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ec_curvedata • Show schema
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{'Ciso': '41001a', 'Clabel': '41001a1', 'Cnumber': 1, 'abc_quality': 0.7803866046826238, 'absD': 123003, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 27334, 'ainvs': [0, -1, 1, -134, 644], 'analytic_rank': 3, 'bad_primes': [3, 79, 173], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 41001, 'degree': 16640, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.066367586128970887836797320313', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [-268086587392, 123003], 'lmfdb_iso': '41001.a', 'lmfdb_label': '41001.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -134, 644], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['27334.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 30, 'optimality': 1, 'potential_good_reduction': False, 'rank': 3, 'regulator': {'__RealLiteral__': 0, 'data': '0.71611791151562589038088049644', 'prec': 103}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.066367586128970887836797320313', 'prec': 110}, 'szpiro_ratio': 2.4775912738074632, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, -2, -1, 2, -2, 2, -3, 0, 1, 4, -6, -2, -2, 6, 2, -4, -7, -2, 2, -4], 'aplist': [-2, -1, -2, -3, -6, -2, -7, 2, -8, -8, -11, -10, -2, -8, -6, 3, 7, -6, 5, 5, -10, 1, -11, -15, -10], 'class_deg': 1, 'class_size': 1, 'conductor': 41001, 'isogeny_matrix': [[1]], 'lmfdb_iso': '41001.a', 'trace_hash': 26603696719307893}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.1419475388945627650916759134', 'prec': 100}, 'conductor': 41001, 'gens': [[7, 0, 1], [8, 4, 1], [6, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.74016120800296992714627199073', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.77409229463442667454229219406', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.3136200988739581000412152571', 'prec': 100}], 'lmfdb_label': '41001.a1', 'ngens': 3, 'rank_bounds': [3, 3], 'real_period': {'__RealLiteral__': 0, 'data': '3.2573504794166676680161259957', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6652940447885735804655137543308161035', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [-13, -12, -7, 2, 4, 6, 7, 8, 11, 13, 29, 42, 46, 251, 602]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 8, 0], '3': [3, 0], '5': [3, 0], '7': [5, 0], '11': [3, 0], '13': [3, 0], '17': [3, 0], '19': [3, 0], '23': [3, 0], '29': [3, 0], '31': [3, 0], '37': [3, 0], '41': [3, 0], '43': [3, 0], '47': [3, 0], '79': [4, 0], '173': [4, 0]}, 'iwp0': 0, 'lmfdb_label': '41001.a1'}
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ec_torsion_growth • Show schema
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id: 2017757
{'degree': 3, 'field': [-282, -58, 0, 1], 'lmfdb_label': '41001.a1', 'torsion': [2]}
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id: 2017758
{'degree': 6, 'field': [209439, -83178, 14259, -592, 5, -2, 1], 'lmfdb_label': '41001.a1', 'torsion': [2, 2]}
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id: 2017759
{'degree': 8, 'field': [-8419, 29113, -29230, 233, -113, -7, 7, -4, 1], 'lmfdb_label': '41001.a1', 'torsion': [3]}
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id: 2017760
{'degree': 12, 'field': [199654065, -395404692, 203007902, -9013828, 1949447, -433008, 253672, -10144, 2723, -132, 82, -4, 1], 'lmfdb_label': '41001.a1', 'torsion': [4]}
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ec_localdata • Show schema
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id: 972666
{'conductor': 41001, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '41001.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 972667
{'conductor': 41001, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '41001.a1', 'prime': 79, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 972668
{'conductor': 41001, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '41001.a1', 'prime': 173, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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{'adelic_gens': [[1, 1, 27333, 0], [27333, 2, 27332, 3], [20069, 2, 20069, 3], [1, 0, 2, 1], [1, 2, 0, 1], [3635, 2, 3635, 3]], 'adelic_image': '27334.2.0.?', 'conductor': 41001, 'lmfdb_label': '41001.a1', 'prime': 0}
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ec_padic • Show schema
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id: 2035519
{'lmfdb_iso': '41001.a', 'p': 5, 'prec': 20, 'unit': 11733182036259, 'val': 3}
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id: 2035520
{'lmfdb_iso': '41001.a', 'p': 7, 'prec': 20, 'unit': 449969102970955, 'val': 4}
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id: 2035521
{'lmfdb_iso': '41001.a', 'p': 11, 'prec': 20, 'unit': 45011693376638121778, 'val': 3}
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id: 2035522
{'lmfdb_iso': '41001.a', 'p': 13, 'prec': 20, 'unit': 116900616440168412479, 'val': 3}
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id: 2035523
{'lmfdb_iso': '41001.a', 'p': 17, 'prec': 20, 'unit': 113287721750712872954272, 'val': 3}
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id: 2035524
{'lmfdb_iso': '41001.a', 'p': 19, 'prec': 20, 'unit': 96000240723036757847720, 'val': 3}
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id: 2035525
{'lmfdb_iso': '41001.a', 'p': 23, 'prec': 20, 'unit': 27189310857540486321914448, 'val': 3}
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id: 2035526
{'lmfdb_iso': '41001.a', 'p': 29, 'prec': 20, 'unit': 4959476135125123210823685937, 'val': 3}
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id: 2035527
{'lmfdb_iso': '41001.a', 'p': 31, 'prec': 20, 'unit': 12351290151307595753162593919, 'val': 3}
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id: 2035528
{'lmfdb_iso': '41001.a', 'p': 37, 'prec': 20, 'unit': 225011421941461377611794799336, 'val': 3}
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id: 2035529
{'lmfdb_iso': '41001.a', 'p': 41, 'prec': 20, 'unit': 3965837718019195727849376528823, 'val': 3}
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id: 2035530
{'lmfdb_iso': '41001.a', 'p': 43, 'prec': 20, 'unit': 8985024293437108775495940201447, 'val': 3}
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id: 2035531
{'lmfdb_iso': '41001.a', 'p': 47, 'prec': 20, 'unit': 45014427127597657511239810390722, 'val': 3}
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id: 2035532
{'lmfdb_iso': '41001.a', 'p': 53, 'prec': 20, 'unit': 467213751396672881754985698501807, 'val': 3}
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id: 2035533
{'lmfdb_iso': '41001.a', 'p': 59, 'prec': 20, 'unit': 2269603629148984331742821768083896, 'val': 3}
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id: 2035534
{'lmfdb_iso': '41001.a', 'p': 61, 'prec': 20, 'unit': 6648696121454514486471461005951414, 'val': 3}
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id: 2035535
{'lmfdb_iso': '41001.a', 'p': 67, 'prec': 20, 'unit': 48870522342111556604346328746782251, 'val': 3}
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id: 2035536
{'lmfdb_iso': '41001.a', 'p': 71, 'prec': 20, 'unit': 39684479205355120221629617861130999, 'val': 3}
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id: 2035537
{'lmfdb_iso': '41001.a', 'p': 73, 'prec': 20, 'unit': 77698671694681430860280273686099009, 'val': 3}
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id: 2035538
{'lmfdb_iso': '41001.a', 'p': 83, 'prec': 20, 'unit': 1093809327663123444781440710239623306, 'val': 3}
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id: 2035539
{'lmfdb_iso': '41001.a', 'p': 89, 'prec': 20, 'unit': 459794685150750641470491279621699672, 'val': 3}
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id: 2035540
{'lmfdb_iso': '41001.a', 'p': 97, 'prec': 20, 'unit': 33529689168068045381551795061241841768, 'val': 3}