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ec_curvedata • Show schema
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{'Ciso': '68952k', 'Clabel': '68952k2', 'Cnumber': 2, 'abc_quality': 0.9332211540954428, 'absD': 31950540880128, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [0, -1, 0, -138636, 19912788], 'analytic_rank': 0, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 68952, 'degree': 344064, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6213039240798105208135029819', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2], 'jinv': [238481570896, 25857], 'lmfdb_iso': '68952.s', 'lmfdb_label': '68952.s1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -820, 9316], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '34.6.0.a.1', '52.6.0.c.1', '884.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.12326887502425472015806215319', 'prec': 107}, 'szpiro_ratio': 4.230475690862175, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -1, 0, 4, 0, -2, 0, 1, 0, 2, 0, 0, 0, -4, 0, 1, 0, 0, 0], 'aplist': [0, -1, 4, -2, 2, 0, 1, 0, 0, -6, -2, -4, -8, 4, 4, 2, -4, 6, 8, 6, -4, 12, 0, -2, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 68952, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '68952.s', 'trace_hash': 149572648102158850}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.039061894665858147796700690892', 'prec': 107}, 'conductor': 68952, 'gens': [], 'heights': [], 'lmfdb_label': '68952.s1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.63150992676303987090759249725', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5260397070521594836303699890114137691', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[217, 0, 1]], 'xcoord_integral_points': [217]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [0, 0], '13': 'a', '17': [3, 0]}, 'iwp0': 3, 'lmfdb_label': '68952.s1'}
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ec_torsion_growth • Show schema
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id: 3278641
{'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '68952.s1', 'torsion': [2, 2]}
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id: 3278642
{'degree': 4, 'field': [17, 0, -9, 0, 1], 'lmfdb_label': '68952.s1', 'torsion': [4]}
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id: 3278645
{'degree': 8, 'field': [-507, 0, -2600, 0, -78, 0, 0, 0, 1], 'lmfdb_label': '68952.s1', 'torsion': [6]}
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id: 3278644
{'degree': 8, 'field': [16, 0, -68, 0, 77, 0, -17, 0, 1], 'lmfdb_label': '68952.s1', 'torsion': [2, 4]}
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id: 3278643
{'degree': 8, 'field': [153664, 0, 57036, 0, 164, 0, -69, 0, 1], 'lmfdb_label': '68952.s1', 'torsion': [2, 4]}
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id: 3278646
{'degree': 16, 'field': [-964716, -5877728, -13502448, -15498176, -8757184, -711216, 2252416, 1411480, 282618, -52056, -39176, -6804, 988, 392, -54, -8, 1], 'lmfdb_label': '68952.s1', 'torsion': [8]}
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id: 3278647
{'degree': 16, 'field': [138753488, 81122944, -69279968, -24551296, 14214296, -1686840, -534356, 1000568, -323995, 46544, -7056, -688, -310, 168, -4, -8, 1], 'lmfdb_label': '68952.s1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 1668796
{'conductor': 68952, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '68952.s1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 1668797
{'conductor': 68952, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '68952.s1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1668798
{'conductor': 68952, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '68952.s1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 1668799
{'conductor': 68952, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '68952.s1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2120194
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [881, 4, 880, 5], [210, 1, 779, 0], [613, 4, 342, 9], [665, 222, 220, 663]], 'adelic_image': '884.12.0.?', 'conductor': 68952, 'lmfdb_label': '68952.s1', 'prime': 0}
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id: 287624
{'conductor': 68952, 'elladic_image': '2.3.0.1', 'lmfdb_label': '68952.s1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 68952.s does not appear in ec_padic