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ec_curvedata • Show schema
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{'Ciso': '258570z', 'Clabel': '258570z2', 'Cnumber': 2, 'abc_quality': 0.9018650734030914, 'absD': 9048374456232202650, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 8840, 'ainvs': [1, -1, 0, -104220, 145329250], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 258570, 'degree': 5111808, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3171422474416446489035611997', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2], 'jinv': [-16194277, 1170450], 'lmfdb_iso': '258570.z', 'lmfdb_label': '258570.z2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -68, -2478], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '104.6.0.?', '680.6.0.?', '4420.6.0.?', '8840.12.0.?'], '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': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15587591498856274883417699993', 'prec': 107}, 'szpiro_ratio': 4.101109906800617, '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, 0, 0, 0, 1, 1, 0, 2, -1], 'aplist': [-1, 0, -1, 0, 0, 0, 1, 2, 0, 8, -8, 6, -6, -4, 0, 12, -2, -8, 12, 0, -4, 6, -4, -4, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 258570, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '258570.z', 'trace_hash': 56054968661490407}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0097130542927005079509548740501', 'prec': 110}, 'conductor': 258570, 'gens': [], 'heights': [], 'lmfdb_label': '258570.z2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.19067625474486022928931835616', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5254100379588818343145468492849767289', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-2365, 2365, 2]], 'xcoord_integral_points': []}
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lmfdb_label 258570.z2 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 11087297
{'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '258570.z2', 'torsion': [2, 2]}
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id: 11087298
{'degree': 4, 'field': [-52650, 0, 195, 0, 1], 'lmfdb_label': '258570.z2', 'torsion': [4]}
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id: 11087299
{'degree': 8, 'field': [28224, 0, -15360, 0, 2776, 0, -32, 0, 1], 'lmfdb_label': '258570.z2', 'torsion': [2, 4]}
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id: 11087300
{'degree': 8, 'field': [181476, 0, 559524, 0, 21637, 0, -224, 0, 1], 'lmfdb_label': '258570.z2', 'torsion': [2, 4]}
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id: 11087301
{'degree': 8, 'field': [305280, -76128, -47888, 3120, 8040, -1456, -48, 0, 1], 'lmfdb_label': '258570.z2', 'torsion': [6]}
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id: 11087303
{'degree': 16, 'field': [5152754721024, 0, 10561602094056, 0, 509006518596, 0, 7664333664, 0, 7443000, 0, -275964, 0, 13264, 0, 234, 0, 1], 'lmfdb_label': '258570.z2', 'torsion': [2, 6]}
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id: 11087302
{'degree': 16, 'field': [250913710145536, 0, 69929939501056, 0, -8477713571840, 0, 317960955904, 0, -5050300736, 0, 16754704, 0, 101905, 0, -674, 0, 1], 'lmfdb_label': '258570.z2', 'torsion': [8]}
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ec_localdata • Show schema
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id: 6407513
{'conductor': 258570, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '258570.z2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 6407514
{'conductor': 258570, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '258570.z2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 6407515
{'conductor': 258570, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '258570.z2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 6407516
{'conductor': 258570, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '258570.z2', 'prime': 13, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 6407517
{'conductor': 258570, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '258570.z2', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 3302454
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [3316, 5529, 1105, 7736], [8837, 4, 8836, 5], [684, 1, 2039, 0], [3537, 4, 7074, 9], [2, 1, 4419, 0], [3641, 4, 7282, 9]], 'adelic_image': '8840.12.0.?', 'conductor': 258570, 'lmfdb_label': '258570.z2', 'prime': 0}
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id: 928701
{'conductor': 258570, 'elladic_image': '2.3.0.1', 'lmfdb_label': '258570.z2', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 258570.z does not appear in ec_padic