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ec_curvedata • Show schema
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{'Ciso': '19320bb', 'Clabel': '19320bb2', 'Cnumber': 2, 'abc_quality': 0.9355980338333827, 'absD': 53333224761600, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 6440, 'ainvs': [0, 1, 0, -9700, 105248], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 19320, 'degree': 57344, 'elladic_images': ['4.24.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3255081415933101674101026672', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2, 4], 'jinv': [394315384276816, 208332909225], 'lmfdb_iso': '19320.ba', 'lmfdb_label': '19320.ba5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -9700, 105248], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '40.48.0-40.h.2.9', '56.48.0-56.l.1.10', '184.48.0.?', '280.96.0.?', '460.48.0.?', '920.96.0.?', '1288.96.0.?', '6440.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 19, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4721016939320573798014932736', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.86341002122001329446528125289', 'prec': 103}, 'szpiro_ratio': 3.967348444006604, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [2, 4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -4, 0, -2, 0, 1, 0, 2, 0, -4, 0], 'aplist': [0, 1, 1, 1, -4, -2, 2, -4, -1, -2, 8, 6, -6, -4, 8, -10, -12, 14, -12, 16, -14, 8, -12, -14, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 19320, 'isogeny_matrix': [[1, 8, 2, 4, 4, 8], [8, 1, 4, 8, 2, 4], [2, 4, 1, 2, 2, 4], [4, 8, 2, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '19320.ba', 'trace_hash': 976220985929437224}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.070579447893524973290193008941', 'prec': 107}, 'conductor': 19320, 'gens': [[8, 168, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4721016939320573798014932736', 'prec': 100}], 'lmfdb_label': '19320.ba5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.55299653220616236801023703917', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.5125370543939611666251741754757091410', 'prec': 130}, 'tamagawa_product': 512, 'torsion_generators': [[11, 0, 1], [-34, 630, 1]], 'xcoord_integral_points': [-104, -97, -58, -34, 8, 11, 92, 146, 218, 386, 3116]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [4, 0], '5': [6, 0], '7': [2, 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, 0]}, 'iwp0': 0, 'lmfdb_label': '19320.ba5'}
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ec_torsion_growth • Show schema
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id: 988082
{'degree': 4, 'field': [81, 0, -74, 0, 1], 'lmfdb_label': '19320.ba5', 'torsion': [2, 8]}
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id: 988083
{'degree': 4, 'field': [81, 0, 38, 0, 1], 'lmfdb_label': '19320.ba5', 'torsion': [2, 8]}
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id: 988081
{'degree': 4, 'field': [841, 0, -57, 0, 1], 'lmfdb_label': '19320.ba5', 'torsion': [4, 4]}
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id: 988084
{'degree': 8, 'field': [-19683, 0, -22392, 0, -486, 0, 0, 0, 1], 'lmfdb_label': '19320.ba5', 'torsion': [2, 12]}
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id: 988087
{'degree': 16, 'field': [12609601, -10070636, 4021448, -2749892, 2621526, -1257736, 468280, -257116, 34039, 14408, -920, 692, -114, -44, 32, -8, 1], 'lmfdb_label': '19320.ba5', 'torsion': [4, 8]}
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id: 988086
{'degree': 16, 'field': [15752961, 0, 14002632, 0, 22981882, 0, 1645812, 0, -159157, 0, -6444, 0, 878, 0, -36, 0, 1], 'lmfdb_label': '19320.ba5', 'torsion': [4, 8]}
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id: 988085
{'degree': 16, 'field': [3811951081, -1304093402, 223069442, -409394096, 171465521, 27431718, 2565490, -97098, -238836, -14064, 12520, -5274, 1121, -28, 8, -4, 1], 'lmfdb_label': '19320.ba5', 'torsion': [4, 8]}
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id: 988089
{'degree': 16, 'field': [275147457025, 0, -238847638400, 0, 69142413340, 0, -6683505920, 0, 304947286, 0, -5900384, 0, 49756, 0, -224, 0, 1], 'lmfdb_label': '19320.ba5', 'torsion': [2, 16]}
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id: 988088
{'degree': 16, 'field': [685154549158849, 0, -96463878955472, 0, 4932775468684, 0, -102432186416, 0, 403566646, 0, 10053232, 0, -35252, 0, -560, 0, 1], 'lmfdb_label': '19320.ba5', 'torsion': [2, 16]}
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ec_localdata • Show schema
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id: 436772
{'conductor': 19320, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '19320.ba5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 436773
{'conductor': 19320, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '19320.ba5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
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id: 436774
{'conductor': 19320, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '19320.ba5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 436775
{'conductor': 19320, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '19320.ba5', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 436776
{'conductor': 19320, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '19320.ba5', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1793070
{'adelic_gens': [[2761, 4, 0, 1], [5159, 2, 5134, 6435], [6433, 8, 6432, 9], [1967, 6, 4754, 6435], [1, 0, 8, 1], [3225, 1612, 1612, 3221], [3, 4838, 6432, 1589], [5, 4, 6436, 6437], [1, 8, 0, 1]], 'adelic_image': '6440.192.1.?', 'conductor': 19320, 'lmfdb_label': '19320.ba5', 'prime': 0}
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id: 90220
{'conductor': 19320, 'elladic_image': '4.24.0.5', 'lmfdb_label': '19320.ba5', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 894313
{'lmfdb_iso': '19320.ba', 'p': 11, 'prec': 20, 'unit': 27299067170072887062, 'val': 1}
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id: 894319
{'lmfdb_iso': '19320.ba', 'p': 13, 'prec': 20, 'unit': 44777336753334249393, 'val': 1}
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id: 894321
{'lmfdb_iso': '19320.ba', 'p': 17, 'prec': 20, 'unit': 65100452402457091419527, 'val': 1}
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id: 894322
{'lmfdb_iso': '19320.ba', 'p': 19, 'prec': 20, 'unit': 1466513952596573411427039, 'val': 1}
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id: 894318
{'lmfdb_iso': '19320.ba', 'p': 29, 'prec': 20, 'unit': 5208183741774505481413233836, 'val': 1}
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id: 894330
{'lmfdb_iso': '19320.ba', 'p': 31, 'prec': 20, 'unit': 18112443724139796210779476507, 'val': 1}
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id: 894314
{'lmfdb_iso': '19320.ba', 'p': 37, 'prec': 20, 'unit': 51945628423829956609491502108, 'val': 1}
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id: 894316
{'lmfdb_iso': '19320.ba', 'p': 41, 'prec': 20, 'unit': 1412634960992029004051865118883, 'val': 1}
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id: 894317
{'lmfdb_iso': '19320.ba', 'p': 43, 'prec': 20, 'unit': 102800325478920022274594928657, 'val': 1}
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id: 894328
{'lmfdb_iso': '19320.ba', 'p': 47, 'prec': 20, 'unit': 253621006796378731740883377876, 'val': 1}
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id: 894323
{'lmfdb_iso': '19320.ba', 'p': 53, 'prec': 20, 'unit': 130588923641241077938901040382214, 'val': 1}
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id: 894324
{'lmfdb_iso': '19320.ba', 'p': 59, 'prec': 20, 'unit': 2406523287879927849920070176670773, 'val': 1}
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id: 894329
{'lmfdb_iso': '19320.ba', 'p': 61, 'prec': 20, 'unit': 2302423511545403194447324516488711, 'val': 1}
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id: 894312
{'lmfdb_iso': '19320.ba', 'p': 67, 'prec': 20, 'unit': 19168477263782752791909180632668056, 'val': 1}
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id: 894315
{'lmfdb_iso': '19320.ba', 'p': 71, 'prec': 20, 'unit': 60240330624690528735319811225137046, 'val': 1}
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id: 894325
{'lmfdb_iso': '19320.ba', 'p': 73, 'prec': 20, 'unit': 171785937663574752977320351869625937, 'val': 1}
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id: 894320
{'lmfdb_iso': '19320.ba', 'p': 79, 'prec': 20, 'unit': 157467161015772328687361576929723872, 'val': 1}
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id: 894326
{'lmfdb_iso': '19320.ba', 'p': 83, 'prec': 20, 'unit': 454513802305759046383218259463780011, 'val': 1}
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id: 894327
{'lmfdb_iso': '19320.ba', 'p': 89, 'prec': 20, 'unit': 5028829620395520503683548609080902477, 'val': 1}
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id: 894311
{'lmfdb_iso': '19320.ba', 'p': 97, 'prec': 20, 'unit': 33865623757962880878299618031250397381, 'val': 1}