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ec_curvedata • Show schema
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{'Ciso': '21a', 'Clabel': '21a1', 'Cnumber': 1, 'abc_quality': 1.1486166056524132, 'absD': 3969, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 168, 'ainvs': [1, 0, 0, -4, -1], 'analytic_rank': 0, 'bad_primes': [3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21, 'degree': 1, 'elladic_images': ['8.48.0.24'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.61894179716900553865896626679', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [7189057, 3969], 'lmfdb_iso': '21.a', 'lmfdb_label': '21.a5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -4, -1], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '8.48.0-8.e.2.2', '24.96.0-24.w.2.6', '28.48.0-28.c.1.1', '56.96.0-56.i.1.1', '168.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 1], [3, 4, 7], [7, 8, 3]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61894179716900553865896626679', 'prec': 107}, 'szpiro_ratio': 5.185729745687264, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 1, -1, -2, -1, -1, 3, 1, 2, 4, -1, -2, 1, -2, -1, -6, -1, 4, 2], 'aplist': [-1, 1, -2, -1, 4, -2, -6, 4, 0, -2, 0, 6, 2, -4, 0, 6, 12, -2, 4, 0, -6, -16, -12, -14, 18], 'class_deg': 8, 'class_size': 6, 'conductor': 21, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '21.a', 'trace_hash': 1161919666425559947}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '3.4483077185485079225446290684', 'prec': 100}, 'conductor': 21, 'gens': [], 'heights': [], 'lmfdb_label': '21.a5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.6089232431079364447472012512', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.45111540538849205559340015640263020881', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-2, 1, 1], [5, 8, 1]], 'xcoord_integral_points': [-2, -1, 2, 5]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 0], '3': [1, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '21.a5'}
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ec_torsion_growth • Show schema
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id: 400
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '21.a5', 'torsion': [2, 8]}
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id: 402
{'degree': 4, 'field': [1, 0, -5, 0, 1], 'lmfdb_label': '21.a5', 'torsion': [2, 8]}
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id: 401
{'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '21.a5', 'torsion': [4, 4]}
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id: 405
{'degree': 8, 'field': [-3, 0, -1, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '21.a5', 'torsion': [2, 12]}
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id: 404
{'degree': 8, 'field': [1, 0, 2, 0, 0, 0, -1, 0, 1], 'lmfdb_label': '21.a5', 'torsion': [2, 16]}
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id: 403
{'degree': 8, 'field': [16, 0, 12, 0, 5, 0, 3, 0, 1], 'lmfdb_label': '21.a5', 'torsion': [4, 8]}
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id: 408
{'degree': 16, 'field': [1, 0, -20, 0, 7, 0, 28, 0, 49, 0, 28, 0, 7, 0, -20, 0, 1], 'lmfdb_label': '21.a5', 'torsion': [2, 16]}
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id: 409
{'degree': 16, 'field': [9, 0, -3, 0, -17, 0, -6, 0, 39, 0, -2, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '21.a5', 'torsion': [2, 24]}
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id: 407
{'degree': 16, 'field': [16, 0, 0, 0, -24, 0, 0, 0, 73, 0, 0, 0, 15, 0, 0, 0, 1], 'lmfdb_label': '21.a5', 'torsion': [4, 8]}
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id: 406
{'degree': 16, 'field': [256, 0, 0, 0, -752, 0, 0, 0, 600, 0, 0, 0, -47, 0, 0, 0, 1], 'lmfdb_label': '21.a5', 'torsion': [4, 8]}
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ec_localdata • Show schema
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id: 46
{'conductor': 21, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '21.a5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 47
{'conductor': 21, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21.a5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1665920
{'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [7, 6, 66, 163], [161, 8, 160, 9], [5, 4, 164, 165], [5, 132, 162, 35], [113, 4, 0, 1], [89, 48, 36, 77]], 'adelic_image': '168.192.1.?', 'conductor': 21, 'lmfdb_label': '21.a5', 'prime': 0}
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id: 42
{'conductor': 21, 'elladic_image': '8.48.0.24', 'lmfdb_label': '21.a5', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 21.a does not appear in ec_padic
