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ec_curvedata • Show schema
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{'Ciso': '73920u', 'Clabel': '73920u3', 'Cnumber': 3, 'abc_quality': 1.0118957830023507, 'absD': 2332411677377569751040, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3080, 'ainvs': [0, -1, 0, -1394401, 2408941921], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 73920, 'degree': 3932160, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7830099993999153368152586089', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 41, 'isogeny_degrees': [1, 2, 4], 'jinv': [-1143792273008057401, 8897444448004035], 'lmfdb_iso': '73920.bp', 'lmfdb_label': '73920.bp3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -21788, 4702241], '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.1.3', '70.6.0.a.1', '88.24.0.?', '140.12.0.?', '280.24.0.?', '3080.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.9441313998170435493747701839', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7432892285599973726894104267', 'prec': 100}, 'szpiro_ratio': 5.060118516074622, '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, -1, 0, 1, 0, 1, 0, 1, 0, -6, 0, 1, 0, 2, 0, -4, 0], 'aplist': [0, -1, -1, 1, 1, -6, 2, -4, -4, 2, 4, 2, 6, -4, 8, 2, 8, -10, 8, 0, -14, -16, 4, -6, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 73920, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '73920.bp', 'trace_hash': 607812055791198195}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0038256763691506973003355548834', 'prec': 110}, 'conductor': 73920, 'gens': [[255, 45496, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9441313998170435493747701839', 'prec': 100}], 'lmfdb_label': '73920.bp3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12482567756117080012390658042', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.4100383617353685259332326147767329156', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-1681, 0, 1]], 'xcoord_integral_points': [-1681, 255]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [2, 0], '11': [6, 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, 0]}, 'iwp0': 0, 'lmfdb_label': '73920.bp3'}
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ec_torsion_growth • Show schema
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id: 3495257
{'degree': 2, 'field': [-70, 0, 1], 'lmfdb_label': '73920.bp3', 'torsion': [4]}
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id: 3495258
{'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '73920.bp3', 'torsion': [4]}
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id: 3495256
{'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '73920.bp3', 'torsion': [2, 2]}
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id: 3495259
{'degree': 4, 'field': [51, -22, 23, -2, 1], 'lmfdb_label': '73920.bp3', 'torsion': [2, 4]}
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id: 3495263
{'degree': 8, 'field': [-48, 0, -104, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '73920.bp3', 'torsion': [6]}
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id: 3495260
{'degree': 8, 'field': [81, 0, 52, 0, 19, 0, -2, 0, 1], 'lmfdb_label': '73920.bp3', 'torsion': [2, 4]}
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id: 3495262
{'degree': 8, 'field': [100, 0, 8, 0, -4, 0, 8, 0, 1], 'lmfdb_label': '73920.bp3', 'torsion': [8]}
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id: 3495261
{'degree': 8, 'field': [58081, 0, -11708, 0, 1634, 0, -92, 0, 1], 'lmfdb_label': '73920.bp3', 'torsion': [8]}
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id: 3495269
{'degree': 16, 'field': [1369, 0, 10486, 0, 7045, 0, 3492, 0, 1290, 0, 522, 0, 100, 0, 16, 0, 1], 'lmfdb_label': '73920.bp3', 'torsion': [12]}
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id: 3495264
{'degree': 16, 'field': [22801, -36844, 29768, -28772, 22278, -7592, 1336, 1124, -2777, 1672, -536, 116, 78, -76, 32, -8, 1], 'lmfdb_label': '73920.bp3', 'torsion': [4, 4]}
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id: 3495266
{'degree': 16, 'field': [65241, -295416, 788140, -392960, 147390, -105680, 112, 18976, 4823, 480, -680, 560, 34, -24, 4, 0, 1], 'lmfdb_label': '73920.bp3', 'torsion': [2, 8]}
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id: 3495267
{'degree': 16, 'field': [30774009, -31922520, 50353772, -41428240, 32675090, -15925112, 8054656, -2613752, 994275, -252840, 77232, -15896, 3802, -560, 100, -8, 1], 'lmfdb_label': '73920.bp3', 'torsion': [2, 6]}
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id: 3495265
{'degree': 16, 'field': [151455236, -65473880, 95756908, -64001976, 40803862, -11104456, 4439386, -314348, -298155, 219232, -13042, -15388, 1412, 504, -52, -8, 1], 'lmfdb_label': '73920.bp3', 'torsion': [2, 8]}
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id: 3495268
{'degree': 16, 'field': [2389547689, 0, -722649620, 0, 48695368, 0, -904448, 0, 52270, 0, -14468, 0, 85, 0, 4, 0, 1], 'lmfdb_label': '73920.bp3', 'torsion': [12]}
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ec_localdata • Show schema
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id: 1792475
{'conductor': 73920, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '73920.bp3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 1792476
{'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '73920.bp3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1792477
{'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '73920.bp3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 1792478
{'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '73920.bp3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 1792479
{'conductor': 73920, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '73920.bp3', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
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ec_galrep • Show schema
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id: 2152082
{'adelic_gens': [[2644, 1, 1343, 6], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [2521, 8, 844, 33], [381, 382, 1142, 2685], [2699, 2696, 1178, 2701], [2468, 1, 1871, 6], [3073, 8, 3072, 9], [7, 6, 3074, 3075]], 'adelic_image': '3080.48.0.?', 'conductor': 73920, 'lmfdb_label': '73920.bp3', 'prime': 0}
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id: 305673
{'conductor': 73920, 'elladic_image': '8.12.0.7', 'lmfdb_label': '73920.bp3', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 3796580
{'lmfdb_iso': '73920.bp', 'p': 13, 'prec': 20, 'unit': 1221415007779446927997, 'val': 1}
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id: 3796582
{'lmfdb_iso': '73920.bp', 'p': 17, 'prec': 20, 'unit': 135762061688391452136896, 'val': 1}
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id: 3796583
{'lmfdb_iso': '73920.bp', 'p': 19, 'prec': 20, 'unit': 307243432823725529741347, 'val': 1}
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id: 3796587
{'lmfdb_iso': '73920.bp', 'p': 23, 'prec': 20, 'unit': 28207191929745117080655362, 'val': 1}
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id: 3796579
{'lmfdb_iso': '73920.bp', 'p': 29, 'prec': 20, 'unit': 4556645654255391749555913476, 'val': 1}
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id: 3796591
{'lmfdb_iso': '73920.bp', 'p': 31, 'prec': 20, 'unit': 13531389804239684822748833387, 'val': 1}
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id: 3796576
{'lmfdb_iso': '73920.bp', 'p': 37, 'prec': 20, 'unit': 182946106229339076157042305451, 'val': 1}
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id: 3796577
{'lmfdb_iso': '73920.bp', 'p': 41, 'prec': 20, 'unit': 2373859930145415044573686347438, 'val': 1}
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id: 3796578
{'lmfdb_iso': '73920.bp', 'p': 43, 'prec': 20, 'unit': 6644454528938978521001183017233, 'val': 1}
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id: 3796589
{'lmfdb_iso': '73920.bp', 'p': 47, 'prec': 20, 'unit': 15434380385056437115948359623512, 'val': 1}
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id: 3796584
{'lmfdb_iso': '73920.bp', 'p': 53, 'prec': 20, 'unit': 319125515143857438288736526521017, 'val': 1}
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id: 3796585
{'lmfdb_iso': '73920.bp', 'p': 59, 'prec': 20, 'unit': 2573732851980184347285627996753491, 'val': 1}
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id: 3796590
{'lmfdb_iso': '73920.bp', 'p': 61, 'prec': 20, 'unit': 4228446612336098266026705728898998, 'val': 1}
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id: 3796575
{'lmfdb_iso': '73920.bp', 'p': 67, 'prec': 20, 'unit': 46335465741175762970024133478810280, 'val': 1}
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id: 3796586
{'lmfdb_iso': '73920.bp', 'p': 73, 'prec': 20, 'unit': 47894963488993032603622245625593772, 'val': 1}
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id: 3796581
{'lmfdb_iso': '73920.bp', 'p': 79, 'prec': 20, 'unit': 239801724455629896405236907215212004, 'val': 1}
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id: 3796574
{'lmfdb_iso': '73920.bp', 'p': 83, 'prec': 20, 'unit': 180239813604322477444654028696686623, 'val': 1}
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id: 3796588
{'lmfdb_iso': '73920.bp', 'p': 89, 'prec': 20, 'unit': 1678251875292897801533900889173868986, 'val': 1}
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id: 3796573
{'lmfdb_iso': '73920.bp', 'p': 97, 'prec': 20, 'unit': 38181565295368733315996411760309374519, 'val': 1}