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ec_curvedata • Show schema
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{'Ciso': '2112y', 'Clabel': '2112y4', 'Cnumber': 4, 'abc_quality': 0.9538342535176972, 'absD': 2878537728, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [0, 1, 0, -417, 1887], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 2112, 'degree': 1536, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.51589431144919078052888998557', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 24, 'isogeny_degrees': [1, 2, 4], 'jinv': [122657188, 43923], 'lmfdb_iso': '2112.y', 'lmfdb_label': '2112.y2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -104, -288], '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.1.4', '12.12.0.h.1', '24.24.0-12.h.1.1', '88.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3540009313541377149456521348', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.40830192929740296536075284304', 'prec': 107}, 'szpiro_ratio': 3.88161234355589, '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, -4, 0, 1, 0, -1, 0, -6, 0, 2, 0, 6, 0, -8, 0], 'aplist': [0, 1, 2, -4, -1, -6, 6, -8, 0, 6, 0, -6, -10, -8, 0, -6, 4, 2, -12, 8, 2, 4, -12, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 2112, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '2112.y', 'trace_hash': 2137125441666691093}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.35636898046758496348799327021', 'prec': 103}, 'conductor': 2112, 'gens': [[-1, 48, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3540009313541377149456521348', 'prec': 100}], 'lmfdb_label': '2112.y2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.3105995506366828505882918480', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5491060243887659050391088641458730896', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[17, 0, 1]], 'xcoord_integral_points': [-1, 17]}
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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, 1, 0], '29': [1, 0], '31': [3, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '2112.y2'}
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ec_torsion_growth • Show schema
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id: 107307
{'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [4]}
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id: 107306
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [2, 2]}
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id: 107308
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [4]}
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id: 107309
{'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [2, 4]}
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id: 107313
{'degree': 8, 'field': [-48, 0, 1472, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [6]}
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id: 107310
{'degree': 8, 'field': [9, 0, -6, 0, 4, -4, 6, -4, 1], 'lmfdb_label': '2112.y2', 'torsion': [2, 4]}
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id: 107312
{'degree': 8, 'field': [25, 0, -2, 0, 3, 0, 4, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [8]}
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id: 107311
{'degree': 8, 'field': [64, 0, -136, 0, 81, 0, -16, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [8]}
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id: 107314
{'degree': 16, 'field': [1, -12, 68, -232, 488, -564, 194, 396, -665, 444, -62, -152, 162, -92, 34, -8, 1], 'lmfdb_label': '2112.y2', 'torsion': [4, 4]}
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id: 107316
{'degree': 16, 'field': [16, 0, -336, 0, 1372, 0, -2316, 0, 1965, 0, -888, 0, 211, 0, -24, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [2, 8]}
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id: 107319
{'degree': 16, 'field': [121, 0, -484, 0, 484, 0, -252, 0, 318, 0, 36, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [12]}
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id: 107318
{'degree': 16, 'field': [1296, 0, 1344, 0, -992, 0, -2256, 0, 1368, 0, -152, 0, 60, 0, -12, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [12]}
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id: 107315
{'degree': 16, 'field': [2473, -1884, 3638, -1428, 3710, -2616, 2238, -1104, 551, -60, 114, -24, 32, -12, -4, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [2, 8]}
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id: 107317
{'degree': 16, 'field': [15876, 0, 55512, 0, 9972, 0, -71712, 0, 17532, 0, -1572, 0, 216, 0, -24, 0, 1], 'lmfdb_label': '2112.y2', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 35046
{'conductor': 2112, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '2112.y2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 35047
{'conductor': 2112, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2112.y2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 35048
{'conductor': 2112, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '2112.y2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1677738
{'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 258, 259], [32, 157, 29, 0], [257, 8, 256, 9], [92, 1, 199, 6], [145, 8, 52, 33], [29, 30, 86, 221]], 'adelic_image': '264.48.0.?', 'conductor': 2112, 'lmfdb_label': '2112.y2', 'prime': 0}
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id: 10396
{'conductor': 2112, 'elladic_image': '8.12.0.8', 'lmfdb_label': '2112.y2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 62296
{'lmfdb_iso': '2112.y', 'p': 5, 'prec': 20, 'unit': 17002612607483, 'val': 1}
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id: 62297
{'lmfdb_iso': '2112.y', 'p': 7, 'prec': 20, 'unit': 5566282712555507, 'val': 1}
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id: 62301
{'lmfdb_iso': '2112.y', 'p': 13, 'prec': 20, 'unit': 953032389627638180047, 'val': 1}
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id: 62303
{'lmfdb_iso': '2112.y', 'p': 17, 'prec': 20, 'unit': 232246188350752852791465, 'val': 1}
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id: 62293
{'lmfdb_iso': '2112.y', 'p': 19, 'prec': 20, 'unit': 1841203667020408562163972, 'val': 1}
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id: 62300
{'lmfdb_iso': '2112.y', 'p': 29, 'prec': 20, 'unit': 402203419648720575728499555, 'val': 1}
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id: 62311
{'lmfdb_iso': '2112.y', 'p': 37, 'prec': 20, 'unit': 521732336853408069043481255114, 'val': 1}
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id: 62298
{'lmfdb_iso': '2112.y', 'p': 41, 'prec': 20, 'unit': 3351445652926292907148256950141, 'val': 1}
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id: 62299
{'lmfdb_iso': '2112.y', 'p': 43, 'prec': 20, 'unit': 1953853052966618795092285519294, 'val': 1}
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id: 62305
{'lmfdb_iso': '2112.y', 'p': 53, 'prec': 20, 'unit': 216253053387943976277547065776219, 'val': 1}
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id: 62309
{'lmfdb_iso': '2112.y', 'p': 59, 'prec': 20, 'unit': 2470702275353574948606734094116672, 'val': 1}
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id: 62310
{'lmfdb_iso': '2112.y', 'p': 61, 'prec': 20, 'unit': 3714391811543014396353799002089266, 'val': 1}
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id: 62295
{'lmfdb_iso': '2112.y', 'p': 67, 'prec': 20, 'unit': 39482003668022003360880889752893888, 'val': 1}
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id: 62308
{'lmfdb_iso': '2112.y', 'p': 71, 'prec': 20, 'unit': 4941563667986765250828026302633197, 'val': 1}
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id: 62306
{'lmfdb_iso': '2112.y', 'p': 73, 'prec': 20, 'unit': 106028701951762999321974462998419224, 'val': 1}
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id: 62302
{'lmfdb_iso': '2112.y', 'p': 79, 'prec': 20, 'unit': 1031039194996227456671423224177226598, 'val': 1}
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id: 62304
{'lmfdb_iso': '2112.y', 'p': 83, 'prec': 20, 'unit': 2161788171487849399142649621740313769, 'val': 1}
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id: 62307
{'lmfdb_iso': '2112.y', 'p': 89, 'prec': 20, 'unit': 313794918238830492780581730826577279, 'val': 1}
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id: 62294
{'lmfdb_iso': '2112.y', 'p': 97, 'prec': 20, 'unit': 36538644423790653137944595809176084130, 'val': 1}