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ec_curvedata • Show schema
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{'Ciso': '163170ep', 'Clabel': '163170ep2', 'Cnumber': 2, 'abc_quality': 1.014550807368251, 'absD': 18281912060953013760000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1036, 'ainvs': [1, -1, 0, -2495021895, 47969511801021], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 163170, 'degree': 90832896, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8435208861358795408597536094', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 24, 'isogeny_degrees': [1, 2], 'jinv': [58389789169255064704903, 621457920000], 'lmfdb_iso': '163170.y', 'lmfdb_label': '163170.y1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5657646, 5177308779], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '148.6.0.?', '1036.12.0.?'], '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': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8347821300103397163331164334', 'prec': 100}, 'szpiro_ratio': 6.375837348546205, '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, 0, -1, 0, 1, 0, 0, 6, 0, 0, 1, 2, 0, 6, -1], 'aplist': [-1, 0, -1, 0, 0, 6, 2, 6, 8, 6, 10, 1, 0, 4, -12, 6, -2, 10, -8, 0, 4, -16, -4, -6, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 163170, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '163170.y', 'trace_hash': 1633335955708882601}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00045873320378350092200772142136', 'prec': 113}, 'conductor': 163170, 'gens': [], 'heights': [], 'lmfdb_label': '163170.y1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.085899216543479182235999535250', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7487749293913338315519851279912098950', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[115347, -115347, 2]], 'xcoord_integral_points': []}
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lmfdb_label 163170.y1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 7289886
{'degree': 2, 'field': [-259, 0, 1], 'lmfdb_label': '163170.y1', 'torsion': [2, 2]}
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id: 7289887
{'degree': 4, 'field': [604, 10, -46, -1, 1], 'lmfdb_label': '163170.y1', 'torsion': [4]}
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id: 7289890
{'degree': 8, 'field': [734203, 289252, 5371, 5282, 3002, -220, -89, -2, 1], 'lmfdb_label': '163170.y1', 'torsion': [6]}
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id: 7289888
{'degree': 8, 'field': [863172, 21744, -23280, -5364, 673, 50, -10, -2, 1], 'lmfdb_label': '163170.y1', 'torsion': [2, 4]}
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id: 7289889
{'degree': 8, 'field': [63282025, 0, -3652492, 0, 5883, 0, -148, 0, 1], 'lmfdb_label': '163170.y1', 'torsion': [2, 4]}
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id: 7289891
{'degree': 16, 'field': [35694976, -137947648, 249511680, -207999488, 57544176, 44810592, -9611480, 395512, 2852160, 364088, -74090, 7398, 6021, -82, -135, -2, 1], 'lmfdb_label': '163170.y1', 'torsion': [8]}
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id: 7289892
{'degree': 16, 'field': [623042258066820, -426172475032452, -46677708466242, 63788408374758, -3235230518271, -2471456272368, 583384057662, -42113538, -10667428634, 950028518, 31196674, -9174692, 363086, 14938, -1136, -4, 1], 'lmfdb_label': '163170.y1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 4038686
{'conductor': 163170, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '163170.y1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 4038687
{'conductor': 163170, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '163170.y1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 4038688
{'conductor': 163170, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '163170.y1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 4038689
{'conductor': 163170, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '163170.y1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 4038690
{'conductor': 163170, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '163170.y1', 'prime': 37, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2719184
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [226, 1, 923, 0], [1, 4, 0, 1], [260, 781, 777, 260], [1033, 4, 1032, 5], [152, 1, 739, 0]], 'adelic_image': '1036.12.0.?', 'conductor': 163170, 'lmfdb_label': '163170.y1', 'prime': 0}
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id: 620438
{'conductor': 163170, 'elladic_image': '2.3.0.1', 'lmfdb_label': '163170.y1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 163170.y does not appear in ec_padic