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ec_curvedata • Show schema
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{'Ciso': '6930bm', 'Clabel': '6930bm4', 'Cnumber': 4, 'abc_quality': 0.9486732153279479, 'absD': 2306391020010, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9240, 'ainvs': [1, -1, 1, 3208, -21931], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6930, 'degree': 16384, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0612472637001952242331415881', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 34, 'isogeny_degrees': [1, 2, 4], 'jinv': [5009866738631, 3163773690], 'lmfdb_iso': '6930.bi', 'lmfdb_label': '6930.bi4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 356, 812], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.2', '40.12.0.s.1', '60.12.0-4.c.1.1', '120.24.0.?', '616.12.0.?', '1848.24.0.?', '3080.24.0.?', '9240.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.51194111936614037853551896964', 'prec': 103}, 'szpiro_ratio': 4.051974649515786, '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, 1, 0, 1, 1, 0, 1, 1, 0, -6, 1, 0, 1, -2, 0, 4, 1], 'aplist': [1, 0, 1, 1, 1, -6, -2, 4, 8, -2, 4, -6, 6, -4, 8, -2, 12, -10, 16, 0, 10, -12, 16, -10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 6930, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '6930.bi', 'trace_hash': 1167297147063009897}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.11973257947330481545545850702', 'prec': 103}, 'conductor': 6930, 'gens': [], 'heights': [], 'lmfdb_label': '6930.bi4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.47069460765723961007811219296', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.7655568612579168806248975436625623164', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[27, -31, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [4, 1], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '6930.bi4'}
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ec_torsion_growth • Show schema
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id: 365022
{'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [4]}
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id: 365023
{'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [4]}
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id: 365021
{'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [2, 2]}
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id: 365024
{'degree': 4, 'field': [1, 0, 8, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [2, 4]}
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id: 365028
{'degree': 8, 'field': [-854, 1064, -1148, 167, -80, -7, 7, -4, 1], 'lmfdb_label': '6930.bi4', 'torsion': [6]}
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id: 365025
{'degree': 8, 'field': [76, -80, 744, -320, 56, -40, 4, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [2, 4]}
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id: 365026
{'degree': 8, 'field': [194481, 0, -17199, 0, 396, 0, -39, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [8]}
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id: 365027
{'degree': 8, 'field': [360000, 0, 35520, 0, 2134, 0, 64, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [8]}
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id: 365033
{'degree': 16, 'field': [-528413564, 2970901528, -2458882440, -974927020, 368242790, 133291854, -28697543, -12393440, 1774530, 819340, -102323, -31464, 3515, 770, -90, -8, 1], 'lmfdb_label': '6930.bi4', 'torsion': [12]}
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id: 365030
{'degree': 16, 'field': [27225, 0, 182028000, 0, 80547580, 0, 11768320, 0, 829166, 0, 57184, 0, 2636, 0, 64, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [2, 8]}
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id: 365029
{'degree': 16, 'field': [34596, -89280, 115200, -129600, 114316, -65840, 32000, -12480, 1821, -1240, 800, 80, 26, -40, 0, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [4, 4]}
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id: 365034
{'degree': 16, 'field': [11357500, 11935000, -9956100, -7353700, 12541850, -11702100, 5715325, -1640600, 523476, -86558, 29053, -7356, 2045, -406, 78, -8, 1], 'lmfdb_label': '6930.bi4', 'torsion': [12]}
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id: 365032
{'degree': 16, 'field': [104228236, 75237128, -37364740, -91015620, 85017590, -51204596, 23576557, -5961240, 1988680, -364110, 105877, -19564, 4565, -630, 110, -8, 1], 'lmfdb_label': '6930.bi4', 'torsion': [2, 6]}
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id: 365031
{'degree': 16, 'field': [43091532225, 0, 8137704960, 0, 1177799184, 0, 95340864, 0, 4776994, 0, 137728, 0, 3216, 0, 64, 0, 1], 'lmfdb_label': '6930.bi4', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 141847
{'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6930.bi4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 141848
{'conductor': 6930, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '6930.bi4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 141849
{'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6930.bi4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 141850
{'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6930.bi4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 141851
{'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6930.bi4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1709744
{'adelic_gens': [[5281, 6168, 5724, 6193], [5548, 3081, 8031, 6166], [9233, 8, 9232, 9], [1, 0, 8, 1], [5008, 393, 1953, 5080], [1, 8, 0, 1], [1, 4, 4, 17], [2521, 6168, 3924, 6193], [3079, 0, 0, 9239], [7, 6, 9234, 9235], [5776, 7323, 1929, 5038]], 'adelic_image': '9240.48.0.?', 'conductor': 6930, 'lmfdb_label': '6930.bi4', 'prime': 0}
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id: 34179
{'conductor': 6930, 'elladic_image': '4.6.0.1', 'lmfdb_label': '6930.bi4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 6930.bi does not appear in ec_padic