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ec_curvedata • Show schema
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{'Ciso': '68400eq', 'Clabel': '68400eq4', 'Cnumber': 4, 'abc_quality': 1.0439330953430468, 'absD': 4308215040000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2280, 'ainvs': [0, 0, 0, -1772928075, 28733252512250], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 68400, 'degree': 17694720, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5346606690314618658193666853', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 158, 'isogeny_degrees': [1, 2, 4], 'jinv': [13209596798923694545921, 92340], 'lmfdb_iso': '68400.gc', 'lmfdb_label': '68400.gc1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -492480, 132819117], 'min_quad_twist_disc': 60, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '120.24.0.?', '152.24.0.?', '570.6.0.?', '1140.24.0.?', '2280.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '14.209574046842135690342674772', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4874883879204115234041322788', 'prec': 100}, 'szpiro_ratio': 6.781678717716068, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, -1, 0], 'aplist': [0, 0, 0, 4, 0, 6, 2, -1, -8, -2, 8, -10, -6, -8, 0, -2, -12, -2, -12, -8, -2, 16, 4, -6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 68400, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '68400.gc', 'trace_hash': 1247683402216479774}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00085081032586089839188062462841', 'prec': 113}, 'conductor': 68400, 'gens': [[6415751, 8826231526, 13]], 'heights': [{'__RealLiteral__': 0, 'data': '14.209574046842135690342674772', 'prec': 100}], 'lmfdb_label': '68400.gc1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14627360603769581741032844364', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.3139425443650144356641015713418585836', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[24295, 4050, 1]], 'xcoord_integral_points': [24295, 24310]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': 'a', '7': [3, 0], '11': [1, 3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '68400.gc1'}
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ec_torsion_growth • Show schema
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id: 3253981
{'degree': 2, 'field': [-71, -1, 1], 'lmfdb_label': '68400.gc1', 'torsion': [2, 4]}
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id: 3253982
{'degree': 4, 'field': [1140, 0, -60, 0, 1], 'lmfdb_label': '68400.gc1', 'torsion': [8]}
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id: 3253986
{'degree': 8, 'field': [-116846, -158300, -24068, 4874, 650, -124, -35, -2, 1], 'lmfdb_label': '68400.gc1', 'torsion': [12]}
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id: 3253985
{'degree': 8, 'field': [1, 0, -72, 0, 158, 0, -72, 0, 1], 'lmfdb_label': '68400.gc1', 'torsion': [2, 8]}
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id: 3253984
{'degree': 8, 'field': [7996, -14416, 15022, -1168, 475, 128, -38, -4, 1], 'lmfdb_label': '68400.gc1', 'torsion': [2, 8]}
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id: 3253983
{'degree': 8, 'field': [81225, 0, 0, 0, 81795, 0, 0, 0, 1], 'lmfdb_label': '68400.gc1', 'torsion': [4, 4]}
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id: 3253988
{'degree': 16, 'field': [150544, 0, -30857872, 0, -8636480, 0, -5416504, 0, -1680380, 0, -150136, 0, -1187, 0, 50, 0, 1], 'lmfdb_label': '68400.gc1', 'torsion': [2, 12]}
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id: 3253987
{'degree': 16, 'field': [21485449857600, 0, 2276738049600, 0, -75098035800, 0, -6044439600, 0, 409632780, 0, -9375360, 0, 105510, 0, -540, 0, 1], 'lmfdb_label': '68400.gc1', 'torsion': [16]}
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ec_localdata • Show schema
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id: 1654837
{'conductor': 68400, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '68400.gc1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 1654838
{'conductor': 68400, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '68400.gc1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 1654839
{'conductor': 68400, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '68400.gc1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 1654840
{'conductor': 68400, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '68400.gc1', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2116556
{'adelic_gens': [[1688, 3, 485, 2], [1421, 1424, 262, 1419], [1, 0, 8, 1], [1, 8, 0, 1], [859, 858, 298, 1435], [1, 4, 4, 17], [452, 2279, 889, 2274], [1516, 2279, 737, 2274], [7, 6, 2274, 2275], [2273, 8, 2272, 9]], 'adelic_image': '2280.48.0.?', 'conductor': 68400, 'lmfdb_label': '68400.gc1', 'prime': 0}
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id: 285596
{'conductor': 68400, 'elladic_image': '4.12.0.7', 'lmfdb_label': '68400.gc1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 3497526
{'lmfdb_iso': '68400.gc', 'p': 7, 'prec': 20, 'unit': 1174145154875872, 'val': 2}
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id: 3497530
{'lmfdb_iso': '68400.gc', 'p': 13, 'prec': 20, 'unit': 607776352244281539328, 'val': 1}
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id: 3497532
{'lmfdb_iso': '68400.gc', 'p': 17, 'prec': 20, 'unit': 191227320994609637529983, 'val': 1}
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id: 3497536
{'lmfdb_iso': '68400.gc', 'p': 23, 'prec': 20, 'unit': 71458652084095816334824379, 'val': 1}
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id: 3497529
{'lmfdb_iso': '68400.gc', 'p': 29, 'prec': 20, 'unit': 2026187761740373809376735722, 'val': 1}
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id: 3497541
{'lmfdb_iso': '68400.gc', 'p': 31, 'prec': 20, 'unit': 14917527597772369127680856229, 'val': 1}
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id: 3497525
{'lmfdb_iso': '68400.gc', 'p': 37, 'prec': 20, 'unit': 314429518724629699297355160170, 'val': 1}
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id: 3497527
{'lmfdb_iso': '68400.gc', 'p': 41, 'prec': 20, 'unit': 3215225656365368391620834226195, 'val': 1}
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id: 3497528
{'lmfdb_iso': '68400.gc', 'p': 43, 'prec': 20, 'unit': 8451269052904421928968781803965, 'val': 1}
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id: 3497534
{'lmfdb_iso': '68400.gc', 'p': 53, 'prec': 20, 'unit': 377882157451579595875588875527402, 'val': 1}
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id: 3497539
{'lmfdb_iso': '68400.gc', 'p': 59, 'prec': 20, 'unit': 4040923365811026369662970482629511, 'val': 1}
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id: 3497540
{'lmfdb_iso': '68400.gc', 'p': 61, 'prec': 20, 'unit': 6406021425636011607626345322303171, 'val': 1}
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id: 3497524
{'lmfdb_iso': '68400.gc', 'p': 67, 'prec': 20, 'unit': 6770395636734820019570214310803178, 'val': 1}
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id: 3497538
{'lmfdb_iso': '68400.gc', 'p': 71, 'prec': 20, 'unit': 110346203465122397297063997665254170, 'val': 1}
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id: 3497535
{'lmfdb_iso': '68400.gc', 'p': 73, 'prec': 20, 'unit': 123252395567116281591455728513879130, 'val': 1}
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id: 3497531
{'lmfdb_iso': '68400.gc', 'p': 79, 'prec': 20, 'unit': 789199229800269906236007871830225306, 'val': 1}
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id: 3497533
{'lmfdb_iso': '68400.gc', 'p': 83, 'prec': 20, 'unit': 646688939801558729859876840288317335, 'val': 1}
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id: 3497537
{'lmfdb_iso': '68400.gc', 'p': 89, 'prec': 20, 'unit': 3191982930615519694939978965983208471, 'val': 1}
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id: 3497523
{'lmfdb_iso': '68400.gc', 'p': 97, 'prec': 20, 'unit': 38484726142309943662592307713540832714, 'val': 1}