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ec_curvedata • Show schema
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{'Ciso': '42a', 'Clabel': '42a5', 'Cnumber': 5, 'abc_quality': 1.0530860389430399, 'absD': 933897762, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 112, 'ainvs': [1, 1, 1, -914, -10915], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 32, 'elladic_images': ['8.96.0.164'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.53567478369769316355008711520', 'prec': 103}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [84448510979617, 933897762], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -914, -10915], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.96.0-8.p.1.4', '112.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.53567478369769316355008711520', 'prec': 103}, 'szpiro_ratio': 8.57945361735277, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, -1, 1, -2, -1, -1, 1, 1, -2, -4, -1, 6, -1, 2, 1, 2, 1, -4, -2], 'aplist': [1, -1, -2, -1, -4, 6, 2, -4, 8, -2, 0, -10, -6, -4, 0, 6, 4, 6, 4, 8, 10, 0, -4, -6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 42, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '42.a', 'trace_hash': 1611795495172191507}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.34254591653300727379612239776', 'prec': 103}, 'conductor': 42, 'gens': [], 'heights': [], 'lmfdb_label': '42.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.86886186437420487794429665753', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.86886186437420487794429665753039351028', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[-77, 73, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 2], '3': [0, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '42.a2'}
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ec_torsion_growth • Show schema
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id: 1305
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [2, 2]}
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id: 1307
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [8]}
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id: 1306
{'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [4]}
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id: 1308
{'degree': 4, 'field': [-2, 0, 0, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [2, 4]}
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id: 1309
{'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [2, 8]}
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id: 1310
{'degree': 4, 'field': [2, 0, 0, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [8]}
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id: 1312
{'degree': 8, 'field': [-162, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [2, 8]}
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id: 1314
{'degree': 8, 'field': [-4, 16, -16, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '42.a2', 'torsion': [6]}
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id: 1311
{'degree': 8, 'field': [1, 0, -4, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [4, 8]}
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id: 1313
{'degree': 8, 'field': [1296, 0, -216, 0, 18, 0, -6, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [16]}
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id: 1319
{'degree': 16, 'field': [-1528, 5872, -164, -11320, 5258, 1272, -2663, 3512, -2344, 266, 477, -76, -139, 42, 14, -8, 1], 'lmfdb_label': '42.a2', 'torsion': [2, 6]}
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id: 1321
{'degree': 16, 'field': [16, 0, 128, 0, 256, 0, -39, 0, -102, 0, 33, 0, 1, 0, 2, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [24]}
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id: 1318
{'degree': 16, 'field': [64, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [16]}
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id: 1320
{'degree': 16, 'field': [984, 4368, -2020, -10744, 23126, -29288, 25033, -17480, 10956, -6246, 3381, -1532, 589, -182, 46, -8, 1], 'lmfdb_label': '42.a2', 'torsion': [12]}
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id: 1317
{'degree': 16, 'field': [20164, 51120, 67128, 53312, 23688, 880, -5788, -6136, -2379, 196, 732, -20, -16, -4, 8, -4, 1], 'lmfdb_label': '42.a2', 'torsion': [2, 16]}
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id: 1315
{'degree': 16, 'field': [25921, -23184, 10368, 22608, 1948, -1440, 10368, 1440, -318, 720, 0, -144, 4, 0, 0, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [8, 8]}
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id: 1316
{'degree': 16, 'field': [104976, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '42.a2', 'torsion': [2, 16]}
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ec_localdata • Show schema
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id: 184
{'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42.a2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 185
{'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '42.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 186
{'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '42.a2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1665970
{'adelic_gens': [[1, 0, 16, 1], [1, 16, 0, 1], [15, 2, 14, 99], [92, 89, 59, 58], [17, 16, 24, 17], [55, 16, 94, 105], [5, 4, 108, 109], [97, 16, 96, 17]], 'adelic_image': '112.192.1.?', 'conductor': 42, 'lmfdb_label': '42.a2', 'prime': 0}
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id: 103
{'conductor': 42, 'elladic_image': '8.96.0.164', 'lmfdb_label': '42.a2', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 42.a does not appear in ec_padic