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ec_curvedata • Show schema
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{'Ciso': '672f', 'Clabel': '672f4', 'Cnumber': 4, 'abc_quality': 0.9710857330134317, 'absD': 3687936, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 1, 0, 16, -84], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 672, 'degree': 128, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.058633227986711720054648936230', 'prec': 110}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4], 'jinv': [830584, 7203], 'lmfdb_iso': '672.f', 'lmfdb_label': '672.f4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 16, 84], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '24.24.0-24.v.1.1', '56.24.0-56.ba.1.12', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.5829836437309415890102051981', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.57849361340667070211757302732', 'prec': 107}, 'szpiro_ratio': 3.457041899317363, '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, -2, 0, -1, 0, 1, 0, -4, 0, -6, 0, -2, 0, -2, 0, 4, 0], 'aplist': [0, 1, -2, -1, -4, -6, -2, 4, -4, -2, 8, -10, -2, 8, 0, -10, -12, 10, -8, 12, 2, 0, 12, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 672, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '672.f', 'trace_hash': 772252924710736021}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.1244189979365211138236954722', 'prec': 100}, 'conductor': 672, 'gens': [[21, 105, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '3.5829836437309415890102051981', 'prec': 100}], 'lmfdb_label': '672.f4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.2336055843599265349339835367', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2099943157883835126970192677470994973', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[3, 0, 1]], 'xcoord_integral_points': [3]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 3, 0]}, 'iwp0': 0, 'lmfdb_label': '672.f4'}
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ec_torsion_growth • Show schema
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id: 31106
{'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [4]}
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id: 31107
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [4]}
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id: 31105
{'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [2, 2]}
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id: 31108
{'degree': 4, 'field': [6, 0, 0, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [2, 4]}
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id: 31109
{'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [2, 4]}
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id: 31113
{'degree': 8, 'field': [-3, 0, 104, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [6]}
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id: 31110
{'degree': 8, 'field': [49, 0, -68, 0, 18, 0, 4, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [4, 4]}
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id: 31112
{'degree': 8, 'field': [49, 0, 56, 0, 2, 0, 8, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [8]}
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id: 31111
{'degree': 8, 'field': [81, 0, 0, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [8]}
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id: 31119
{'degree': 16, 'field': [36, -144, 288, -240, -48, 456, -640, 496, -68, -264, 328, -256, 164, -84, 32, -8, 1], 'lmfdb_label': '672.f4', 'torsion': [12]}
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id: 31116
{'degree': 16, 'field': [58, 504, 1188, -2648, 3318, -4792, 6488, -6884, 5763, -4060, 2424, -1204, 494, -164, 44, -8, 1], 'lmfdb_label': '672.f4', 'torsion': [2, 8]}
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id: 31114
{'degree': 16, 'field': [1296, 0, 0, 0, 4320, 0, 5760, 0, 1464, 0, -960, 0, 120, 0, 0, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [2, 8]}
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id: 31115
{'degree': 16, 'field': [3364, 0, 21200, 0, 11752, 0, -832, 0, 1624, 0, 152, 0, -20, 0, 8, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [2, 8]}
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id: 31118
{'degree': 16, 'field': [10449, 34992, 23004, -4536, -702, -11772, -11232, 4032, -3276, 1296, -492, 504, 18, -36, -12, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [12]}
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id: 31117
{'degree': 16, 'field': [23814, 0, -15876, 36288, -3024, -10584, 19332, -6336, 2124, 1404, -300, 144, 126, -36, 12, 0, 1], 'lmfdb_label': '672.f4', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 8245
{'conductor': 672, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '672.f4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 8246
{'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '672.f4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 8247
{'conductor': 672, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '672.f4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1668965
{'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [64, 3, 61, 2], [7, 6, 162, 163], [64, 155, 25, 54], [161, 8, 160, 9], [55, 60, 58, 145], [73, 8, 124, 33], [1, 4, 4, 17]], 'adelic_image': '168.48.0.?', 'conductor': 672, 'lmfdb_label': '672.f4', 'prime': 0}
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id: 3059
{'conductor': 672, 'elladic_image': '4.12.0.8', 'lmfdb_label': '672.f4', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 12292
{'lmfdb_iso': '672.f', 'p': 5, 'prec': 20, 'unit': 18533787149331, 'val': 1}
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id: 12299
{'lmfdb_iso': '672.f', 'p': 11, 'prec': 20, 'unit': 54478706042324169281, 'val': 1}
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id: 12297
{'lmfdb_iso': '672.f', 'p': 13, 'prec': 20, 'unit': 268406341907490123640, 'val': 1}
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id: 12300
{'lmfdb_iso': '672.f', 'p': 17, 'prec': 20, 'unit': 65697884186424241659342, 'val': 1}
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id: 12301
{'lmfdb_iso': '672.f', 'p': 19, 'prec': 20, 'unit': 794106992236792451672387, 'val': 1}
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id: 12304
{'lmfdb_iso': '672.f', 'p': 23, 'prec': 20, 'unit': 41758343706617461217304737, 'val': 1}
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id: 12298
{'lmfdb_iso': '672.f', 'p': 29, 'prec': 20, 'unit': 3965291752958759478610876149, 'val': 1}
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id: 12294
{'lmfdb_iso': '672.f', 'p': 31, 'prec': 20, 'unit': 8376188261341271808211425876, 'val': 1}
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id: 12308
{'lmfdb_iso': '672.f', 'p': 37, 'prec': 20, 'unit': 443294982391459196324114315936, 'val': 1}
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id: 12295
{'lmfdb_iso': '672.f', 'p': 41, 'prec': 20, 'unit': 1706132802937806073241578723849, 'val': 1}
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id: 12296
{'lmfdb_iso': '672.f', 'p': 43, 'prec': 20, 'unit': 8585526288966873311275422669249, 'val': 1}
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id: 12302
{'lmfdb_iso': '672.f', 'p': 53, 'prec': 20, 'unit': 399138596427344291076831560908314, 'val': 1}
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id: 12306
{'lmfdb_iso': '672.f', 'p': 59, 'prec': 20, 'unit': 3885652926168877044958447577371524, 'val': 1}
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id: 12307
{'lmfdb_iso': '672.f', 'p': 61, 'prec': 20, 'unit': 6315506160164323880288280823645085, 'val': 1}
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id: 12291
{'lmfdb_iso': '672.f', 'p': 67, 'prec': 20, 'unit': 19363873330130602859800267691098547, 'val': 1}
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id: 12293
{'lmfdb_iso': '672.f', 'p': 71, 'prec': 20, 'unit': 61198660380416477531131795872771465, 'val': 1}
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id: 12303
{'lmfdb_iso': '672.f', 'p': 73, 'prec': 20, 'unit': 60896983993927221371257311651492418, 'val': 1}
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id: 12290
{'lmfdb_iso': '672.f', 'p': 83, 'prec': 20, 'unit': 2890907441537512452599808910754601395, 'val': 1}
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id: 12305
{'lmfdb_iso': '672.f', 'p': 89, 'prec': 20, 'unit': 6078300011402461196538275997884559793, 'val': 1}
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id: 12289
{'lmfdb_iso': '672.f', 'p': 97, 'prec': 20, 'unit': 12813575785742669376819045575640312995, 'val': 1}