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ec_curvedata • Show schema
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{'Ciso': '4800c', 'Clabel': '4800c2', 'Cnumber': 2, 'abc_quality': 0.972547111469975, 'absD': 2304000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 120, 'ainvs': [0, -1, 0, -433, 2737], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4800, 'degree': 2048, 'elladic_images': ['8.48.0.138'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.50594026041716556934998505052', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 4], 'jinv': [35152, 9], 'lmfdb_iso': '4800.q', 'lmfdb_label': '4800.q4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -4, 4], 'min_quad_twist_disc': 40, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.h.1', '12.24.0.c.1', '24.96.1.bu.1', '40.96.0-8.h.1.1', '120.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 11, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.1249115230640545117527166346', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 1600], [5, 14, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1074504064531541456038320911', 'prec': 103}, 'szpiro_ratio': 3.5189734031458157, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, -4, 0, -2, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, -1, 0, 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': 4800, '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': '4800.q', 'trace_hash': 229465160862369965}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.36353470179314388805624933343', 'prec': 103}, 'conductor': 4800, 'gens': [[1, 48, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.1249115230640545117527166346', 'prec': 100}], 'lmfdb_label': '4800.q4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.3639002511783338651137987116', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0685342177209321149525512669598914929', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[7, 0, 1], [17, 0, 1]], 'xcoord_integral_points': [-23, -8, 1, 7, 17, 27, 57]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [3, 0], '5': 'a', '7': [1, 3, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [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': '4800.q4'}
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ec_torsion_growth • Show schema
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id: 248852
{'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '4800.q4', 'torsion': [2, 4]}
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id: 248853
{'degree': 4, 'field': [25, 0, 20, 0, 1], 'lmfdb_label': '4800.q4', 'torsion': [2, 4]}
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id: 248854
{'degree': 4, 'field': [100, 0, -10, 0, 1], 'lmfdb_label': '4800.q4', 'torsion': [2, 4]}
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id: 248859
{'degree': 8, 'field': [-1875, 0, -1250, 0, -150, 0, 0, 0, 1], 'lmfdb_label': '4800.q4', 'torsion': [2, 6]}
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id: 248857
{'degree': 8, 'field': [1, 0, -12, 0, 23, 0, -12, 0, 1], 'lmfdb_label': '4800.q4', 'torsion': [2, 8]}
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id: 248858
{'degree': 8, 'field': [1, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '4800.q4', 'torsion': [2, 8]}
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id: 248856
{'degree': 8, 'field': [529, 184, 146, -128, 100, -28, 14, -4, 1], 'lmfdb_label': '4800.q4', 'torsion': [2, 8]}
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id: 248855
{'degree': 8, 'field': [625, 0, 0, 0, -25, 0, 0, 0, 1], 'lmfdb_label': '4800.q4', 'torsion': [4, 4]}
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id: 248861
{'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 48, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '4800.q4', 'torsion': [4, 8]}
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id: 248860
{'degree': 16, 'field': [1, 0, 6, 0, 46, 0, 72, 0, 111, 0, 72, 0, 46, 0, 6, 0, 1], 'lmfdb_label': '4800.q4', 'torsion': [2, 8]}
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id: 248862
{'degree': 16, 'field': [52036, 9472, 39432, 93968, 16584, -61752, -33800, 13160, 13860, -608, -2684, -144, 264, 28, -12, -4, 1], 'lmfdb_label': '4800.q4', 'torsion': [4, 8]}
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id: 248863
{'degree': 16, 'field': [544959, -2292492, 3967556, -3570124, 1616312, -22772, -389768, 217132, -55890, 9900, -3618, 1348, -272, 40, 10, -8, 1], 'lmfdb_label': '4800.q4', 'torsion': [2, 12]}
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ec_localdata • Show schema
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id: 91840
{'conductor': 4800, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '4800.q4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 91841
{'conductor': 4800, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4800.q4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 91842
{'conductor': 4800, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4800.q4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1695274
{'adelic_gens': [[79, 0, 80, 19], [113, 8, 112, 9], [71, 50, 30, 91], [1, 0, 8, 1], [101, 80, 70, 51], [5, 4, 116, 117], [23, 0, 0, 119], [1, 8, 0, 1]], 'adelic_image': '120.192.1.?', 'conductor': 4800, 'lmfdb_label': '4800.q4', 'prime': 0}
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id: 23814
{'conductor': 4800, 'elladic_image': '8.48.0.138', 'lmfdb_label': '4800.q4', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 174471
{'lmfdb_iso': '4800.q', 'p': 11, 'prec': 20, 'unit': 60943333722651770392, 'val': 1}
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id: 174469
{'lmfdb_iso': '4800.q', 'p': 13, 'prec': 20, 'unit': 922415405603380870764, 'val': 1}
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id: 174472
{'lmfdb_iso': '4800.q', 'p': 17, 'prec': 20, 'unit': 180113860829963107367475, 'val': 1}
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id: 174473
{'lmfdb_iso': '4800.q', 'p': 19, 'prec': 20, 'unit': 539801142108374696039804, 'val': 1}
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id: 174476
{'lmfdb_iso': '4800.q', 'p': 23, 'prec': 20, 'unit': 29796951541351757598590756, 'val': 1}
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id: 174468
{'lmfdb_iso': '4800.q', 'p': 29, 'prec': 20, 'unit': 3991531822191242864406379211, 'val': 1}
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id: 174480
{'lmfdb_iso': '4800.q', 'p': 31, 'prec': 20, 'unit': 19008008477751227472014722077, 'val': 1}
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id: 174464
{'lmfdb_iso': '4800.q', 'p': 37, 'prec': 20, 'unit': 277080421457622375752145110018, 'val': 1}
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id: 174466
{'lmfdb_iso': '4800.q', 'p': 41, 'prec': 20, 'unit': 78178370229197170775222921662, 'val': 1}
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id: 174467
{'lmfdb_iso': '4800.q', 'p': 43, 'prec': 20, 'unit': 6199678019181694952034277908981, 'val': 1}
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id: 174474
{'lmfdb_iso': '4800.q', 'p': 53, 'prec': 20, 'unit': 256600103991867580127548212280928, 'val': 1}
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id: 174478
{'lmfdb_iso': '4800.q', 'p': 59, 'prec': 20, 'unit': 1801344544841032914144779297821281, 'val': 1}
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id: 174479
{'lmfdb_iso': '4800.q', 'p': 61, 'prec': 20, 'unit': 5757220290733134168115710861500975, 'val': 1}
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id: 174463
{'lmfdb_iso': '4800.q', 'p': 67, 'prec': 20, 'unit': 24311555777103770251759824145364087, 'val': 1}
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id: 174465
{'lmfdb_iso': '4800.q', 'p': 71, 'prec': 20, 'unit': 61205446482722322855712028515695224, 'val': 1}
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id: 174475
{'lmfdb_iso': '4800.q', 'p': 73, 'prec': 20, 'unit': 235176514435381451214708143087097272, 'val': 1}
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id: 174470
{'lmfdb_iso': '4800.q', 'p': 79, 'prec': 20, 'unit': 196654300069466970503936320003464961, 'val': 1}
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id: 174462
{'lmfdb_iso': '4800.q', 'p': 83, 'prec': 20, 'unit': 188297028266587737628418663688779448, 'val': 1}
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id: 174477
{'lmfdb_iso': '4800.q', 'p': 89, 'prec': 20, 'unit': 10570817693786707543189067791182890002, 'val': 1}
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id: 174461
{'lmfdb_iso': '4800.q', 'p': 97, 'prec': 20, 'unit': 14477952280761062775290147554772464598, 'val': 1}