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ec_curvedata • Show schema
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{'Ciso': '2142i', 'Clabel': '2142i1', 'Cnumber': 1, 'abc_quality': 0.8065381791955314, 'absD': 520506, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 2856, 'ainvs': [1, -1, 0, 9, 31], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 2142, 'degree': 320, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.22144854462146777875247859994', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [103823, 714], 'lmfdb_iso': '2142.b', 'lmfdb_label': '2142.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 1, -1], 'min_quad_twist_disc': -3, 'modell_images': [], 'modm_images': ['2856.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.23794019537835994597084757198', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.77075468895552262445010121840', 'prec': 107}, 'szpiro_ratio': 2.6767569203455994, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, 1, -3, 0, 1, -1, 0, 3, 1, 0, 3, -1, 0, 1, -1, 0, -6, -3], 'aplist': [-1, 0, -3, 1, 1, 3, -1, -6, 2, -6, 0, 3, 0, 11, 0, 9, 4, -14, -7, -12, -1, -5, -3, 1, -13], 'class_deg': 1, 'class_size': 1, 'conductor': 2142, 'isogeny_matrix': [[1]], 'lmfdb_iso': '2142.b', 'trace_hash': 495716625279499494}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.5572120722223104978861730811', 'prec': 100}, 'conductor': 2142, 'gens': [[-1, 5, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.23794019537835994597084757198', 'prec': 103}], 'lmfdb_label': '2142.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.1312014867359221614702269030', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0283939925783860479177632133221131789', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-1, 5, 1511]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '2142.b1'}
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ec_torsion_growth • Show schema
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id: 108702
{'degree': 3, 'field': [-21, 9, -1, 1], 'lmfdb_label': '2142.b1', 'torsion': [2]}
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id: 108703
{'degree': 6, 'field': [2478, 1008, 739, -84, 10, 0, 1], 'lmfdb_label': '2142.b1', 'torsion': [2, 2]}
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id: 108704
{'degree': 8, 'field': [-731, -165, 1219, -674, 204, -26, 7, -3, 1], 'lmfdb_label': '2142.b1', 'torsion': [3]}
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id: 108705
{'degree': 12, 'field': [2982, 308, -19995, -50388, 1931, 3208, 1115, -2544, 647, -32, -7, -4, 1], 'lmfdb_label': '2142.b1', 'torsion': [4]}
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ec_localdata • Show schema
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id: 35589
{'conductor': 2142, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2142.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 35590
{'conductor': 2142, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '2142.b1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 35591
{'conductor': 2142, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2142.b1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 35592
{'conductor': 2142, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2142.b1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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{'adelic_gens': [[2143, 2, 2143, 3], [2855, 2, 2854, 3], [1429, 2, 1429, 3], [1, 0, 2, 1], [1, 2, 0, 1], [1, 1, 2855, 0], [409, 2, 409, 3], [953, 2, 953, 3], [2689, 2, 2689, 3]], 'adelic_image': '2856.2.0.?', 'conductor': 2142, 'lmfdb_label': '2142.b1', 'prime': 0}
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ec_padic • Show schema
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id: 63313
{'lmfdb_iso': '2142.b', 'p': 5, 'prec': 20, 'unit': 18765101903449, 'val': 1}
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id: 63320
{'lmfdb_iso': '2142.b', 'p': 11, 'prec': 20, 'unit': 217852323980287995301, 'val': -1}
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id: 63318
{'lmfdb_iso': '2142.b', 'p': 13, 'prec': 20, 'unit': 144687949720204365580, 'val': 1}
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id: 63321
{'lmfdb_iso': '2142.b', 'p': 19, 'prec': 20, 'unit': 82508628588506970963994, 'val': 1}
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id: 63323
{'lmfdb_iso': '2142.b', 'p': 23, 'prec': 20, 'unit': 10382356260413540204156548, 'val': 1}
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id: 63317
{'lmfdb_iso': '2142.b', 'p': 29, 'prec': 20, 'unit': 4191108725819469571341510012, 'val': 1}
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id: 63327
{'lmfdb_iso': '2142.b', 'p': 37, 'prec': 20, 'unit': 57061353707693247465484283043, 'val': 1}
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id: 63316
{'lmfdb_iso': '2142.b', 'p': 43, 'prec': 20, 'unit': 9169680527377323278814205333025, 'val': 1}
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id: 63322
{'lmfdb_iso': '2142.b', 'p': 53, 'prec': 20, 'unit': 139522598201641105921274757398769, 'val': 1}
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id: 63325
{'lmfdb_iso': '2142.b', 'p': 59, 'prec': 20, 'unit': 2553909773681362266099051980844816, 'val': 1}
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id: 63326
{'lmfdb_iso': '2142.b', 'p': 61, 'prec': 20, 'unit': 6931625942625097274610309505445599, 'val': 1}
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id: 63312
{'lmfdb_iso': '2142.b', 'p': 67, 'prec': 20, 'unit': 3847942390797470732952034566483534, 'val': 1}
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id: 63314
{'lmfdb_iso': '2142.b', 'p': 71, 'prec': 20, 'unit': 105378523562072311438129098173438506, 'val': 1}
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id: 63315
{'lmfdb_iso': '2142.b', 'p': 73, 'prec': 20, 'unit': 237737691445418004718557718695361200, 'val': 1}
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id: 63319
{'lmfdb_iso': '2142.b', 'p': 79, 'prec': 20, 'unit': 1076196656264773536826635265519807099, 'val': 1}
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id: 63311
{'lmfdb_iso': '2142.b', 'p': 83, 'prec': 20, 'unit': 1010920720362572568821038806672568271, 'val': 1}
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id: 63324
{'lmfdb_iso': '2142.b', 'p': 89, 'prec': 20, 'unit': 686137175740827539781279021614898088878, 'val': -1}
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id: 63310
{'lmfdb_iso': '2142.b', 'p': 97, 'prec': 20, 'unit': 51476330053558316237332515618820870635, 'val': 1}