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ec_curvedata • Show schema
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{'Ciso': '11774k', 'Clabel': '11774k1', 'Cnumber': 1, 'abc_quality': 1.0171207213859017, 'absD': 16655052988, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 14616, 'ainvs': [1, 1, 1, -438, 6959], 'analytic_rank': 1, 'bad_primes': [2, 7, 29], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 11774, 'degree': 8064, 'elladic_images': ['8.6.0.1', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.65156301646823912506855707337', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [-15625, 28], 'lmfdb_iso': '11774.m', 'lmfdb_label': '11774.m5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1, 0], 'min_quad_twist_disc': 29, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.c.1', '9.12.0.a.1', '14.6.0.b.1', '18.36.0.a.1', '24.24.0.bw.1', '42.24.0.b.1', '56.12.0.n.1', '63.36.0.d.2', '72.72.1.?', '87.8.0.?', '126.216.7.?', '168.48.1.?', '174.24.0.?', '261.24.0.?', '504.432.21.?', '522.72.0.?', '696.48.0.?', '1218.48.0.?', '1827.72.0.?', '2088.144.1.?', '3654.432.7.?', '4872.96.1.?', '14616.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.2676588188456893180750583263', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0320848985249978885230789428', 'prec': 103}, 'szpiro_ratio': 3.336006499934838, '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, -2, 0], 'aplist': [1, 2, 0, 1, 0, -4, -6, -2, 0, 0, 4, -2, -6, -8, 12, 6, -6, -8, -4, 0, -2, -8, -6, 6, 10], 'class_deg': 18, 'class_size': 6, 'conductor': 11774, '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': '11774.m', 'trace_hash': 1398253986630097751}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.27168117988779477791357120368', 'prec': 103}, 'conductor': 11774, 'gens': [[1917, 79393, 4]], 'heights': [{'__RealLiteral__': 0, 'data': '4.2676588188456893180750583263', 'prec': 100}], 'lmfdb_label': '11774.m5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.1037778937286639528833256393', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.4210949244361055842699584129071037637', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-27, 13, 1]], 'xcoord_integral_points': [-27]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 0], '3': [3, 0], '5': [1, 1, 0], '7': [2, 0], '11': [3, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': 'a', '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '11774.m5'}
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ec_torsion_growth • Show schema
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id: 609567
{'degree': 2, 'field': [-7, -1, 1], 'lmfdb_label': '11774.m5', 'torsion': [6]}
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id: 609566
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '11774.m5', 'torsion': [2, 2]}
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id: 609568
{'degree': 4, 'field': [-386, 44, 15, -2, 1], 'lmfdb_label': '11774.m5', 'torsion': [4]}
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id: 609569
{'degree': 4, 'field': [81, 0, -11, 0, 1], 'lmfdb_label': '11774.m5', 'torsion': [2, 6]}
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id: 609571
{'degree': 6, 'field': [-169, -64, 159, 17, -26, -1, 1], 'lmfdb_label': '11774.m5', 'torsion': [18]}
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id: 609570
{'degree': 6, 'field': [6342, -168, 1456, -55, 75, -1, 1], 'lmfdb_label': '11774.m5', 'torsion': [6]}
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id: 609574
{'degree': 8, 'field': [2372, 616, -1466, -56, 323, -4, -30, 0, 1], 'lmfdb_label': '11774.m5', 'torsion': [12]}
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id: 609573
{'degree': 8, 'field': [8786, -5872, 2047, -722, 449, -84, 21, -2, 1], 'lmfdb_label': '11774.m5', 'torsion': [2, 4]}
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id: 609572
{'degree': 8, 'field': [171278, -40602, -5751, -18, 1245, -58, -29, -2, 1], 'lmfdb_label': '11774.m5', 'torsion': [2, 4]}
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id: 609578
{'degree': 12, 'field': [117649, 16807, 19208, 5145, 3479, 1232, 673, -176, 71, -15, 8, -1, 1], 'lmfdb_label': '11774.m5', 'torsion': [2, 18]}
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id: 609575
{'degree': 12, 'field': [126736, 0, -107536, 0, 58140, 0, -8057, 0, 759, 0, -43, 0, 1], 'lmfdb_label': '11774.m5', 'torsion': [3, 6]}
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id: 609576
{'degree': 12, 'field': [153028, 31568, -123064, -12634, 42312, 1350, -7583, 0, 777, -4, -43, 0, 1], 'lmfdb_label': '11774.m5', 'torsion': [18]}
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id: 609577
{'degree': 12, 'field': [3196936, -4409844, 2479778, -4047, -154947, -2016, -13460, 2310, 654, 48, 14, -3, 1], 'lmfdb_label': '11774.m5', 'torsion': [2, 6]}
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id: 609580
{'degree': 16, 'field': [20389532, 12893776, -11596936, -8215924, 3442685, 2352730, -729554, -402830, 117622, 44732, -13246, -3266, 958, 154, -42, -4, 1], 'lmfdb_label': '11774.m5', 'torsion': [2, 12]}
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id: 609579
{'degree': 16, 'field': [27659392, 76328960, 84480768, 33244544, -3943440, -5841344, -1754256, -292800, 94748, 60208, 9592, -32, -860, -136, 8, 0, 1], 'lmfdb_label': '11774.m5', 'torsion': [8]}
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id: 609581
{'degree': 16, 'field': [28514756, 2297016, -19167520, -2242356, 5935023, 981576, -1105126, -237132, 137992, 34844, -12428, -3184, 842, 168, -40, -4, 1], 'lmfdb_label': '11774.m5', 'torsion': [2, 12]}
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ec_localdata • Show schema
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id: 253632
{'conductor': 11774, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '11774.m5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 253633
{'conductor': 11774, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '11774.m5', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 253634
{'conductor': 11774, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '11774.m5', 'prime': 29, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1742134
{'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [11369, 1044, 0, 1], [2176, 7569, 551, 3046], [7309, 1044, 3538, 10441], [14581, 36, 14580, 37], [19, 36, 3240, 6139], [3655, 1044, 10846, 10441], [10583, 0, 0, 14615], [1, 18, 14, 253]], 'adelic_image': '14616.864.21.?', 'conductor': 11774, 'lmfdb_label': '11774.m5', 'prime': 0}
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id: 56462
{'conductor': 11774, 'elladic_image': '8.6.0.1', 'lmfdb_label': '11774.m5', 'modell_image': '2B', 'prime': 2}
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id: 56463
{'conductor': 11774, 'elladic_image': '9.12.0.1', 'lmfdb_label': '11774.m5', 'modell_image': '3B', 'prime': 3}
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ec_padic • Show schema
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id: 511395
{'lmfdb_iso': '11774.m', 'p': 13, 'prec': 20, 'unit': 1444793956151857052715, 'val': 1}
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id: 511397
{'lmfdb_iso': '11774.m', 'p': 17, 'prec': 20, 'unit': 111803446934583534106602, 'val': 1}
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id: 511389
{'lmfdb_iso': '11774.m', 'p': 19, 'prec': 20, 'unit': 1966307755569524931676064, 'val': 1}
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id: 511405
{'lmfdb_iso': '11774.m', 'p': 31, 'prec': 20, 'unit': 18646508927722454111292926062, 'val': 1}
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id: 511392
{'lmfdb_iso': '11774.m', 'p': 37, 'prec': 20, 'unit': 445293602712716270132179899076, 'val': 1}
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id: 511393
{'lmfdb_iso': '11774.m', 'p': 41, 'prec': 20, 'unit': 1349905210107172198179971803661, 'val': 1}
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id: 511394
{'lmfdb_iso': '11774.m', 'p': 43, 'prec': 20, 'unit': 4814043311382517990595825348573, 'val': 1}
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id: 511403
{'lmfdb_iso': '11774.m', 'p': 47, 'prec': 20, 'unit': 38700382947334003273911691491934, 'val': 1}
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id: 511399
{'lmfdb_iso': '11774.m', 'p': 53, 'prec': 20, 'unit': 104102539581149466244199090276678, 'val': 1}
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id: 511400
{'lmfdb_iso': '11774.m', 'p': 59, 'prec': 20, 'unit': 3222179668742576486897594508302115, 'val': 1}
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id: 511404
{'lmfdb_iso': '11774.m', 'p': 61, 'prec': 20, 'unit': 6052430559975841702440764783199099, 'val': 1}
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id: 511391
{'lmfdb_iso': '11774.m', 'p': 67, 'prec': 20, 'unit': 15468982438712682221008298406812958, 'val': 1}
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id: 511401
{'lmfdb_iso': '11774.m', 'p': 73, 'prec': 20, 'unit': 93500781866270998193934935106068304, 'val': 1}
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id: 511396
{'lmfdb_iso': '11774.m', 'p': 79, 'prec': 20, 'unit': 134965603593594237743143465707254620, 'val': 1}
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id: 511398
{'lmfdb_iso': '11774.m', 'p': 83, 'prec': 20, 'unit': 631280159070438536429335210459711565, 'val': 1}
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id: 511402
{'lmfdb_iso': '11774.m', 'p': 89, 'prec': 20, 'unit': 1218279507234149001307246286524465516, 'val': 1}
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id: 511390
{'lmfdb_iso': '11774.m', 'p': 97, 'prec': 20, 'unit': 54204663853535245605877505502452595976, 'val': 1}