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ec_curvedata • Show schema
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{'Ciso': '16830t', 'Clabel': '16830t5', 'Cnumber': 5, 'abc_quality': 0.9918812413886786, 'absD': 276896064650926050, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 8976, 'ainvs': [1, -1, 0, -2629260, 1641423766], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 16830, 'degree': 393216, 'elladic_images': ['8.24.0.100'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3644738720043001048141057163', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [2757381641970898311361, 379829992662450], 'lmfdb_iso': '16830.l', 'lmfdb_label': '16830.l1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -292140, -60890853], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.r.1', '12.12.0-4.c.1.1', '24.48.0-8.r.1.6', '88.48.0.?', '264.96.0.?', '272.48.0.?', '816.96.0.?', '2992.96.0.?', '8976.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.1142022360353461016818747865', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8151677276702452591164830978', 'prec': 100}, 'szpiro_ratio': 5.750766842588965, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, 1, -1, 0, 0, -1, 0, 1, 1, 0, 6, 0, 0, 1, -1, 0, 4, -1], 'aplist': [-1, 0, -1, 0, 1, 6, -1, 4, 0, -6, 0, -2, 6, -4, 8, -14, -12, -2, 4, 0, -6, -8, -4, 6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 16830, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '16830.l', 'trace_hash': 676997206436535951}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0088357636349982907283147693517', 'prec': 110}, 'conductor': 16830, 'gens': [[947, -127, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.1142022360353461016818747865', 'prec': 100}], 'lmfdb_label': '16830.l1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.29809818224992151881242685349', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.7133521028831108534846541573889091277', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[3779, -3779, 2]], 'xcoord_integral_points': [947, 21825]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [6, 0], '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '16830.l1'}
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ec_torsion_growth • Show schema
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id: 862763
{'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [4]}
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id: 862762
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [4]}
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id: 862761
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [2, 2]}
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id: 862764
{'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [2, 4]}
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id: 862766
{'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [8]}
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id: 862765
{'degree': 4, 'field': [121, 0, -44, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [8]}
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id: 862770
{'degree': 8, 'field': [-381404, 42989, -45098, 4217, -2105, -7, 7, -4, 1], 'lmfdb_label': '16830.l1', 'torsion': [6]}
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id: 862769
{'degree': 8, 'field': [-18, 108, -162, 0, 103, -12, -22, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [2, 8]}
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id: 862768
{'degree': 8, 'field': [2500, 0, 0, 0, -50, 0, 0, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [8]}
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id: 862767
{'degree': 8, 'field': [36602500, 0, 0, 0, 6050, 0, 0, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [2, 4]}
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id: 862772
{'degree': 16, 'field': [390625, 0, -312500, 0, 125000, 0, -75000, 0, 29375, 0, -3000, 0, 200, 0, -20, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [2, 8]}
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id: 862776
{'degree': 16, 'field': [34503876, 0, 19633581, 0, 3857722, 0, 389883, 0, 19995, 0, -3833, 0, -453, 0, -6, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [12]}
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id: 862777
{'degree': 16, 'field': [56250000, 0, 21038544, 0, -3176060, 0, -2008128, 0, 305592, 0, -10300, 0, 960, 0, -48, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [12]}
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id: 862775
{'degree': 16, 'field': [3517438864, 0, -4265089936, 0, 1046643940, 0, -18327232, 0, 1734520, 0, 61868, 0, -320, 0, -16, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [2, 6]}
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id: 862774
{'degree': 16, 'field': [124493242896, 0, 27665165088, 0, 17977699872, 0, 1081559952, 0, 156127752, 0, 1820808, 0, 50952, 0, 132, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [16]}
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id: 862771
{'degree': 16, 'field': [83733937890625, 0, -6089740937500, 0, 221445125000, 0, -12078825000, 0, 430079375, 0, -3993000, 0, 24200, 0, -220, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [4, 4]}
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id: 862773
{'degree': 16, 'field': [67578079396626562500, 0, -3857673526492500000, 0, 60758647716937500, 0, -450644589450000, 0, 1841110363125, 0, -4345110000, 0, 5808000, 0, -3960, 0, 1], 'lmfdb_label': '16830.l1', 'torsion': [16]}
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ec_localdata • Show schema
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id: 374831
{'conductor': 16830, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '16830.l1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 374832
{'conductor': 16830, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '16830.l1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 374833
{'conductor': 16830, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '16830.l1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 374834
{'conductor': 16830, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '16830.l1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 374835
{'conductor': 16830, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '16830.l1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1776236
{'adelic_gens': [[5971, 8960, 3248, 315], [8961, 16, 8960, 17], [829, 16, 3008, 8661], [1, 16, 0, 1], [2252, 2249, 4491, 4490], [1057, 16, 8456, 129], [1, 0, 16, 1], [5, 4, 8972, 8973], [5623, 16, 7598, 1929], [15, 2, 8878, 8963]], 'adelic_image': '8976.192.1.?', 'conductor': 16830, 'lmfdb_label': '16830.l1', 'prime': 0}
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id: 79126
{'conductor': 16830, 'elladic_image': '8.24.0.100', 'lmfdb_label': '16830.l1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 765736
{'lmfdb_iso': '16830.l', 'p': 13, 'prec': 20, 'unit': 1031691893920260429240, 'val': 1}
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id: 765739
{'lmfdb_iso': '16830.l', 'p': 19, 'prec': 20, 'unit': 747704632240816569946956, 'val': 1}
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id: 765735
{'lmfdb_iso': '16830.l', 'p': 29, 'prec': 20, 'unit': 4374055162925590180386742823, 'val': 1}
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id: 765732
{'lmfdb_iso': '16830.l', 'p': 37, 'prec': 20, 'unit': 137912721577481600751851027589, 'val': 1}
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id: 765733
{'lmfdb_iso': '16830.l', 'p': 41, 'prec': 20, 'unit': 711405631871726812257175996960, 'val': 1}
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id: 765734
{'lmfdb_iso': '16830.l', 'p': 43, 'prec': 20, 'unit': 3869323768262185721638658801841, 'val': 1}
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id: 765743
{'lmfdb_iso': '16830.l', 'p': 47, 'prec': 20, 'unit': 31516929875440907850661063839208, 'val': 1}
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id: 765740
{'lmfdb_iso': '16830.l', 'p': 53, 'prec': 20, 'unit': 330993882806578990181380456702065, 'val': 1}
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id: 765738
{'lmfdb_iso': '16830.l', 'p': 59, 'prec': 20, 'unit': 1679627492674660822829590132032191, 'val': 1}
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id: 765744
{'lmfdb_iso': '16830.l', 'p': 61, 'prec': 20, 'unit': 2862151571965726229117394433712205, 'val': 1}
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id: 765731
{'lmfdb_iso': '16830.l', 'p': 67, 'prec': 20, 'unit': 42507850363180130474562396067495943, 'val': 1}
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id: 765741
{'lmfdb_iso': '16830.l', 'p': 73, 'prec': 20, 'unit': 73125043244267474615546868676529442, 'val': 1}
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id: 765737
{'lmfdb_iso': '16830.l', 'p': 79, 'prec': 20, 'unit': 329450304822853710572738386343734689, 'val': 1}
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id: 765730
{'lmfdb_iso': '16830.l', 'p': 83, 'prec': 20, 'unit': 2858537499939903983008891962208880339, 'val': 1}
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id: 765742
{'lmfdb_iso': '16830.l', 'p': 89, 'prec': 20, 'unit': 7547599274456797731956560096763741364, 'val': 1}
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id: 765729
{'lmfdb_iso': '16830.l', 'p': 97, 'prec': 20, 'unit': 19544825010629408635503357615741875833, 'val': 1}