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ec_curvedata • Show schema
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{'Ciso': '6270l', 'Clabel': '6270l8', 'Cnumber': 8, 'abc_quality': 1.0456592169621262, 'absD': 45195275784938365817280, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 25080, 'ainvs': [1, 0, 1, 8716517, -2549957914], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 19], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 6270, 'degree': 774144, 'elladic_images': ['4.6.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0362448055625931087940960261', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [73240740785321709623685719, 45195275784938365817280], 'lmfdb_iso': '6270.l', 'lmfdb_label': '6270.l8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 8716517, -2549957914], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '12.48.0-12.g.1.10', '20.12.0-4.c.1.1', '60.96.0-60.c.3.12', '76.12.0.?', '88.12.0.?', '190.6.0.?', '228.96.0.?', '264.96.0.?', '380.24.0.?', '440.24.0.?', '570.48.0.?', '1140.192.1.?', '1320.192.1.?', '1672.24.0.?', '5016.192.1.?', '8360.48.0.?', '25080.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.0362448055625931087940960261', 'prec': 100}, 'szpiro_ratio': 6.811411745461771, '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, 1, -1, -4, -1, 1, -1, -1, 1, 2, 4, 1, 1, 6, -1, 1, 1], 'aplist': [-1, 1, 1, -4, -1, 2, 6, 1, 0, -6, -4, 2, 6, 8, 0, -6, 0, 14, -4, -12, -10, 8, 0, -6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 6270, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '6270.l', 'trace_hash': 2023840264930280173}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0023054264446393024390292976221', 'prec': 110}, 'conductor': 6270, 'gens': [], 'heights': [], 'lmfdb_label': '6270.l8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.065675590468787654789559212653', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5762141712509037149494211036660088588', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[1159, -1163, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 1], '3': [1, 1], '5': [1, 0], '11': [0, 0], '19': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '6270.l8'}
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ec_torsion_growth • Show schema
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id: 326557
{'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [4]}
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id: 326559
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '6270.l8', 'torsion': [6]}
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id: 326558
{'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [4]}
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id: 326556
{'degree': 2, 'field': [24, -1, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 2]}
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id: 326560
{'degree': 3, 'field': [-45, 0, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [6]}
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id: 326564
{'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [12]}
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id: 326561
{'degree': 4, 'field': [36, 0, -7, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 4]}
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id: 326563
{'degree': 4, 'field': [361, 0, 19, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [12]}
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id: 326562
{'degree': 4, 'field': [576, -24, -23, -1, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 6]}
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id: 326567
{'degree': 6, 'field': [-4834, -5130, 1083, -90, -57, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [12]}
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id: 326568
{'degree': 6, 'field': [45, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [12]}
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id: 326565
{'degree': 6, 'field': [75, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [3, 6]}
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id: 326566
{'degree': 6, 'field': [9720, 0, 0, -195, 0, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 6]}
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id: 326572
{'degree': 8, 'field': [1296, 0, 252, 0, 13, 0, 7, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 12]}
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id: 326571
{'degree': 8, 'field': [1521, 0, 2186, 0, -69, 0, 6, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [8]}
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id: 326569
{'degree': 8, 'field': [147061, -6076, 6842, -1528, 755, 8, 2, -4, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 4]}
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id: 326570
{'degree': 8, 'field': [364816, 0, -295304, 0, -5695, 0, 46, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [8]}
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id: 326575
{'degree': 12, 'field': [2116, -276, -654, 1750, -585, -396, 231, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '6270.l8', 'torsion': [3, 12]}
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id: 326576
{'degree': 12, 'field': [4356, 0, -21951, 0, 42255, 0, -3775, 0, 165, 0, -21, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 12]}
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id: 326574
{'degree': 12, 'field': [48080356, 0, -14044344, 0, 1997565, 0, -137030, 0, 5415, 0, -114, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [3, 12]}
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id: 326573
{'degree': 12, 'field': [98327056, -5860356, -5600319, 3909280, 84195, -170766, 53511, 3384, -1665, 340, 21, -6, 1], 'lmfdb_label': '6270.l8', 'torsion': [6, 6]}
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id: 326582
{'degree': 16, 'field': [2313441, 0, -3324906, 0, 4883545, 0, 169086, 0, -9876, 0, 4786, 0, 105, 0, -6, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [24]}
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id: 326579
{'degree': 16, 'field': [8503056, 0, 8465148, 0, 1966113, 0, -397764, 0, 77440, 0, -7834, 0, 888, 0, -52, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 8]}
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id: 326577
{'degree': 16, 'field': [69906321, 0, 30883752, 0, -1477382, 0, -536796, 0, 54155, 0, 1284, 0, -322, 0, 12, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [4, 4]}
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id: 326580
{'degree': 16, 'field': [20474184541, 845024248, -914617420, 129390000, -39753770, -31187416, 12482352, -1766120, 408375, 30280, -14328, 4616, -830, 0, 20, -8, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 12]}
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id: 326581
{'degree': 16, 'field': [3667179040144, 0, -329404099168, 0, 3098405576, 0, 193159872, 0, 15521081, 0, -844602, 0, 2339, 0, 182, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [24]}
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id: 326578
{'degree': 16, 'field': [4827969085696, 0, -557634526912, 0, 20140490084, 0, 868301292, 0, -10595311, 0, -534888, 0, 1562, 0, 140, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [2, 8]}
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id: 326583
{'degree': 18, 'field': [17429379606421875, 0, 0, -140402153778750, 0, 0, 390344727675, 0, 0, -502833720, 0, 0, 596473, 0, 0, -662, 0, 0, 1], 'lmfdb_label': '6270.l8', 'torsion': [18]}
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ec_localdata • Show schema
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id: 125355
{'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '6270.l8', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 125356
{'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '6270.l8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
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id: 125357
{'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6270.l8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 125358
{'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '6270.l8', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 125359
{'conductor': 6270, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '6270.l8', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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ec_galrep • Show schema
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id: 1705061
{'adelic_gens': [[5241, 1048, 11036, 7229], [5032, 3, 4557, 24994], [7936, 21, 24795, 24706], [1, 12, 12, 145], [6271, 24, 6282, 289], [20901, 16724, 20, 12621], [9121, 24, 9132, 289], [15, 106, 23774, 15851], [25057, 24, 25056, 25], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '25080.384.5.?', 'conductor': 6270, 'lmfdb_label': '6270.l8', 'prime': 0}
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id: 30766
{'conductor': 6270, 'elladic_image': '4.6.0.1', 'lmfdb_label': '6270.l8', 'modell_image': '2B', 'prime': 2}
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id: 30767
{'conductor': 6270, 'elladic_image': '3.8.0.2', 'lmfdb_label': '6270.l8', 'modell_image': '3B.1.2', 'prime': 3}
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lmfdb_iso 6270.l does not appear in ec_padic