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ec_curvedata • Show schema
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{'Ciso': '17661a', 'Clabel': '17661a2', 'Cnumber': 2, 'abc_quality': 1.1486166056524132, 'absD': 2360853761049, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 4872, 'ainvs': [1, 1, 0, -3381, -17640], 'analytic_rank': 1, 'bad_primes': [3, 7, 29], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 17661, 'degree': 25088, 'elladic_images': ['8.24.0.10'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0647061178242314749326697494', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4], 'jinv': [7189057, 3969], 'lmfdb_iso': '17661.f', 'lmfdb_label': '17661.f5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -4, -1], 'min_quad_twist_disc': 29, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.2', '24.48.0.w.2', '28.24.0.c.1', '56.48.0.i.1', '116.24.0.?', '168.96.1.?', '232.48.0.?', '696.96.0.?', '812.48.0.?', '1624.96.0.?', '4872.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.5138571509355444793722996550', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61894179716900553865896626678', 'prec': 107}, 'szpiro_ratio': 3.6804811956444974, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, -1, -1, -2, -1, -1, -3, 1, -2, -4, 1, -2, -1, 2, -1, 6, 1, -4, 2], 'aplist': [1, -1, -2, -1, -4, -2, 6, -4, 0, 0, 0, -6, -2, 4, 0, 6, 12, 2, 4, 0, 6, 16, -12, 14, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 17661, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '17661.f', 'trace_hash': 1379573409541193003}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.11890716270856923870843548512', 'prec': 103}, 'conductor': 17661, 'gens': [[-49, 1239, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '4.5138571509355444793722996550', 'prec': 100}], 'lmfdb_label': '17661.f5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.67016022208395101273509425965', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0250075107261948751496009438170118158', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-56, 28, 1], [60, -30, 1]], 'xcoord_integral_points': [-56, 60]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 0], '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': 'a', '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '17661.f5'}
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ec_torsion_growth • Show schema
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id: 903996
{'degree': 2, 'field': [-7, -1, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 4]}
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id: 903999
{'degree': 4, 'field': [49, 7, 8, -1, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 8]}
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id: 903997
{'degree': 4, 'field': [81, 0, 11, 0, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 4]}
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id: 903998
{'degree': 4, 'field': [758, -62, 63, -2, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 4]}
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id: 904002
{'degree': 8, 'field': [-16111, 7235, 35, 560, -109, -103, 1, -2, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 6]}
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id: 904001
{'degree': 8, 'field': [4, 1084, -698, -734, 273, 110, -32, -4, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 8]}
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id: 904000
{'degree': 8, 'field': [981, -1362, 1784, -882, 537, -118, 44, -4, 1], 'lmfdb_label': '17661.f5', 'torsion': [4, 4]}
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id: 904005
{'degree': 16, 'field': [4787344, 0, 4582012, 0, 2313137, 0, 816876, 0, 187868, 0, 24306, 0, 1724, 0, 64, 0, 1], 'lmfdb_label': '17661.f5', 'torsion': [4, 8]}
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id: 904006
{'degree': 16, 'field': [5764801, 0, -1764735, 0, 1032430, 0, -165375, 0, 39159, 0, -3375, 0, 430, 0, -15, 0, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 16]}
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id: 904007
{'degree': 16, 'field': [8014561, 0, -7583977, 0, 3972196, 0, -1147569, 0, 196353, 0, -21327, 0, 1471, 0, -58, 0, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 12]}
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id: 904003
{'degree': 16, 'field': [27964836, -52885032, 57355940, -42241536, 26065170, -12161120, 5160966, -1697708, 548965, -138712, 38982, -8452, 2216, -392, 80, -8, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 8]}
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id: 904004
{'degree': 16, 'field': [3996563608, 4454401136, 345169436, -823924980, -6631487, 89395672, -8686878, -5548828, 974058, 244832, -50268, -10100, 2158, 336, -64, -4, 1], 'lmfdb_label': '17661.f5', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 395216
{'conductor': 17661, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '17661.f5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 395217
{'conductor': 17661, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '17661.f5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 395218
{'conductor': 17661, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '17661.f5', 'prime': 29, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1781769
{'adelic_gens': [[4865, 8, 4864, 9], [1, 0, 8, 1], [929, 1392, 1044, 581], [1, 8, 0, 1], [5, 4, 4868, 4869], [1625, 3364, 0, 1], [175, 174, 1914, 4699], [839, 0, 0, 4871], [3365, 3828, 4698, 4235]], 'adelic_image': '4872.192.1.?', 'conductor': 17661, 'lmfdb_label': '17661.f5', 'prime': 0}
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id: 82732
{'conductor': 17661, 'elladic_image': '8.24.0.10', 'lmfdb_label': '17661.f5', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 808466
{'lmfdb_iso': '17661.f', 'p': 5, 'prec': 20, 'unit': 3222093809884, 'val': 1}
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id: 808456
{'lmfdb_iso': '17661.f', 'p': 11, 'prec': 20, 'unit': 34275376576949650691, 'val': 1}
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id: 808457
{'lmfdb_iso': '17661.f', 'p': 13, 'prec': 20, 'unit': 41206083569042051974, 'val': 1}
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id: 808454
{'lmfdb_iso': '17661.f', 'p': 17, 'prec': 20, 'unit': 238190004785876455983962, 'val': 1}
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id: 808460
{'lmfdb_iso': '17661.f', 'p': 19, 'prec': 20, 'unit': 1867169145802056454929096, 'val': 1}
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id: 808453
{'lmfdb_iso': '17661.f', 'p': 37, 'prec': 20, 'unit': 306742327650729973218376118059, 'val': 1}
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id: 808455
{'lmfdb_iso': '17661.f', 'p': 41, 'prec': 20, 'unit': 1479763995377071076905673717862, 'val': 1}
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id: 808459
{'lmfdb_iso': '17661.f', 'p': 43, 'prec': 20, 'unit': 5645331305378826539437961801607, 'val': 1}
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id: 808461
{'lmfdb_iso': '17661.f', 'p': 53, 'prec': 20, 'unit': 556708170590878226721939982856432, 'val': 1}
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id: 808464
{'lmfdb_iso': '17661.f', 'p': 59, 'prec': 20, 'unit': 178970282865457326040601521617979, 'val': 1}
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id: 808465
{'lmfdb_iso': '17661.f', 'p': 61, 'prec': 20, 'unit': 7881601420678756217085731570237500, 'val': 1}
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id: 808452
{'lmfdb_iso': '17661.f', 'p': 67, 'prec': 20, 'unit': 18090486982349432573757943872700581, 'val': 1}
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id: 808462
{'lmfdb_iso': '17661.f', 'p': 73, 'prec': 20, 'unit': 71785690540099519768587227002553238, 'val': 1}
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id: 808458
{'lmfdb_iso': '17661.f', 'p': 79, 'prec': 20, 'unit': 238524570316657708073922149301569887, 'val': 1}
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id: 808451
{'lmfdb_iso': '17661.f', 'p': 83, 'prec': 20, 'unit': 1747339095159484146534549073950004307, 'val': 1}
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id: 808463
{'lmfdb_iso': '17661.f', 'p': 89, 'prec': 20, 'unit': 8425213374249340473198560015567312744, 'val': 1}
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id: 808450
{'lmfdb_iso': '17661.f', 'p': 97, 'prec': 20, 'unit': 6485580814429695989746848518646304525, 'val': 1}