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ec_curvedata • Show schema
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{'Ciso': '271062x', 'Clabel': '271062x2', 'Cnumber': 2, 'abc_quality': 1.0214304364495703, 'absD': 5720094583430029795029312, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 4884, 'ainvs': [1, -1, 1, -164830595, 806398039235], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 37], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 271062, 'degree': 75644928, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5632125896146212265336418605', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [264788619837198625, 3058196150592], 'lmfdb_iso': '271062.x', 'lmfdb_label': '271062.x3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -13378, -590716], 'min_quad_twist_disc': -111, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.24.0-6.a.1.3', '74.6.0.?', '111.8.0.?', '132.48.0.?', '222.48.0.?', '4884.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0907939194524104767470217468', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2084474889584541586519714065', 'prec': 100}, 'szpiro_ratio': 5.465573723622741, '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, 0, 0, -4, 1, 0, 0, -1, 0, 4, -4, 0, 1, -6, 0, -2, 0], 'aplist': [1, 0, 0, -4, -1, 4, -6, -2, -6, -6, 4, 0, -6, -2, 0, -6, 6, -8, -4, 12, 2, -2, 12, 0, -2], 'class_deg': 6, 'class_size': 4, 'conductor': 271062, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '271062.x', 'trace_hash': 1287163230308564350}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00080358693822641581521454823392', 'prec': 113}, 'conductor': 271062, 'gens': [[-12219, -991892, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0907939194524104767470217468', 'prec': 100}], 'lmfdb_label': '271062.x3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.076234153491725968704882083225', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.6507154196049152915911588777979030457', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[32043, -32047, 2]], 'xcoord_integral_points': [-12219]}
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lmfdb_label 271062.x3 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 11581073
{'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '271062.x3', 'torsion': [2, 2]}
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id: 11581074
{'degree': 2, 'field': [28, -1, 1], 'lmfdb_label': '271062.x3', 'torsion': [6]}
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id: 11581075
{'degree': 4, 'field': [37, 0, -26, 0, 1], 'lmfdb_label': '271062.x3', 'torsion': [4]}
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id: 11581076
{'degree': 4, 'field': [81, 9, 10, -1, 1], 'lmfdb_label': '271062.x3', 'torsion': [2, 6]}
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id: 11581077
{'degree': 6, 'field': [-37, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '271062.x3', 'torsion': [2, 6]}
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id: 11581080
{'degree': 8, 'field': [2304, 0, 528, 0, 184, 0, -11, 0, 1], 'lmfdb_label': '271062.x3', 'torsion': [12]}
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id: 11581079
{'degree': 8, 'field': [15129, 0, -7923, 0, 1144, 0, -59, 0, 1], 'lmfdb_label': '271062.x3', 'torsion': [2, 4]}
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id: 11581078
{'degree': 8, 'field': [2125684, -652808, 90116, -912, -2845, 438, -1, -2, 1], 'lmfdb_label': '271062.x3', 'torsion': [2, 4]}
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id: 11581081
{'degree': 12, 'field': [1296, 216, 576, -1530, 645, 96, 67, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '271062.x3', 'torsion': [6, 6]}
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id: 11581082
{'degree': 16, 'field': [-2989986, -295804056, 179931492, 116919234, -35465525, -20043910, -3267916, 1191528, 682225, 14596, -30980, -3878, 1477, 282, -52, -4, 1], 'lmfdb_label': '271062.x3', 'torsion': [8]}
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id: 11581084
{'degree': 16, 'field': [1679616, 0, -513216, 0, 36288, 0, -8316, 0, 2997, 0, -231, 0, 28, 0, -11, 0, 1], 'lmfdb_label': '271062.x3', 'torsion': [2, 12]}
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id: 11581083
{'degree': 16, 'field': [249513616, 273839456, 167534576, 99971168, 48514260, 16102568, 6282108, 2280896, 180265, 31282, 43287, 886, -126, 310, 5, -2, 1], 'lmfdb_label': '271062.x3', 'torsion': [2, 12]}
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id: 11581085
{'degree': 18, 'field': [893717303065344, -629755422914304, 249656961081024, -68440046943312, 16004627248320, -2150383543056, 251350578288, -4546144980, -4197853512, 504855789, -55956591, -818676, 1832596, -39954, 19878, 272, 204, -3, 1], 'lmfdb_label': '271062.x3', 'torsion': [18]}
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ec_localdata • Show schema
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id: 6717889
{'conductor': 271062, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '271062.x3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
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id: 6717890
{'conductor': 271062, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '271062.x3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 6717891
{'conductor': 271062, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '271062.x3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 6717892
{'conductor': 271062, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '271062.x3', 'prime': 37, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 3377850
{'adelic_gens': [[11, 2, 4834, 4875], [4873, 12, 4872, 13], [1, 0, 12, 1], [3247, 4882, 3252, 4883], [1, 6, 6, 37], [1333, 12, 3114, 73], [1, 12, 0, 1], [4346, 4881, 4383, 8], [2859, 4480, 2822, 4469]], 'adelic_image': '4884.96.1.?', 'conductor': 271062, 'lmfdb_label': '271062.x3', 'prime': 0}
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id: 968892
{'conductor': 271062, 'elladic_image': '2.3.0.1', 'lmfdb_label': '271062.x3', 'modell_image': '2B', 'prime': 2}
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id: 968893
{'conductor': 271062, 'elladic_image': '3.4.0.1', 'lmfdb_label': '271062.x3', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 271062.x does not appear in ec_padic