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ec_curvedata • Show schema
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{'Ciso': '68970cw', 'Clabel': '68970cw3', 'Cnumber': 3, 'abc_quality': 0.957439047611507, 'absD': 552102556747500, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 8360, 'ainvs': [1, 0, 0, -54150, -4720968], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 68970, 'degree': 655360, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6036351183586368789952045377', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 74, 'isogeny_degrees': [1, 2, 4], 'jinv': [9912050027641, 311647500], 'lmfdb_iso': '68970.cw', 'lmfdb_label': '68970.cw2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -448, 3506], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '40.12.0.z.1', '44.12.0-4.c.1.2', '76.12.0.?', '440.24.0.?', '760.24.0.?', '836.24.0.?', '8360.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.40468748195945160696423274872', 'prec': 103}, 'szpiro_ratio': 3.9772413638200184, '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, 0, 1, 6, 4, 1, 1, 6, 1, 1, 1], 'aplist': [1, 1, 1, 4, 0, 6, 6, 1, 4, -6, -8, 2, -10, 8, 12, 2, -4, 2, -12, -16, 14, -8, 0, -6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 68970, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '68970.cw', 'trace_hash': 954332291646337371}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.040466927770888900431716012906', 'prec': 107}, 'conductor': 68970, 'gens': [], 'heights': [], 'lmfdb_label': '68970.cw2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.31357107550697473581759008050', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.034274416223191546162882575984941988', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-609, 609, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 1], '3': [1, 0], '5': [1, 0], '11': 'a', '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '68970.cw2'}
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ec_torsion_growth • Show schema
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id: 3280545
{'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '68970.cw2', 'torsion': [2, 2]}
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id: 3280547
{'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '68970.cw2', 'torsion': [4]}
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id: 3280546
{'degree': 2, 'field': [209, 0, 1], 'lmfdb_label': '68970.cw2', 'torsion': [4]}
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id: 3280548
{'degree': 4, 'field': [465, 32, -31, -2, 1], 'lmfdb_label': '68970.cw2', 'torsion': [2, 4]}
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id: 3280552
{'degree': 8, 'field': [-980932, -39292, -46132, 4668, 1506, 144, 55, -2, 1], 'lmfdb_label': '68970.cw2', 'torsion': [6]}
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id: 3280549
{'degree': 8, 'field': [-50, 224, -196, -46, -1, 26, -4, -4, 1], 'lmfdb_label': '68970.cw2', 'torsion': [2, 4]}
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id: 3280551
{'degree': 8, 'field': [16955, 2900, -2496, -784, 333, 68, -18, -4, 1], 'lmfdb_label': '68970.cw2', 'torsion': [8]}
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id: 3280550
{'degree': 8, 'field': [4626801, 0, 115704, 0, 26206, 0, -296, 0, 1], 'lmfdb_label': '68970.cw2', 'torsion': [8]}
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id: 3280553
{'degree': 16, 'field': [2500, 0, 30576, 0, 59124, 0, 12972, 0, 5653, 0, 1428, 0, 222, 0, 24, 0, 1], 'lmfdb_label': '68970.cw2', 'torsion': [4, 4]}
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id: 3280558
{'degree': 16, 'field': [564705, 681480, -360540, -1118496, 1804314, -1645816, 807152, -233128, 73235, -11032, 3632, -1256, 634, -224, 52, -8, 1], 'lmfdb_label': '68970.cw2', 'torsion': [12]}
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id: 3280554
{'degree': 16, 'field': [1750500, -1818600, 2524580, -1525560, 1053554, -368984, 159882, -39148, 20513, -9072, 3526, -684, -68, 56, 12, -8, 1], 'lmfdb_label': '68970.cw2', 'torsion': [2, 8]}
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id: 3280555
{'degree': 16, 'field': [3663225, 34246800, 302273910, -723341340, 489241704, -158187424, 61244522, -7333588, 1902053, -85312, 56966, -22244, 4132, -224, 52, -8, 1], 'lmfdb_label': '68970.cw2', 'torsion': [2, 8]}
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id: 3280556
{'degree': 16, 'field': [572965185600, 66067833600, -245385984960, -104434028352, -34273272816, -9571948896, -1708423344, -242647008, -28146688, -141872, -45304, 62472, 4416, 1056, 76, -4, 1], 'lmfdb_label': '68970.cw2', 'torsion': [2, 6]}
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id: 3280557
{'degree': 16, 'field': [5904900000000, 0, 113724000000, 0, -14811457500, 0, 252720000, 0, 26868192, 0, 127088, 0, 9264, 0, 0, 0, 1], 'lmfdb_label': '68970.cw2', 'torsion': [12]}
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ec_localdata • Show schema
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id: 1669827
{'conductor': 68970, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '68970.cw2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 1669828
{'conductor': 68970, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '68970.cw2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
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id: 1669829
{'conductor': 68970, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '68970.cw2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 1669830
{'conductor': 68970, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '68970.cw2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 1669831
{'conductor': 68970, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '68970.cw2', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2120362
{'adelic_gens': [[8353, 8, 8352, 9], [1, 0, 8, 1], [5017, 2288, 308, 793], [1, 8, 0, 1], [3884, 7601, 5423, 4566], [1, 4, 4, 17], [7599, 0, 0, 8359], [7888, 7513, 4873, 3400], [859, 858, 7898, 6755], [7, 6, 8354, 8355]], 'adelic_image': '8360.48.0.?', 'conductor': 68970, 'lmfdb_label': '68970.cw2', 'prime': 0}
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id: 287769
{'conductor': 68970, 'elladic_image': '4.6.0.1', 'lmfdb_label': '68970.cw2', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 68970.cw does not appear in ec_padic