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ec_curvedata • Show schema
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{'Ciso': '207214r', 'Clabel': '207214r3', 'Cnumber': 3, 'abc_quality': 0.9764068945931376, 'absD': 77841564097701078824735614, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 392616, 'ainvs': [1, 1, 0, -575535809, 5297209642831], 'analytic_rank': 2, 'bad_primes': [2, 7, 19, 41], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 207214, 'degree': 91445760, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8282157077709080815713804812', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 4, 'isogeny_degrees': [1, 3, 9], 'jinv': [448145621407159343029153, 1654588296427078894], 'lmfdb_iso': '207214.e', 'lmfdb_label': '207214.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1594282, -772468394], 'min_quad_twist_disc': -19, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '57.8.0-3.a.1.2', '171.24.0.?', '1197.72.0.?', '2296.2.0.?', '6888.8.0.?', '20664.24.1.?', '130872.16.0.?', '392616.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '3.2931895066951869996469021625', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.3559962181876878515668667653', 'prec': 100}, 'szpiro_ratio': 5.8919246597392245, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, -1, 1, -3, 1, 1, -1, -2, 3, 0, -1, 4, -1, 3, 1, 3, 2, 0, -3], 'aplist': [-1, -1, -3, 1, 0, 4, 3, 0, -6, 3, -5, -2, 1, -1, 0, -9, 0, -1, -14, -15, 2, 1, -6, -15, 1], 'class_deg': 9, 'class_size': 3, 'conductor': 207214, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '207214.e', 'trace_hash': 227250119946375885}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00047299231567155854831041053784', 'prec': 113}, 'conductor': 207214, 'gens': [[12899, 134160, 1], [627175, 159538181, 6]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2374971381201603400115610030', 'prec': 100}, {'__RealLiteral__': 0, 'data': '2.7733132549041474985974771581', 'prec': 100}], 'lmfdb_label': '207214.e1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.061367181439154365155039597923', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.2753752869517807850290851253737612783', 'prec': 130}, 'tamagawa_product': 36, 'torsion_generators': [], 'xcoord_integral_points': [8225, 12899, 44667, 47913]}
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lmfdb_label 207214.e1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 9062757
{'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '207214.e1', 'torsion': [3]}
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id: 9062758
{'degree': 3, 'field': [-14, -14, -1, 1], 'lmfdb_label': '207214.e1', 'torsion': [2]}
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id: 9062759
{'degree': 6, 'field': [8, -8, -94, 144, -47, -2, 1], 'lmfdb_label': '207214.e1', 'torsion': [2, 2]}
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id: 9062762
{'degree': 6, 'field': [196, 798, 784, 85, -71, -1, 1], 'lmfdb_label': '207214.e1', 'torsion': [6]}
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id: 9062760
{'degree': 6, 'field': [3724, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '207214.e1', 'torsion': [3]}
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id: 9062761
{'degree': 6, 'field': [215992, 189924, 33516, -931, -399, 0, 1], 'lmfdb_label': '207214.e1', 'torsion': [9]}
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id: 9062763
{'degree': 12, 'field': [-21731116, -38633232, 17254376, 4549872, -3664836, 353128, 47756, -5856, -2057, 424, -8, -4, 1], 'lmfdb_label': '207214.e1', 'torsion': [4]}
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id: 9062764
{'degree': 12, 'field': [13875625, -22350, -55839, 148910, -55770, -22470, 7589, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '207214.e1', 'torsion': [3, 3]}
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id: 9062765
{'degree': 12, 'field': [15253504, 0, 0, -476672, 0, 0, 18608, 0, 0, -244, 0, 0, 1], 'lmfdb_label': '207214.e1', 'torsion': [9]}
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id: 9062766
{'degree': 12, 'field': [27814432, 2349088, -14294580, -781744, 2633716, 91948, -227355, -5042, 9623, 144, -181, -2, 1], 'lmfdb_label': '207214.e1', 'torsion': [2, 6]}
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id: 9062768
{'degree': 18, 'field': [-10627202062502648, -24280185034229208, -15360459108901284, -1541949965365684, 1675175083005354, 560996130837366, 21496053541809, -14149289172039, -1582197092175, 130666043256, 23886473226, -455910315, -170301256, -108429, 647319, 3907, -1266, -6, 1], 'lmfdb_label': '207214.e1', 'torsion': [18]}
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id: 9062767
{'degree': 18, 'field': [202759532752, -165457635168, 106354427088, -25879476224, 5613318480, 437349696, 256148872, 19152336, 5531316, 7253960, 2101008, -33264, -46227, -5886, 2535, 316, -69, -6, 1], 'lmfdb_label': '207214.e1', 'torsion': [6]}
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ec_localdata • Show schema
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id: 5132756
{'conductor': 207214, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '207214.e1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 5132757
{'conductor': 207214, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '207214.e1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 5132758
{'conductor': 207214, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '207214.e1', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 5132759
{'conductor': 207214, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '207214.e1', 'prime': 41, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
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ec_galrep • Show schema
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id: 2990152
{'adelic_gens': [[1, 18, 0, 1], [19153, 18, 172377, 163], [1, 18, 10, 181], [10, 9, 81, 73], [98155, 196326, 0, 141779], [196309, 18, 196317, 163], [392599, 18, 392598, 19], [168277, 18, 336897, 511], [1, 0, 18, 1], [294463, 18, 294471, 163], [82643, 392598, 310410, 623]], 'adelic_image': '392616.144.3.?', 'conductor': 207214, 'lmfdb_label': '207214.e1', 'prime': 0}
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id: 765393
{'conductor': 207214, 'elladic_image': '9.12.0.1', 'lmfdb_label': '207214.e1', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 207214.e does not appear in ec_padic