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ec_curvedata • Show schema
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{'Ciso': '112a', 'Clabel': '112a2', 'Cnumber': 2, 'abc_quality': 1.080363610213567, 'absD': 100352, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 56, 'ainvs': [0, 1, 0, -40, 84], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 112, 'degree': 16, 'elladic_images': ['8.6.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.23466883556014264871132483940', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [3543122, 49], 'lmfdb_iso': '112.a', 'lmfdb_label': '112.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -40, -84], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.b.1', '28.6.0.c.1', '56.12.0.k.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 15, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.11995994936260128800581988562', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.87005375107342584901045428407', 'prec': 107}, 'szpiro_ratio': 4.811940920794933, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -2, 0, -4, 0, -1, 0, 1, 0, 0, 0, 0, 0, 8, 0, -2, 0, 2, 0], 'aplist': [0, -2, -4, -1, 0, 0, -2, 2, -8, 2, -4, -6, -2, -8, 4, -10, -6, 4, 12, 0, -14, 8, -6, 10, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 112, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '112.a', 'trace_hash': 1890724171953078067}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.5989348217207118961257432505', 'prec': 100}, 'conductor': 112, 'gens': [[2, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.11995994936260128800581988562', 'prec': 103}], 'lmfdb_label': '112.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '3.3732121966451230056953422145', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.80930072859771602816480510307397366295', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[3, 0, 1]], 'xcoord_integral_points': [-6, -4, 2, 3, 4, 7, 10, 178]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 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': '112.a1'}
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ec_torsion_growth • Show schema
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id: 4074
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '112.a1', 'torsion': [2, 2]}
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id: 4075
{'degree': 4, 'field': [1, 1, 0, -1, 1], 'lmfdb_label': '112.a1', 'torsion': [4]}
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id: 4078
{'degree': 8, 'field': [-12, 0, 20, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '112.a1', 'torsion': [6]}
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id: 4076
{'degree': 8, 'field': [1, 0, -4, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '112.a1', 'torsion': [2, 4]}
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id: 4077
{'degree': 8, 'field': [4, 0, -6, 0, 1, 0, 4, 0, 1], 'lmfdb_label': '112.a1', 'torsion': [2, 4]}
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id: 4079
{'degree': 16, 'field': [4, 0, -14, 0, 39, 0, -63, 0, 61, 0, -42, 0, 23, 0, -7, 0, 1], 'lmfdb_label': '112.a1', 'torsion': [8]}
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id: 4080
{'degree': 16, 'field': [36, 0, -288, 0, 12, 0, -32, 0, 152, 0, 28, 0, 16, 0, -4, 0, 1], 'lmfdb_label': '112.a1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 715
{'conductor': 112, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '112.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 716
{'conductor': 112, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '112.a1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1666205
{'adelic_gens': [[1, 2, 2, 5], [17, 4, 34, 9], [2, 1, 27, 0], [3, 4, 8, 11], [9, 50, 48, 7], [53, 4, 52, 5], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '56.12.0.?', 'conductor': 112, 'lmfdb_label': '112.a1', 'prime': 0}
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id: 388
{'conductor': 112, 'elladic_image': '8.6.0.6', 'lmfdb_label': '112.a1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 424
{'lmfdb_iso': '112.a', 'p': 5, 'prec': 20, 'unit': 37984477193428, 'val': -1}
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id: 430
{'lmfdb_iso': '112.a', 'p': 17, 'prec': 20, 'unit': 174194067478295759127009, 'val': 1}
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id: 421
{'lmfdb_iso': '112.a', 'p': 19, 'prec': 20, 'unit': 661137538917056726171375, 'val': 1}
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id: 435
{'lmfdb_iso': '112.a', 'p': 23, 'prec': 20, 'unit': 11273122144536742889458787, 'val': 1}
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id: 428
{'lmfdb_iso': '112.a', 'p': 29, 'prec': 20, 'unit': 2104205731165485349719225571, 'val': 1}
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id: 425
{'lmfdb_iso': '112.a', 'p': 31, 'prec': 20, 'unit': 21539105763621372855048830204, 'val': 1}
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id: 439
{'lmfdb_iso': '112.a', 'p': 37, 'prec': 20, 'unit': 183931524006167284789695217952, 'val': 1}
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id: 426
{'lmfdb_iso': '112.a', 'p': 41, 'prec': 20, 'unit': 3727808753051774469353718092828, 'val': 1}
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id: 427
{'lmfdb_iso': '112.a', 'p': 43, 'prec': 20, 'unit': 7226144661833657218892077113266, 'val': 1}
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id: 437
{'lmfdb_iso': '112.a', 'p': 47, 'prec': 20, 'unit': 22576996644190223215881338971243, 'val': 1}
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id: 432
{'lmfdb_iso': '112.a', 'p': 53, 'prec': 20, 'unit': 427914532617135257590057206087736, 'val': 1}
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id: 433
{'lmfdb_iso': '112.a', 'p': 59, 'prec': 20, 'unit': 4209595933282475053680835937886440, 'val': 1}
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id: 438
{'lmfdb_iso': '112.a', 'p': 61, 'prec': 20, 'unit': 5862896775772134412249953163865009, 'val': 1}
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id: 423
{'lmfdb_iso': '112.a', 'p': 67, 'prec': 20, 'unit': 9629541596736810524005537894048584, 'val': 1}
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id: 434
{'lmfdb_iso': '112.a', 'p': 73, 'prec': 20, 'unit': 47551353958149397435539534717352861, 'val': 1}
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id: 429
{'lmfdb_iso': '112.a', 'p': 79, 'prec': 20, 'unit': 759802745789135532747809665530975317, 'val': 1}
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id: 431
{'lmfdb_iso': '112.a', 'p': 83, 'prec': 20, 'unit': 2125323855775877756639063933567428913, 'val': 1}
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id: 436
{'lmfdb_iso': '112.a', 'p': 89, 'prec': 20, 'unit': 9481833404202089192629834543744402399, 'val': 1}
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id: 422
{'lmfdb_iso': '112.a', 'p': 97, 'prec': 20, 'unit': 2770876994275904301377131288465769243, 'val': 1}