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ec_curvedata • Show schema
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{'Ciso': '209814bv', 'Clabel': '209814bv3', 'Cnumber': 3, 'abc_quality': 0.96548780150265, 'absD': 2804868770121323045625474, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1496, 'ainvs': [1, 0, 1, -67735682, 198862833530], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 209814, 'degree': 53084160, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4338136649598371772086792570', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 37, 'isogeny_degrees': [1, 2, 4], 'jinv': [803760366578833, 65593817586], 'lmfdb_iso': '209814.bl', 'lmfdb_label': '209814.bl1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1937, -31219], 'min_quad_twist_disc': -187, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '44.12.0-4.c.1.1', '88.24.0.?', '136.24.0.?', '1496.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '23.042272898962816922121689431', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 34969], [3, 4, 69938], [11, 72, 1734], [17, 162, 726]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.81825935653254386505294015908', 'prec': 103}, 'szpiro_ratio': 5.362093921277024, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 1, 1, -2, -1, 4, -1, 1, 2, 0, 1, 2, -4, -2, 1, 0, -1, -4, -2], 'aplist': [-1, 1, -2, 4, 0, 2, 0, -4, 4, -6, 4, -2, 10, -4, -8, 6, -4, -6, 12, 12, 2, 4, 4, 10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 209814, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '209814.bl', 'trace_hash': 2199669218815840275}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0010409439534750477057699758794', 'prec': 110}, 'conductor': 209814, 'gens': [[291373588047, 78172198041866231, 6278]], 'heights': [{'__RealLiteral__': 0, 'data': '23.042272898962816922121689431', 'prec': 100}], 'lmfdb_label': '209814.bl1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.078712982676104519846008177320', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.2549041100565315262968086901554608124', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[23063, -23067, 2]], 'xcoord_integral_points': []}
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lmfdb_label 209814.bl1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 9171818
{'degree': 2, 'field': [-374, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [4]}
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id: 9171816
{'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 2]}
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id: 9171817
{'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [4]}
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id: 9171819
{'degree': 4, 'field': [529, 0, -90, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 4]}
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id: 9171821
{'degree': 8, 'field': [-14522, 30078, -14465, -4870, 3581, 250, -123, -2, 1], 'lmfdb_label': '209814.bl1', 'torsion': [8]}
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id: 9171822
{'degree': 8, 'field': [68644, 0, 7824, 0, 902, 0, 48, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [8]}
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id: 9171820
{'degree': 8, 'field': [1489689, -39276, 36882, 4776, -2357, -40, 18, -4, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 4]}
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id: 9171823
{'degree': 8, 'field': [2567151, 2608425, 776349, 70470, 1332, 936, 73, -1, 1], 'lmfdb_label': '209814.bl1', 'torsion': [6]}
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id: 9171826
{'degree': 16, 'field': [668286, 1020780, -3377670, -5536524, 3275395, 5810228, -1613790, -2126428, 497565, 305572, -70794, -18644, 4377, 476, -114, -4, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 8]}
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id: 9171825
{'degree': 16, 'field': [5564900, 399520, 1681216, -3129248, 718296, -874320, 215024, -100288, 122248, -17856, 25360, -1520, 2068, -56, 72, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 8]}
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id: 9171828
{'degree': 16, 'field': [7750656, 0, -25850619, 0, -2521494, 0, -781613, 0, -42373, 0, 223, 0, 607, 0, -22, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [12]}
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id: 9171827
{'degree': 16, 'field': [780420096, 0, -571162752, 0, 63137664, 0, -6297952, 0, 388976, 0, -44632, 0, 1660, 0, -68, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [2, 6]}
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id: 9171824
{'degree': 16, 'field': [9188947881, 0, 1822692780, 0, 242132670, 0, 10260000, 0, 331231, 0, 5080, 0, 1410, 0, -20, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [4, 4]}
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id: 9171829
{'degree': 16, 'field': [641485661184, 0, 357820563744, 0, 78325769124, 0, 7041726288, 0, 198258804, 0, -3467988, 0, -47612, 0, -22, 0, 1], 'lmfdb_label': '209814.bl1', 'torsion': [12]}
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ec_localdata • Show schema
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id: 5199746
{'conductor': 209814, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '209814.bl1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 5199747
{'conductor': 209814, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '209814.bl1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 5199748
{'conductor': 209814, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '209814.bl1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 5199749
{'conductor': 209814, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '209814.bl1', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 3006535
{'adelic_gens': [[331, 1276, 506, 397], [7, 6, 1490, 1491], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [496, 297, 451, 166], [384, 1221, 1243, 406], [1087, 0, 0, 1495], [1489, 8, 1488, 9]], 'adelic_image': '1496.48.0.?', 'conductor': 209814, 'lmfdb_label': '209814.bl1', 'prime': 0}
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id: 774312
{'conductor': 209814, 'elladic_image': '8.12.0.11', 'lmfdb_label': '209814.bl1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 209814.bl does not appear in ec_padic