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ec_curvedata • Show schema
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{'Ciso': '25872bk', 'Clabel': '25872bk1', 'Cnumber': 1, 'abc_quality': 1.0970565641289056, 'absD': 143121420288, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [0, -1, 0, -5112, -137808], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 25872, 'degree': 27648, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.96032300741096805431023025152', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 30, 'isogeny_degrees': [1, 2, 4], 'jinv': [30664297, 297], 'lmfdb_iso': '25872.be', 'lmfdb_label': '25872.be3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -6, -9], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '56.12.0-4.c.1.5', '66.6.0.a.1', '84.12.0.?', '88.12.0.?', '132.12.0.?', '168.24.0.?', '264.24.0.?', '308.12.0.?', '616.24.0.?', '924.24.0.?', '1848.48.0.?'], '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': '4.5973487447512101858391488791', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.70577924767663390765967824166', 'prec': 107}, 'szpiro_ratio': 3.664220282971185, '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, -1, 0, 2, 0, -2, 0, 2, 0, 0, 0], 'aplist': [0, -1, 2, 0, -1, 2, 2, 0, -8, -6, -8, 6, 2, 0, 8, 6, -4, -6, 4, 0, 14, 4, 12, 6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 25872, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '25872.be', 'trace_hash': 1160933300186421714}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.14651228244534759249058513216', 'prec': 103}, 'conductor': 25872, 'gens': [[356, 6560, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.5973487447512101858391488791', 'prec': 100}], 'lmfdb_label': '25872.be3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.56493529427150219964838582703', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.1944091319694923598870665001629669335', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-44, 0, 1]], 'xcoord_integral_points': [-44, 356]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [7, 0], '5': [3, 0], '7': 'a', '11': [5, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '25872.be3'}
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ec_torsion_growth • Show schema
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id: 1302334
{'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '25872.be3', 'torsion': [2, 2]}
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id: 1302336
{'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '25872.be3', 'torsion': [4]}
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id: 1302335
{'degree': 2, 'field': [77, 0, 1], 'lmfdb_label': '25872.be3', 'torsion': [4]}
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id: 1302337
{'degree': 4, 'field': [196, 0, 49, 0, 1], 'lmfdb_label': '25872.be3', 'torsion': [2, 4]}
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id: 1302341
{'degree': 8, 'field': [-7203, 0, 6517, 0, -294, 0, 0, 0, 1], 'lmfdb_label': '25872.be3', 'torsion': [6]}
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id: 1302338
{'degree': 8, 'field': [-629, 2612, -2528, -148, 25, 56, -14, -4, 1], 'lmfdb_label': '25872.be3', 'torsion': [2, 4]}
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id: 1302340
{'degree': 8, 'field': [169, 0, 58, 0, 27, 0, -2, 0, 1], 'lmfdb_label': '25872.be3', 'torsion': [8]}
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id: 1302339
{'degree': 8, 'field': [1941, 72, -809, -278, 292, 48, -29, -2, 1], 'lmfdb_label': '25872.be3', 'torsion': [8]}
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id: 1302343
{'degree': 16, 'field': [36052, -45312, 72176, -62692, 55793, -35370, 22886, -11742, 6046, -2532, 898, -146, -6, -14, 22, -8, 1], 'lmfdb_label': '25872.be3', 'torsion': [2, 8]}
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id: 1302342
{'degree': 16, 'field': [1713481, 0, -897820, 0, 688930, 0, -63580, 0, 32803, 0, -7300, 0, 754, 0, -40, 0, 1], 'lmfdb_label': '25872.be3', 'torsion': [4, 4]}
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id: 1302345
{'degree': 16, 'field': [5764801, 0, -10706059, 0, -12235496, 0, -3747961, 0, -357749, 0, 9947, 0, 1960, 0, -91, 0, 1], 'lmfdb_label': '25872.be3', 'torsion': [2, 6]}
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id: 1302344
{'degree': 16, 'field': [8316900, 1778760, -6997356, -2865060, 3630769, 1044244, -944439, -200078, 156267, 23564, -16770, -1804, 1191, 88, -51, -2, 1], 'lmfdb_label': '25872.be3', 'torsion': [2, 8]}
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id: 1302347
{'degree': 16, 'field': [51883209, 0, 19765032, 0, 4000066, 0, 504210, 0, 36015, 0, 5831, 0, 735, 0, 42, 0, 1], 'lmfdb_label': '25872.be3', 'torsion': [12]}
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id: 1302346
{'degree': 16, 'field': [767107313, -56358316, 70358121, -28020382, 14566844, -2093376, 3109339, -2136908, 617253, -48670, 3101, 3540, -499, -70, 30, -8, 1], 'lmfdb_label': '25872.be3', 'torsion': [12]}
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ec_localdata • Show schema
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id: 596067
{'conductor': 25872, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '25872.be3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 596068
{'conductor': 25872, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '25872.be3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 596069
{'conductor': 25872, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '25872.be3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 596070
{'conductor': 25872, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '25872.be3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1836824
{'adelic_gens': [[263, 0, 0, 1847], [1841, 8, 1840, 9], [1555, 1554, 1498, 43], [1688, 1323, 1253, 1058], [1, 0, 8, 1], [223, 756, 490, 97], [92, 1057, 1519, 1590], [7, 6, 1842, 1843], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '1848.48.0.?', 'conductor': 25872, 'lmfdb_label': '25872.be3', 'prime': 0}
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id: 117844
{'conductor': 25872, 'elladic_image': '4.6.0.1', 'lmfdb_label': '25872.be3', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 1234421
{'lmfdb_iso': '25872.be', 'p': 5, 'prec': 20, 'unit': 2277229716657, 'val': 2}
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id: 1234426
{'lmfdb_iso': '25872.be', 'p': 13, 'prec': 20, 'unit': 291591940638447654750, 'val': 1}
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id: 1234428
{'lmfdb_iso': '25872.be', 'p': 17, 'prec': 20, 'unit': 102266318873404484494225, 'val': 1}
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id: 1234424
{'lmfdb_iso': '25872.be', 'p': 23, 'prec': 20, 'unit': 70580209732454531430523183, 'val': 1}
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id: 1234425
{'lmfdb_iso': '25872.be', 'p': 29, 'prec': 20, 'unit': 4316596752240520899637493757, 'val': 1}
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id: 1234422
{'lmfdb_iso': '25872.be', 'p': 31, 'prec': 20, 'unit': 11324292190355032350598818299, 'val': 1}
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id: 1234436
{'lmfdb_iso': '25872.be', 'p': 37, 'prec': 20, 'unit': 335386683587971715213606899057, 'val': 1}
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id: 1234423
{'lmfdb_iso': '25872.be', 'p': 41, 'prec': 20, 'unit': 2559823335352025424013335397418, 'val': 1}
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id: 1234434
{'lmfdb_iso': '25872.be', 'p': 47, 'prec': 20, 'unit': 21326231741411891579918484469738, 'val': 1}
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id: 1234430
{'lmfdb_iso': '25872.be', 'p': 53, 'prec': 20, 'unit': 450861694514519103849810455918318, 'val': 1}
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id: 1234431
{'lmfdb_iso': '25872.be', 'p': 59, 'prec': 20, 'unit': 3475017329211898713130813648202018, 'val': 1}
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id: 1234435
{'lmfdb_iso': '25872.be', 'p': 61, 'prec': 20, 'unit': 1680872557654878286822568433942973, 'val': 1}
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id: 1234420
{'lmfdb_iso': '25872.be', 'p': 67, 'prec': 20, 'unit': 19854885326684204775656267391640684, 'val': 1}
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id: 1234432
{'lmfdb_iso': '25872.be', 'p': 73, 'prec': 20, 'unit': 77465061535033312437421119065270364, 'val': 1}
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id: 1234427
{'lmfdb_iso': '25872.be', 'p': 79, 'prec': 20, 'unit': 935692271713589005893700290305986773, 'val': 1}
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id: 1234429
{'lmfdb_iso': '25872.be', 'p': 83, 'prec': 20, 'unit': 1023378540295598668558647738756363120, 'val': 1}
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id: 1234433
{'lmfdb_iso': '25872.be', 'p': 89, 'prec': 20, 'unit': 10348649163935027590017089572695064597, 'val': 1}
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id: 1234419
{'lmfdb_iso': '25872.be', 'p': 97, 'prec': 20, 'unit': 41963059183376334283697522473421478254, 'val': 1}