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ec_curvedata • Show schema
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{'Ciso': '4560q', 'Clabel': '4560q1', 'Cnumber': 1, 'abc_quality': 1.0394954084659127, 'absD': 482262292616970240, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, -1, 0, 58824, 32937840], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4560, 'degree': 53760, 'elladic_images': ['8.12.0.12'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0734070868168341984800830494', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [5495662324535111, 117739817533440], 'lmfdb_iso': '4560.a', 'lmfdb_label': '4560.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 3676, -514654], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.2', '12.12.0-4.c.1.1', '20.12.0-4.c.1.1', '24.24.0-24.y.1.10', '30.6.0.a.1', '40.24.0-40.bb.1.1', '60.24.0-60.g.1.2', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.8382873318200944143511328005', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3802599062568888890628509279', 'prec': 100}, 'szpiro_ratio': 5.7144398848140705, '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, -1, 0, -4, 0, 1, 0, 0, 0, 2, 0, 1, 0, -2, 0, 1, 0], 'aplist': [0, -1, -1, -4, 0, 2, -2, 1, 0, 10, 0, 2, 2, 4, 0, -6, -8, 6, -12, 0, -14, 0, 12, 10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 4560, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '4560.a', 'trace_hash': 330543780514879952}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.015814719263956132980301697588', 'prec': 107}, 'conductor': 4560, 'gens': [[1261, 45942, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.8382873318200944143511328005', 'prec': 100}], 'lmfdb_label': '4560.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.22078605711870848605952306879', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5780248806373270589063332705211526537', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-260, 0, 1]], 'xcoord_integral_points': [-260, 1261]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '4560.a4'}
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ec_torsion_growth • Show schema
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id: 237855
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [4]}
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id: 237854
{'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '4560.a4', 'torsion': [2, 2]}
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id: 237856
{'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [4]}
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id: 237857
{'degree': 4, 'field': [4, 0, 1, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [2, 4]}
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id: 237861
{'degree': 8, 'field': [-12288, 0, 3124, 0, -384, 0, 0, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [6]}
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id: 237859
{'degree': 8, 'field': [4, 0, -20, 0, 21, 0, -2, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [8]}
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id: 237860
{'degree': 8, 'field': [106276, 0, -26412, 0, 1189, 0, 102, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [8]}
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id: 237858
{'degree': 8, 'field': [1833316, 0, -190772, 0, 7749, 0, -143, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [2, 4]}
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id: 237864
{'degree': 16, 'field': [16, 0, 48, 0, 52, 0, 48, 0, 168, 0, 24, 0, 13, 0, 6, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [2, 8]}
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id: 237867
{'degree': 16, 'field': [784, 0, 34144, 0, -10160, 0, 5037, 0, -990, 0, -3, 0, 97, 0, 10, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [12]}
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id: 237866
{'degree': 16, 'field': [1296, 0, -18336, 0, -6116, 0, -3603, 0, 306, 0, 77, 0, 69, 0, -6, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [12]}
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id: 237865
{'degree': 16, 'field': [150994944, 0, 97646736, 0, 72403840, 0, -5963232, 0, 171885, 0, 6248, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [2, 6]}
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id: 237863
{'degree': 16, 'field': [1760305936, 0, 1005576304, 0, 237815540, 0, 31112496, 0, 2535224, 0, 133896, 0, 4565, 0, 94, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [2, 8]}
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id: 237862
{'degree': 16, 'field': [19565295376, 0, 0, 0, 146079784, 0, 0, 0, 456801, 0, 0, 0, 934, 0, 0, 0, 1], 'lmfdb_label': '4560.a4', 'torsion': [4, 4]}
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ec_localdata • Show schema
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id: 87000
{'conductor': 4560, 'conductor_valuation': 4, 'discriminant_valuation': 40, 'j_denominator_valuation': 28, 'kodaira_symbol': -36, 'lmfdb_label': '4560.a4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 87001
{'conductor': 4560, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '4560.a4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 87002
{'conductor': 4560, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4560.a4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 87003
{'conductor': 4560, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4560.a4', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1693629
{'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [71, 72, 2, 65], [88, 3, 85, 2], [113, 8, 112, 9], [83, 78, 50, 107], [7, 6, 114, 115], [1, 4, 4, 17], [28, 1, 71, 6]], 'adelic_image': '120.48.0.?', 'conductor': 4560, 'lmfdb_label': '4560.a4', 'prime': 0}
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id: 22604
{'conductor': 4560, 'elladic_image': '8.12.0.12', 'lmfdb_label': '4560.a4', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 164274
{'lmfdb_iso': '4560.a', 'p': 7, 'prec': 20, 'unit': 8071832597487529, 'val': 1}
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id: 164277
{'lmfdb_iso': '4560.a', 'p': 13, 'prec': 20, 'unit': 1415918711978777625904, 'val': 1}
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id: 164279
{'lmfdb_iso': '4560.a', 'p': 17, 'prec': 20, 'unit': 90129377402142455778214, 'val': 1}
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id: 164278
{'lmfdb_iso': '4560.a', 'p': 29, 'prec': 20, 'unit': 1422101968833941694667609287, 'val': 1}
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id: 164273
{'lmfdb_iso': '4560.a', 'p': 37, 'prec': 20, 'unit': 447867085374405647309694340664, 'val': 1}
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id: 164275
{'lmfdb_iso': '4560.a', 'p': 41, 'prec': 20, 'unit': 3217388998934026556134449714939, 'val': 1}
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id: 164276
{'lmfdb_iso': '4560.a', 'p': 43, 'prec': 20, 'unit': 9722899952155021464692780225007, 'val': 1}
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id: 164281
{'lmfdb_iso': '4560.a', 'p': 53, 'prec': 20, 'unit': 523006817444134070954761721654534, 'val': 1}
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id: 164284
{'lmfdb_iso': '4560.a', 'p': 59, 'prec': 20, 'unit': 379736682146053209164669162457670, 'val': 1}
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id: 164285
{'lmfdb_iso': '4560.a', 'p': 61, 'prec': 20, 'unit': 6841614704858482691594962732120312, 'val': 1}
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id: 164272
{'lmfdb_iso': '4560.a', 'p': 67, 'prec': 20, 'unit': 32772951525369580183107383998540032, 'val': 1}
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id: 164282
{'lmfdb_iso': '4560.a', 'p': 73, 'prec': 20, 'unit': 69938366248614365954733197512658119, 'val': 1}
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id: 164280
{'lmfdb_iso': '4560.a', 'p': 83, 'prec': 20, 'unit': 1612829318396334592485163976880552319, 'val': 1}
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id: 164283
{'lmfdb_iso': '4560.a', 'p': 89, 'prec': 20, 'unit': 2759290385511794726043118002546860261, 'val': 1}
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id: 164271
{'lmfdb_iso': '4560.a', 'p': 97, 'prec': 20, 'unit': 423332367295086200328617614677486786, 'val': 1}