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ec_curvedata • Show schema
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{'Ciso': '6720bu', 'Clabel': '6720bu1', 'Cnumber': 1, 'abc_quality': 1.0638597912103416, 'absD': 3810240, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, -1, 0, -79380, 8634762], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6720, 'degree': 15360, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1636834470806870687954653800', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 4], 'jinv': [864335783029582144, 59535], 'lmfdb_iso': '6720.bg', 'lmfdb_label': '6720.bg3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -317521, -68760575], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '24.24.0-24.bb.1.6', '40.24.0-40.bb.1.5', '60.12.0.h.1', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.81710985680071441408684931927', 'prec': 103}, 'szpiro_ratio': 5.158337505060743, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 6, 0, -1, 0, 6, 0, 0, 0], 'aplist': [0, -1, 1, 1, 4, 6, 6, 0, 4, 6, 0, -2, 2, 4, -4, 6, 12, 10, 4, -8, -14, -8, -12, -6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 6720, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '6720.bg', 'trace_hash': 1396786929471627832}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.097552274673192774302923679007', 'prec': 107}, 'conductor': 6720, 'gens': [], 'heights': [], 'lmfdb_label': '6720.bg3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.3719114056766201127419994710', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7438228113532402254839989420555875767', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[163, 0, 1]], 'xcoord_integral_points': [163]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [0, 0], '5': [1, 0], '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '6720.bg3'}
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ec_torsion_growth • Show schema
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id: 352967
{'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [2, 2]}
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id: 352968
{'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [4]}
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id: 352969
{'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [4]}
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id: 352970
{'degree': 4, 'field': [1, 0, -8, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [2, 4]}
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id: 352971
{'degree': 4, 'field': [2940, 0, -140, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [8]}
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id: 352975
{'degree': 8, 'field': [-3, 0, -1952, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [6]}
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id: 352974
{'degree': 8, 'field': [1, 0, -121116, 0, 7766, 0, -156, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [2, 8]}
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id: 352973
{'degree': 8, 'field': [225, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [8]}
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id: 352972
{'degree': 8, 'field': [139876, 0, 4804, 0, -1059, 0, 4, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [2, 4]}
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id: 352979
{'degree': 16, 'field': [9, 0, 89994432, 0, -30480740, 0, 2903424, 0, -11490, 0, -3904, 0, -372, 0, 0, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [2, 6]}
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id: 352977
{'degree': 16, 'field': [346, -544, 5276, -2832, -982, 2416, 1228, -4212, 4771, -3636, 2212, -1108, 458, -156, 44, -8, 1], 'lmfdb_label': '6720.bg3', 'torsion': [2, 8]}
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id: 352976
{'degree': 16, 'field': [19069600, -44704000, 39413600, -16010000, 3025370, -94580, -99870, -61500, 48241, -8688, 5082, -1280, 536, -140, 8, -4, 1], 'lmfdb_label': '6720.bg3', 'torsion': [4, 4]}
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id: 352981
{'degree': 16, 'field': [113103225, 0, -114822000, 0, 17038900, 0, 1481136, 0, -206418, 0, -16144, 0, 996, 0, -48, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [12]}
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id: 352980
{'degree': 16, 'field': [294877584, 0, 99712512, 0, -5489280, 0, -2543616, 0, 145320, 0, 6016, 0, -672, 0, 0, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [12]}
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id: 352978
{'degree': 16, 'field': [135047522241, 3664815840, -229799364768, 64082340000, 23153077908, -412902000, 752487744, -196566720, -87242390, -3029600, -660096, 59360, 37468, -560, -288, 0, 1], 'lmfdb_label': '6720.bg3', 'torsion': [16]}
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ec_localdata • Show schema
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id: 136758
{'conductor': 6720, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '6720.bg3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 136759
{'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '6720.bg3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 136760
{'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6720.bg3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 136761
{'conductor': 6720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6720.bg3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1708213
{'adelic_gens': [[37, 42, 70, 13], [1, 8, 0, 1], [1, 0, 8, 1], [88, 3, 85, 2], [113, 8, 112, 9], [7, 6, 114, 115], [1, 4, 4, 17], [28, 1, 71, 6], [16, 83, 19, 48]], 'adelic_image': '120.48.0.?', 'conductor': 6720, 'lmfdb_label': '6720.bg3', 'prime': 0}
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id: 33073
{'conductor': 6720, 'elladic_image': '8.12.0.6', 'lmfdb_label': '6720.bg3', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 6720.bg does not appear in ec_padic