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ec_curvedata • Show schema
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{'Ciso': '5054c', 'Clabel': '5054c2', 'Cnumber': 2, 'abc_quality': 0.9676277689392396, 'absD': 4610496338, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 9576, 'ainvs': [1, 1, 1, -3798, -91615], 'analytic_rank': 0, 'bad_primes': [2, 7, 19], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 5054, 'degree': 4752, 'elladic_images': ['8.6.0.6', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.78670818133819499619005083386', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [128787625, 98], 'lmfdb_iso': '5054.c', 'lmfdb_label': '5054.c4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -11, 12], 'min_quad_twist_disc': -19, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.b.1', '9.12.0.a.1', '18.36.0.a.1', '24.24.0.y.1', '28.6.0.c.1', '56.12.0.k.1', '57.8.0-3.a.1.1', '63.36.0.d.2', '72.72.1.?', '84.24.0.?', '114.24.0.?', '126.108.2.?', '168.48.1.?', '171.24.0.?', '252.216.7.?', '342.72.0.?', '456.48.0.?', '504.432.21.?', '1197.72.0.?', '1368.144.1.?', '1596.48.0.?', '2394.216.2.?', '3192.96.1.?', '4788.432.7.?', '9576.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.68551130824502523381446288208', 'prec': 107}, 'szpiro_ratio': 4.261325624055992, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 2, 1, 0, 2, 1, 1, 1, 0, 0, 2, 4, 1, 0, 1, 6, 1, 0, 0], 'aplist': [1, 2, 0, 1, 0, 4, 6, 0, 0, 6, 4, -2, -6, 8, -12, -6, 6, 8, 4, 0, 2, -8, -6, 6, 10], 'class_deg': 18, 'class_size': 6, 'conductor': 5054, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '5054.c', 'trace_hash': 346606733482046324}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.20733563728279075156562012912', 'prec': 103}, 'conductor': 5054, 'gens': [], 'heights': [], 'lmfdb_label': '5054.c4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.60817709098151674228887984272', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.4735938188336506805999185845067634179', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-141, 137, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 0], '3': [2, 0], '7': [1, 0], '19': 'a'}, 'iwp0': 5, 'lmfdb_label': '5054.c4'}
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ec_torsion_growth • Show schema
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id: 264856
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '5054.c4', 'torsion': [2, 2]}
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id: 264857
{'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '5054.c4', 'torsion': [6]}
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id: 264859
{'degree': 4, 'field': [47, -6, 7, -2, 1], 'lmfdb_label': '5054.c4', 'torsion': [2, 6]}
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id: 264858
{'degree': 4, 'field': [722, 0, 19, 0, 1], 'lmfdb_label': '5054.c4', 'torsion': [4]}
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id: 264860
{'degree': 6, 'field': [-5034, -456, 628, 17, -33, -1, 1], 'lmfdb_label': '5054.c4', 'torsion': [6]}
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id: 264861
{'degree': 6, 'field': [239, -16, 75, -7, 10, -1, 1], 'lmfdb_label': '5054.c4', 'torsion': [18]}
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id: 264864
{'degree': 8, 'field': [959, -434, 578, -306, 199, -58, 24, -4, 1], 'lmfdb_label': '5054.c4', 'torsion': [12]}
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id: 264863
{'degree': 8, 'field': [4624, 0, -1280, 0, 70, 0, -8, 0, 1], 'lmfdb_label': '5054.c4', 'torsion': [2, 4]}
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id: 264862
{'degree': 8, 'field': [36481, 0, 1542, 0, 370, 0, 22, 0, 1], 'lmfdb_label': '5054.c4', 'torsion': [2, 4]}
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id: 264865
{'degree': 12, 'field': [784, 9408, 35672, -23520, 3528, 546, -1163, 219, 90, 39, -10, -3, 1], 'lmfdb_label': '5054.c4', 'torsion': [3, 6]}
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id: 264866
{'degree': 12, 'field': [10276, 6608, 15008, 3254, 7584, 486, 2185, 0, 345, -4, 29, 0, 1], 'lmfdb_label': '5054.c4', 'torsion': [18]}
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id: 264867
{'degree': 12, 'field': [147456, 0, 135168, 0, 33472, 0, -2002, 0, -648, 0, -22, 0, 1], 'lmfdb_label': '5054.c4', 'torsion': [2, 6]}
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id: 264868
{'degree': 12, 'field': [188657, -33628, 94346, -10842, 18875, -1868, 2443, -242, 194, -14, 9, -2, 1], 'lmfdb_label': '5054.c4', 'torsion': [2, 18]}
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id: 264870
{'degree': 16, 'field': [311521, -235284, 409502, -460664, 552000, -509040, 399462, -249032, 133437, -57272, 21922, -6552, 1820, -364, 72, -8, 1], 'lmfdb_label': '5054.c4', 'torsion': [2, 12]}
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id: 264871
{'degree': 16, 'field': [4072271, -2803360, 3829636, -2290472, 1778644, -872664, 492320, -201528, 89377, -30712, 11220, -3248, 966, -224, 52, -8, 1], 'lmfdb_label': '5054.c4', 'torsion': [2, 12]}
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id: 264869
{'degree': 16, 'field': [63744256, 0, -47166208, 0, 14272226, 0, -710132, 0, -52123, 0, 2326, 0, 804, 0, -54, 0, 1], 'lmfdb_label': '5054.c4', 'torsion': [8]}
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ec_localdata • Show schema
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id: 98236
{'conductor': 5054, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5054.c4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 98237
{'conductor': 5054, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5054.c4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 98238
{'conductor': 5054, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '5054.c4', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1697022
{'adelic_gens': [[1, 36, 0, 1], [7183, 2052, 4294, 1369], [1, 0, 36, 1], [1825, 2052, 1938, 2281], [9541, 36, 9540, 37], [19, 36, 3240, 6139], [1540, 1539, 57, 7354], [8567, 0, 0, 9575], [1, 18, 14, 253], [5321, 2052, 0, 1]], 'adelic_image': '9576.864.21.?', 'conductor': 5054, 'lmfdb_label': '5054.c4', 'prime': 0}
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id: 25154
{'conductor': 5054, 'elladic_image': '8.6.0.6', 'lmfdb_label': '5054.c4', 'modell_image': '2B', 'prime': 2}
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id: 25155
{'conductor': 5054, 'elladic_image': '9.12.0.1', 'lmfdb_label': '5054.c4', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 5054.c does not appear in ec_padic