec': 20, 'unit': 5963259857538478852225968598, 'val': 2}
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id: 3549496
{'lmfdb_iso': '69360.n', 'p': 37, 'prec': 20, 'unit': 328444583066515380277510082995, 'val': 2}
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id: 3549498
{'lmfdb_iso': '69360.n', 'p': 41, 'prec': 20, 'unit': 728678789515122014756438419151, 'val': 2}
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id: 3549499
{'lmfdb_iso': '69360.n', 'p': 43, 'prec': 20, 'unit': 5053846069781129793889258381914, 'val': 2}
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id: 3549502
{'lmfdb_iso': '69360.n', 'p': 47, 'prec': 20, 'unit': 58610942932400716916683135758318, 'val': 2}
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id: 3549504
{'lmfdb_iso': '69360.n', 'p': 53, 'prec': 20, 'unit': 168810236407820113623982308547775, 'val': 2}
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id: 3549508
{'lmfdb_iso': '69360.n', 'p': 59, 'prec': 20, 'unit': 2581123726265594751680031760601758, 'val': 2}
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id: 3549509
{'lmfdb_iso': '69360.n', 'p': 61, 'prec': 20, 'unit': 6435656182382480623949477133275861, 'val': 2}
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id: 3549494
{'lmfdb_iso': '69360.n', 'p': 67, 'prec': 20, 'unit': 35547229740767177280487415489900499, 'val': 2}
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id: 3549497
{'lmfdb_iso': '69360.n', 'p': 71, 'prec': 20, 'unit': 144759738133112468080328179968608423, 'val': 2}
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id: 3549505
{'lmfdb_iso': '69360.n', 'p': 73, 'prec': 20, 'unit': 237426889007059484261622940413222566, 'val': 2}
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id: 3549506
{'lmfdb_iso': '69360.n', 'p': 83, 'prec': 20, 'unit': 853719497213697476150851866549502487, 'val': 2}
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id: 3549507
{'lmfdb_iso': '69360.n', 'p': 89, 'prec': 20, 'unit': 9297204562455818993028126230202213012, 'val': 2}
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id: 3549493
{'lmfdb_iso': '69360.n', 'p': 97, 'prec': 20, 'unit': 31108967545607954975981449789104290978, 'val': 2}