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ec_curvedata • Show schema
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{'Ciso': '117117z', 'Clabel': '117117z1', 'Cnumber': 1, 'abc_quality': 1.0717755889436964, 'absD': 152843917837313351288697057, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 12012, 'ainvs': [1, -1, 1, -4588557395, 119635801234850], 'analytic_rank': 1, 'bad_primes': [3, 7, 11, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 117117, 'degree': 78653952, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.1636462296731768551060846344', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [1382084250541230782125, 19771083137421], 'lmfdb_iso': '117117.p', 'lmfdb_label': '117117.p1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3016803, -2017053000], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '546.6.0.?', '572.6.0.?', '924.6.0.?', '12012.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '14.212066875077559656791258466', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.6906280672429694573683464348', 'prec': 100}, 'szpiro_ratio': 6.7136129015628985, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, -1, 0, 0, -1, 3, 0, 0, -1, 0, 0, 1, 0, -1, -2, 0, -4, 0], 'aplist': [-1, 0, 0, -1, -1, 0, -2, -4, 8, 4, -8, -8, 2, -12, 2, -6, 10, 4, 10, 0, 6, -12, -12, -12, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 117117, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '117117.p', 'trace_hash': 184018487098771201}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00024182591278210948657519641787', 'prec': 113}, 'conductor': 117117, 'gens': [[143093805, 2014036880869, 76]], 'heights': [{'__RealLiteral__': 0, 'data': '14.212066875077559656791258466', 'prec': 100}], 'lmfdb_label': '117117.p1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.052732934731729686434410845970', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9977759797057697453920641279023464470', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[38997, -19499, 1]], 'xcoord_integral_points': [38997]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 1, 0], '7': [1, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [3, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '117117.p1'}
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ec_torsion_growth • Show schema
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id: 5368465
{'degree': 2, 'field': [-68, -1, 1], 'lmfdb_label': '117117.p1', 'torsion': [2, 2]}
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id: 5368466
{'degree': 4, 'field': [828, 32, -31, -2, 1], 'lmfdb_label': '117117.p1', 'torsion': [4]}
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id: 5368467
{'degree': 8, 'field': [-774752, -344944, 364652, -50248, -7343, 1486, -34, -2, 1], 'lmfdb_label': '117117.p1', 'torsion': [2, 4]}
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id: 5368469
{'degree': 8, 'field': [-2545, 13764, 6796, 2752, 405, 29, -22, -3, 1], 'lmfdb_label': '117117.p1', 'torsion': [6]}
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id: 5368468
{'degree': 8, 'field': [257104, -29596, 29056, -2981, 581, -158, 10, -1, 1], 'lmfdb_label': '117117.p1', 'torsion': [2, 4]}
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id: 5368471
{'degree': 16, 'field': [16780401, -35363922, -5134394, 27896717, -173729, -9718661, 4660265, 96601, -669099, 187752, -15759, 325, -433, 181, -23, -4, 1], 'lmfdb_label': '117117.p1', 'torsion': [2, 6]}
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id: 5368470
{'degree': 16, 'field': [175807698192, 126531334440, 97907372136, 42976908762, 15825606691, 4135126440, 777968312, 103970328, 6574348, 429506, 287848, 10616, -3860, 612, 52, -8, 1], 'lmfdb_label': '117117.p1', 'torsion': [8]}
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ec_localdata • Show schema
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id: 2882634
{'conductor': 117117, 'conductor_valuation': 2, 'discriminant_valuation': 19, 'j_denominator_valuation': 13, 'kodaira_symbol': -17, 'lmfdb_label': '117117.p1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 2882635
{'conductor': 117117, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '117117.p1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 2882636
{'conductor': 117117, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '117117.p1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 2882637
{'conductor': 117117, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '117117.p1', 'prime': 13, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 2429631
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [4006, 1, 4003, 0], [1, 4, 0, 1], [3005, 9010, 9008, 3003], [6866, 1, 8579, 0], [12009, 4, 12008, 5], [3700, 1, 11087, 0], [4369, 4, 8738, 9]], 'adelic_image': '12012.12.0.?', 'conductor': 117117, 'lmfdb_label': '117117.p1', 'prime': 0}
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id: 461850
{'conductor': 117117, 'elladic_image': '2.3.0.1', 'lmfdb_label': '117117.p1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 6118292
{'lmfdb_iso': '117117.p', 'p': 17, 'prec': 20, 'unit': 141477909578800204454866, 'val': 1}
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id: 6118284
{'lmfdb_iso': '117117.p', 'p': 19, 'prec': 20, 'unit': 1608587625589586272149, 'val': 3}
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id: 6118297
{'lmfdb_iso': '117117.p', 'p': 23, 'prec': 20, 'unit': 47826545809418288757196496, 'val': 1}
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id: 6118290
{'lmfdb_iso': '117117.p', 'p': 29, 'prec': 20, 'unit': 3592519852491848977731194500, 'val': 1}
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id: 6118301
{'lmfdb_iso': '117117.p', 'p': 31, 'prec': 20, 'unit': 17086199617677218798961055355, 'val': 1}
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id: 6118287
{'lmfdb_iso': '117117.p', 'p': 37, 'prec': 20, 'unit': 412150566409631431020951239633, 'val': 1}
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id: 6118288
{'lmfdb_iso': '117117.p', 'p': 41, 'prec': 20, 'unit': 357309316403982862387972967863, 'val': 1}
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id: 6118289
{'lmfdb_iso': '117117.p', 'p': 43, 'prec': 20, 'unit': 6694750364151834424016961270355, 'val': 1}
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id: 6118299
{'lmfdb_iso': '117117.p', 'p': 47, 'prec': 20, 'unit': 806389585351734505058880411945, 'val': 1}
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id: 6118294
{'lmfdb_iso': '117117.p', 'p': 53, 'prec': 20, 'unit': 411206400889087910773863716943920, 'val': 1}
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id: 6118295
{'lmfdb_iso': '117117.p', 'p': 59, 'prec': 20, 'unit': 2682663864189386110661576812850081, 'val': 1}
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id: 6118300
{'lmfdb_iso': '117117.p', 'p': 61, 'prec': 20, 'unit': 5038795404426351551105143760491528, 'val': 1}
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id: 6118286
{'lmfdb_iso': '117117.p', 'p': 67, 'prec': 20, 'unit': 32339963633649267947954986238568254, 'val': 1}
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id: 6118296
{'lmfdb_iso': '117117.p', 'p': 73, 'prec': 20, 'unit': 27952832801253648987586999517054865, 'val': 1}
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id: 6118291
{'lmfdb_iso': '117117.p', 'p': 79, 'prec': 20, 'unit': 667572118199132714150129105345235844, 'val': 1}
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id: 6118293
{'lmfdb_iso': '117117.p', 'p': 83, 'prec': 20, 'unit': 2700301396171844157948176178869367403, 'val': 1}
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id: 6118298
{'lmfdb_iso': '117117.p', 'p': 89, 'prec': 20, 'unit': 9174456766506863961265766234114579571, 'val': 1}
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id: 6118285
{'lmfdb_iso': '117117.p', 'p': 97, 'prec': 20, 'unit': 2612918928620475774035386486430313658, 'val': 1}