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ec_curvedata • Show schema
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{'Ciso': '24a', 'Clabel': '24a5', 'Cnumber': 5, 'abc_quality': 1.2105879594055395, 'absD': 18432, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 48, 'ainvs': [0, -1, 0, -384, -2772], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 24, 'degree': 4, 'elladic_images': ['16.96.0.135'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.047794894480088036758221444632', 'prec': 107}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [3065617154, 9], 'lmfdb_iso': '24.a', 'lmfdb_label': '24.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -384, -2772], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.48.0-8.r.1.6', '16.96.0-16.l.1.6', '24.96.0-24.bf.1.4', '48.192.1-48.bv.1.4'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, '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': '-0.58759002103319516354090800004', 'prec': 107}, 'szpiro_ratio': 9.272383446160896, '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, -2, 0, 0, 0, 1, 0, 4, 0, -2, 0, 2, 0, 2, 0, -4, 0], 'aplist': [0, -1, -2, 0, 4, -2, 2, -4, -8, 6, 8, 6, -6, 4, 0, -2, 4, -2, -4, 8, 10, -8, -4, -6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 24, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '24.a', 'trace_hash': 906478665263567321}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.90883675448285972014062333356', 'prec': 103}, 'conductor': 24, 'gens': [], 'heights': [], 'lmfdb_label': '24.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0782578237498216177193374994', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.53912891187491080885966874970005048289', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[-11, 0, 1]], 'xcoord_integral_points': [-11]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '24.a1'}
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ec_torsion_growth • Show schema
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id: 544
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 2]}
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id: 546
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [4]}
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id: 545
{'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [4]}
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id: 547
{'degree': 4, 'field': [-18, 0, 0, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 4]}
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id: 551
{'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [8]}
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id: 548
{'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 4]}
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id: 549
{'degree': 4, 'field': [2, 0, 0, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [8]}
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id: 550
{'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [8]}
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id: 556
{'degree': 8, 'field': [-3, 0, 4, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [6]}
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id: 554
{'degree': 8, 'field': [1, 0, -4, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 8]}
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id: 553
{'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 8]}
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id: 555
{'degree': 8, 'field': [36, 0, 36, 0, 6, 0, -6, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [16]}
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id: 552
{'degree': 8, 'field': [81, 0, -108, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [4, 4]}
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id: 564
{'degree': 16, 'field': [1, -4, 6, -10, 28, -30, 24, -36, 60, -36, 24, -30, 28, -10, 6, -4, 1], 'lmfdb_label': '24.a1', 'torsion': [12]}
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id: 558
{'degree': 16, 'field': [1, 0, -4, 0, 8, 0, -24, 0, 47, 0, -24, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [4, 8]}
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id: 562
{'degree': 16, 'field': [4, 0, -40, 0, 28, 0, -32, 0, 56, 0, -20, 0, -8, 0, 2, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 6]}
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id: 563
{'degree': 16, 'field': [4, 0, 40, 0, 28, 0, 32, 0, 56, 0, 20, 0, -8, 0, -2, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [12]}
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id: 561
{'degree': 16, 'field': [25, -220, 972, -2780, 5736, -9024, 11224, -11276, 9297, -6328, 3580, -1668, 642, -196, 48, -8, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 16]}
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id: 560
{'degree': 16, 'field': [81, 0, 0, 0, -108, 0, 0, 0, 135, 0, 0, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 16]}
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id: 557
{'degree': 16, 'field': [196, 0, -3552, 0, 5296, 0, -2112, 0, -12, 0, -240, 0, -8, 0, 0, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 8]}
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id: 559
{'degree': 16, 'field': [324, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '24.a1', 'torsion': [2, 16]}
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ec_localdata • Show schema
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id: 66
{'conductor': 24, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '24.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 67
{'conductor': 24, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '24.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1665922
{'adelic_gens': [[15, 2, 46, 35], [33, 16, 32, 17], [19, 16, 6, 37], [5, 4, 44, 45], [1, 0, 16, 1], [4, 37, 39, 34], [1, 16, 0, 1], [29, 16, 16, 21]], 'adelic_image': '48.192.1.?', 'conductor': 24, 'lmfdb_label': '24.a1', 'prime': 0}
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id: 44
{'conductor': 24, 'elladic_image': '16.96.0.135', 'lmfdb_label': '24.a1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 24.a does not appear in ec_padic