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ec_curvedata • Show schema
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{'Ciso': '67830i', 'Clabel': '67830i4', 'Cnumber': 4, 'abc_quality': 0.9830813961190478, 'absD': 2791475820, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 90440, 'ainvs': [1, 1, 0, -114247, 14815801], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 7, 17, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 67830, 'degree': 278528, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3549275100118203439005032214', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4], 'jinv': [164916483627583086841, 2791475820], 'lmfdb_iso': '67830.f', 'lmfdb_label': '67830.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -114247, 14815801], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '152.24.0.?', '2380.24.0.?', '90440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 14, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '6.5159765183762154304170954706', 'prec': 100}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3549275100118203439005032214', 'prec': 100}, 'szpiro_ratio': 4.184537146959702, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -4, -1, -2, 1, -1, 1, 1, -1, 1, 1], 'aplist': [-1, -1, 1, -1, -4, -2, 1, 1, -8, -6, 4, -10, -6, -4, -8, 2, 4, -2, 12, 0, 2, -8, 4, -2, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 67830, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '67830.f', 'trace_hash': 1314239891970658948}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.066546453918990221821306964624', 'prec': 107}, 'conductor': 67830, 'gens': [[76, 2527, 1], [201, 52, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0051436591289047611679316263', 'prec': 100}, {'__RealLiteral__': 0, 'data': '3.2526799445793490839161944530', 'prec': 100}], 'lmfdb_label': '67830.f1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '1.0250547216041655008818798512', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.6792324960234110980214244971678706416', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[190, 19, 1]], 'xcoord_integral_points': [-380, 76, 190, 195, 201, 285, 305]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [7, 0], '3': [2, 0], '5': [3, 0], '7': [2, 0], '11': [2, 0], '13': [2, 0], '17': [3, 0], '19': [3, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '67830.f1'}
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ec_torsion_growth • Show schema
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id: 3229570
{'degree': 2, 'field': [-595, 0, 1], 'lmfdb_label': '67830.f1', 'torsion': [2, 4]}
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id: 3229571
{'degree': 4, 'field': [21420, 0, -288, 0, 1], 'lmfdb_label': '67830.f1', 'torsion': [8]}
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id: 3229575
{'degree': 8, 'field': [-14746, 52909, -53044, 269, -131, -7, 7, -4, 1], 'lmfdb_label': '67830.f1', 'torsion': [12]}
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id: 3229573
{'degree': 8, 'field': [353749, -272444, 291404, -37652, 18157, 800, -262, -4, 1], 'lmfdb_label': '67830.f1', 'torsion': [2, 8]}
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id: 3229572
{'degree': 8, 'field': [1792921, -2678, 2, 5350, -2669, -10, 8, -4, 1], 'lmfdb_label': '67830.f1', 'torsion': [4, 4]}
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id: 3229574
{'degree': 8, 'field': [102701661841, 0, -790513496, 0, 2148926, 0, -2456, 0, 1], 'lmfdb_label': '67830.f1', 'torsion': [2, 8]}
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id: 3229576
{'degree': 16, 'field': [210512488908960000, 0, -11321680075776000, 0, 272669080723200, 0, -3769635542400, 0, 32359301100, 0, -175986720, 0, 594288, 0, -1152, 0, 1], 'lmfdb_label': '67830.f1', 'torsion': [16]}
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id: 3229577
{'degree': 16, 'field': [400397007141112326, 14608212461957622, -14363945068230191, -485794829139590, 236070906625840, 8126466828434, -2600346989671, -92122127578, 21963608345, 705165710, -134933455, -3305522, 532963, 8260, -1160, -8, 1], 'lmfdb_label': '67830.f1', 'torsion': [2, 12]}
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ec_localdata • Show schema
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id: 1641040
{'conductor': 67830, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '67830.f1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1641041
{'conductor': 67830, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '67830.f1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1641042
{'conductor': 67830, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '67830.f1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 1641043
{'conductor': 67830, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '67830.f1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 1641044
{'conductor': 67830, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '67830.f1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 1641045
{'conductor': 67830, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '67830.f1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2113016
{'adelic_gens': [[1, 0, 8, 1], [56528, 11313, 56553, 56600], [47884, 1, 26623, 6], [1, 8, 0, 1], [9521, 8, 38084, 33], [1, 4, 4, 17], [90433, 8, 90432, 9], [54268, 1, 18111, 6], [79139, 79138, 56538, 11315], [7, 6, 90434, 90435], [38764, 1, 64623, 6]], 'adelic_image': '90440.48.0.?', 'conductor': 67830, 'lmfdb_label': '67830.f1', 'prime': 0}
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id: 283523
{'conductor': 67830, 'elladic_image': '4.12.0.7', 'lmfdb_label': '67830.f1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 3468526
{'lmfdb_iso': '67830.f', 'p': 11, 'prec': 20, 'unit': 24912281080139792211, 'val': 2}
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id: 3468531
{'lmfdb_iso': '67830.f', 'p': 13, 'prec': 20, 'unit': 1002223325449575993358, 'val': 2}
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id: 3468537
{'lmfdb_iso': '67830.f', 'p': 23, 'prec': 20, 'unit': 59053781675632095593847207, 'val': 2}
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id: 3468530
{'lmfdb_iso': '67830.f', 'p': 29, 'prec': 20, 'unit': 2200580577635787931868260278, 'val': 2}
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id: 3468541
{'lmfdb_iso': '67830.f', 'p': 31, 'prec': 20, 'unit': 9905301425672215777539439001, 'val': 2}
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id: 3468527
{'lmfdb_iso': '67830.f', 'p': 37, 'prec': 20, 'unit': 239761122840062579638794738816, 'val': 2}
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id: 3468528
{'lmfdb_iso': '67830.f', 'p': 41, 'prec': 20, 'unit': 4069223956722394975289599013029, 'val': 2}
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id: 3468529
{'lmfdb_iso': '67830.f', 'p': 43, 'prec': 20, 'unit': 1423400903723495881076812847308, 'val': 2}
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id: 3468539
{'lmfdb_iso': '67830.f', 'p': 47, 'prec': 20, 'unit': 35098094613546411178705354369657, 'val': 2}
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id: 3468535
{'lmfdb_iso': '67830.f', 'p': 53, 'prec': 20, 'unit': 316321352503071260457155591017680, 'val': 2}
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id: 3468533
{'lmfdb_iso': '67830.f', 'p': 59, 'prec': 20, 'unit': 1674826783644080149053573328384115, 'val': 2}
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id: 3468540
{'lmfdb_iso': '67830.f', 'p': 61, 'prec': 20, 'unit': 3152898132903615545043756948992550, 'val': 2}
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id: 3468534
{'lmfdb_iso': '67830.f', 'p': 67, 'prec': 20, 'unit': 29749637391303624462505887475154938, 'val': 2}
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id: 3468536
{'lmfdb_iso': '67830.f', 'p': 73, 'prec': 20, 'unit': 54012407316251759424333894777339895, 'val': 2}
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id: 3468532
{'lmfdb_iso': '67830.f', 'p': 79, 'prec': 20, 'unit': 61996486453343550757383079858283321, 'val': 2}
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id: 3468525
{'lmfdb_iso': '67830.f', 'p': 83, 'prec': 20, 'unit': 532424646600997628564244797484212727, 'val': 2}
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id: 3468538
{'lmfdb_iso': '67830.f', 'p': 89, 'prec': 20, 'unit': 728676196672734874363849228815701039, 'val': 2}
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id: 3468524
{'lmfdb_iso': '67830.f', 'p': 97, 'prec': 20, 'unit': 7190058152769646780877379957297486869, 'val': 2}