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ec_curvedata • Show schema
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{'Ciso': '78400v', 'Clabel': '78400v1', 'Cnumber': 1, 'abc_quality': 0.9802957926219806, 'absD': 1404928000000, 'ainvs': [0, 0, 0, -3500, -98000], 'analytic_rank': 2, 'bad_primes': [2, 5, 7], 'class_deg': 14, 'class_size': 4, 'cm': -7, 'conductor': 78400, 'degree': 73728, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0453013380013457343019161391', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 130, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [-3375, 1], 'lmfdb_iso': '78400.fa', 'lmfdb_label': '78400.fa4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -2, -1], 'min_quad_twist_disc': 40, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 11, 'optimality': 1, 'potential_good_reduction': True, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '8.3038836606010522259232263775', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 175], [5, 14, 3136], [7, 20, 1600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2856159263194507434006498956', 'prec': 103}, 'szpiro_ratio': 3.2395700304745643, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, 0, 0, -4, 0, 0, 0, -8, -2, 0, -6, 0, -12, 0, -10, 0, 0, 4, 16, 0, 8, 0, 0, 0], 'class_deg': 14, 'class_size': 4, 'conductor': 78400, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '78400.fa', 'trace_hash': 1481772271088705487}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.12361261500706366841245492420', 'prec': 103}, 'conductor': 78400, 'gens': [[120, 1100, 1], [84, 448, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.7453248339773072582000452587', 'prec': 100}, {'__RealLiteral__': 0, 'data': '3.1195671664762486631391335670', 'prec': 100}], 'lmfdb_label': '78400.fa4', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.30568342084070347041007275619', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.153438254543010845470511393163920654', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[70, 0, 1]], 'xcoord_integral_points': [70, 84, 120, 294, 870, 1645]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [4, 2, 0], '5': 'a', '7': 'a', '11': [2, 0], '13': [2, 2, 0], '17': [2, 2, 0], '19': [2, 4, 0], '23': [2, 0], '29': [2, 0], '31': [2, 2, 0], '37': [2, 0], '41': [2, 2, 0], '43': [2, 0], '47': [2, 2, 0]}, 'iwp0': 0, 'lmfdb_label': '78400.fa4'}
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ec_torsion_growth • Show schema
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id: 3699843
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 2]}
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id: 3699844
{'degree': 4, 'field': [-175, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [4]}
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id: 3699845
{'degree': 4, 'field': [700, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 4]}
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id: 3699846
{'degree': 6, 'field': [7000, 0, 1400, 0, 70, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [14]}
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id: 3699849
{'degree': 8, 'field': [-1470000, 0, 147000, 0, -4200, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [6]}
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id: 3699847
{'degree': 8, 'field': [30276, 0, 2104, 0, -344, 0, 4, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [4, 4]}
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id: 3699848
{'degree': 8, 'field': [37249, 0, -6002, 0, 570, 0, -34, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 8]}
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id: 3699850
{'degree': 12, 'field': [1000000, 0, 100000, 0, 10000, 0, 1000, 0, 100, 0, 10, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 14]}
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id: 3699851
{'degree': 16, 'field': [5636, -18136, 1524, 30320, -7422, -10632, 5734, -1532, -555, 1344, -854, 132, 160, -112, 36, -8, 1], 'lmfdb_label': '78400.fa4', 'torsion': [8]}
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id: 3699852
{'degree': 16, 'field': [7890481, 0, 0, 0, 110177, 0, 0, 0, -3936, 0, 0, 0, -47, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [4, 8]}
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id: 3699853
{'degree': 16, 'field': [288898009, 0, -172987350, 0, 45358259, 0, -7020922, 0, 716270, 0, -49526, 0, 2291, 0, -66, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 16]}
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id: 3699854
{'degree': 16, 'field': [2160900000000, 0, 216090000000, 0, 15435000000, 0, 617400000, 0, 19110000, 0, 294000, 0, 4200, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [6, 6]}
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id: 3699855
{'degree': 20, 'field': [1848770000000000, 0, 0, 0, 5282200000000, 0, 0, 0, 3773000000, 0, -68600000, 0, 3920000, 0, 98000, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '78400.fa4', 'torsion': [2, 22]}
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ec_localdata • Show schema
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id: 1907907
{'conductor': 78400, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '78400.fa4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 1907908
{'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '78400.fa4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 1907909
{'conductor': 78400, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '78400.fa4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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lmfdb_label 78400.fa4 does not appear in ec_galrep
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ec_padic • Show schema
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id: 4036717
{'lmfdb_iso': '78400.fa', 'p': 11, 'prec': 20, 'unit': 35679361905533204654, 'val': 2}
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id: 4036719
{'lmfdb_iso': '78400.fa', 'p': 23, 'prec': 20, 'unit': 38368826457217918954255383, 'val': 2}
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id: 4036720
{'lmfdb_iso': '78400.fa', 'p': 29, 'prec': 20, 'unit': 335613865694526179580200966, 'val': 2}
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id: 4036713
{'lmfdb_iso': '78400.fa', 'p': 37, 'prec': 20, 'unit': 175161545738592744098807154873, 'val': 2}
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id: 4036715
{'lmfdb_iso': '78400.fa', 'p': 43, 'prec': 20, 'unit': 9460614565682704932049125337997, 'val': 2}
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id: 4036718
{'lmfdb_iso': '78400.fa', 'p': 53, 'prec': 20, 'unit': 489972216093277609206541162891041, 'val': 2}
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id: 4036712
{'lmfdb_iso': '78400.fa', 'p': 67, 'prec': 20, 'unit': 3834954619107892587517883220129735, 'val': 2}
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id: 4036714
{'lmfdb_iso': '78400.fa', 'p': 71, 'prec': 20, 'unit': 127429817149241793996271655870489947, 'val': 2}
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id: 4036716
{'lmfdb_iso': '78400.fa', 'p': 79, 'prec': 20, 'unit': 671701800899557995101901736702872366, 'val': 2}