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ec_curvedata • Show schema
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{'Ciso': '1200p', 'Clabel': '1200p5', 'Cnumber': 5, 'abc_quality': 1.0339287621454463, 'absD': 340122240000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, 1, 0, -27408, 1495188], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 1200, 'degree': 4608, 'elladic_images': ['4.12.0.7', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5127259776592923313092314912', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 4, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [35578826569, 5314410], 'lmfdb_iso': '1200.k', 'lmfdb_label': '1200.k5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -69, -194], 'min_quad_twist_disc': -20, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.12.0-4.c.1.1', '6.12.0.a.1', '12.48.0-12.g.1.1', '24.192.1-24.dj.4.13', '40.24.0-40.v.1.3', '60.96.0-60.c.4.9', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 19, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.44811768362898181507347265555', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703129', 'prec': 107}, 'szpiro_ratio': 5.961770395294205, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 0, 0, -4, 0, 1, 0, 0, 0, -2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 1, 0, -4, 0, -2, -6, 4, 0, -6, -8, -2, -6, -4, 0, 6, 0, -10, -4, 0, -2, -8, 12, 18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 1200, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '1200.k', 'trace_hash': 1060515526536690942}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.048535880262978992387393752081', 'prec': 107}, 'conductor': 1200, 'gens': [[42, 648, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.44811768362898181507347265555', 'prec': 103}], 'lmfdb_label': '1200.k5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.51804870109955817783027952757', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7857614073248413034447420955686775507', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-12, 1350, 1]], 'xcoord_integral_points': [-166, -102, -12, 42, 63, 123, 138, 204, 348, 1338]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': [1, 0], '11': [1, 3, 0], '13': [1, 0], '17': [3, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1200.k5'}
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ec_torsion_growth • Show schema
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id: 59571
{'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [2, 4]}
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id: 59572
{'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [12]}
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id: 59573
{'degree': 4, 'field': [6, -6, 1, -1, 1], 'lmfdb_label': '1200.k5', 'torsion': [8]}
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id: 59574
{'degree': 4, 'field': [9, 0, -4, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [2, 12]}
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id: 59575
{'degree': 6, 'field': [-15, 0, -5, 0, -5, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [12]}
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id: 59579
{'degree': 8, 'field': [6, 0, 52, 0, 9, -10, 3, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [24]}
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id: 59577
{'degree': 8, 'field': [36, 0, -6, 0, 1, 0, 4, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [2, 8]}
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id: 59578
{'degree': 8, 'field': [81, 0, -180, 0, 112, 0, -20, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [2, 8]}
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id: 59576
{'degree': 8, 'field': [121, 0, -116, 0, 26, 0, 4, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [4, 4]}
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id: 59580
{'degree': 12, 'field': [81, -108, 9, 0, 60, -48, 19, -2, -10, 10, -1, -2, 1], 'lmfdb_label': '1200.k5', 'torsion': [3, 12]}
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id: 59581
{'degree': 12, 'field': [81, 0, -216, 0, 135, 0, -60, 0, -5, 0, 4, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [2, 12]}
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id: 59584
{'degree': 16, 'field': [36, 0, -96, 0, 340, 0, -204, 0, -51, 0, 46, 0, 15, 0, -6, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [2, 24]}
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id: 59585
{'degree': 16, 'field': [81, 0, 108, 0, -108, 0, 408, 0, 823, 0, -136, 0, -12, 0, -4, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [2, 24]}
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id: 59583
{'degree': 16, 'field': [625, 0, 0, 0, 0, 0, 0, 0, 850, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [4, 12]}
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id: 59582
{'degree': 16, 'field': [10000, 0, -20000, 0, -2000, 0, 24400, 0, 14440, 0, 2440, 0, -20, 0, -20, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [16]}
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id: 59586
{'degree': 18, 'field': [253125, 0, 911250, 0, 658125, 0, 100350, 0, 5400, 0, -5625, 0, -865, 0, -15, 0, 15, 0, 1], 'lmfdb_label': '1200.k5', 'torsion': [36]}
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ec_localdata • Show schema
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id: 17643
{'conductor': 1200, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '1200.k5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 17644
{'conductor': 1200, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '1200.k5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
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id: 17645
{'conductor': 1200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1200.k5', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1672113
{'adelic_gens': [[89, 96, 90, 119], [1, 12, 12, 25], [1, 24, 0, 1], [97, 24, 96, 25], [42, 79, 77, 92], [1, 0, 24, 1], [8, 117, 3, 86], [15, 106, 14, 11], [61, 24, 92, 29]], 'adelic_image': '120.384.5.?', 'conductor': 1200, 'lmfdb_label': '1200.k5', 'prime': 0}
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id: 5732
{'conductor': 1200, 'elladic_image': '4.12.0.7', 'lmfdb_label': '1200.k5', 'modell_image': '2B', 'prime': 2}
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id: 5733
{'conductor': 1200, 'elladic_image': '3.4.0.1', 'lmfdb_label': '1200.k5', 'modell_image': '3B', 'prime': 3}
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ec_padic • Show schema
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id: 29618
{'lmfdb_iso': '1200.k', 'p': 7, 'prec': 20, 'unit': 4479301866621222, 'val': 1}
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id: 29622
{'lmfdb_iso': '1200.k', 'p': 13, 'prec': 20, 'unit': 1426580148430129424684, 'val': 1}
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id: 29624
{'lmfdb_iso': '1200.k', 'p': 17, 'prec': 20, 'unit': 11296914599245843271025, 'val': 2}
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id: 29614
{'lmfdb_iso': '1200.k', 'p': 19, 'prec': 20, 'unit': 574682262168784720865354, 'val': 1}
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id: 29621
{'lmfdb_iso': '1200.k', 'p': 29, 'prec': 20, 'unit': 866255873847176441281463, 'val': 1}
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id: 29630
{'lmfdb_iso': '1200.k', 'p': 31, 'prec': 20, 'unit': 12835786089801502534144642134, 'val': 1}
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id: 29617
{'lmfdb_iso': '1200.k', 'p': 37, 'prec': 20, 'unit': 624107406841802359399580018221, 'val': 1}
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id: 29619
{'lmfdb_iso': '1200.k', 'p': 41, 'prec': 20, 'unit': 1964811669102606010125097917847, 'val': 1}
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id: 29620
{'lmfdb_iso': '1200.k', 'p': 43, 'prec': 20, 'unit': 903688038573451697105210062943, 'val': 1}
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id: 29626
{'lmfdb_iso': '1200.k', 'p': 53, 'prec': 20, 'unit': 189838945616838290213162051845198, 'val': 1}
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id: 29629
{'lmfdb_iso': '1200.k', 'p': 61, 'prec': 20, 'unit': 2586350387148562729456627345593690, 'val': 1}
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id: 29616
{'lmfdb_iso': '1200.k', 'p': 67, 'prec': 20, 'unit': 166350373518686871759124019862751, 'val': 1}
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id: 29627
{'lmfdb_iso': '1200.k', 'p': 73, 'prec': 20, 'unit': 182641148605892861646508793095049549, 'val': 1}
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id: 29623
{'lmfdb_iso': '1200.k', 'p': 79, 'prec': 20, 'unit': 1072511775348153478487376274871616774, 'val': 1}
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id: 29625
{'lmfdb_iso': '1200.k', 'p': 83, 'prec': 20, 'unit': 384677771885633866378418999966208148, 'val': 1}
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id: 29628
{'lmfdb_iso': '1200.k', 'p': 89, 'prec': 20, 'unit': 2320815966053971002532247238272111865, 'val': 1}
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id: 29615
{'lmfdb_iso': '1200.k', 'p': 97, 'prec': 20, 'unit': 42831665810636271500167232733109736897, 'val': 1}