Elliptic curve data - 31680.cs1

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '31680bh', 'Clabel': '31680bh4', 'Cnumber': 4, 'abc_quality': 1.0771710471613196, 'absD': 1313832960000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1320, 'ainvs': [0, 0, 0, -34092, -2422224], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 31680, 'degree': 65536, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3033614351992139091604833910', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 70, 'isogeny_degrees': [1, 2, 4], 'jinv': [22930509321, 6875], 'lmfdb_iso': '31680.cs', 'lmfdb_label': '31680.cs1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -59, 190], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.2', '40.12.0.z.1', '44.12.0.h.1', '120.24.0.?', '264.24.0.?', '440.24.0.?', '1320.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.9846411093907961929144749633', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 99], [3, 6, 3520], [5, 6, 6336], [11, 12, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.28566547997475890066298740965', 'prec': 107}, 'szpiro_ratio': 4.141873125518389, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, 1, 0, -1, -2, -6, 4, -4, 6, -8, 2, -2, -4, 12, -2, 4, 10, 16, -8, 14, 8, -4, -10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 31680, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '31680.cs', 'trace_hash': 1236271469648234128}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.073775921289855853304233067264', 'prec': 107}, 'conductor': 31680, 'gens': [[216, 540, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.9846411093907961929144749633', 'prec': 100}], 'lmfdb_label': '31680.cs1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.35135347143404060298647429198', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6000699448129718705550457380442433949', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-108, 0, 1]], 'xcoord_integral_points': [-108, 216]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': [5, 3, 0], '11': [3, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [3, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [3, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '31680.cs1'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 1577416
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [2, 2]}
  • id: 1577418
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [4]}
  • id: 1577417
    {'degree': 2, 'field': [66, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [4]}
  • id: 1577419
    {'degree': 4, 'field': [289, 0, -10, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [2, 4]}
  • id: 1577423
    {'degree': 8, 'field': [-432, 0, 0, 0, 72, 0, 6, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [6]}
  • id: 1577422
    {'degree': 8, 'field': [81, 0, 270, 0, 198, 0, 30, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [8]}
  • id: 1577420
    {'degree': 8, 'field': [625, 0, -1656, 0, 194, 0, -24, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [2, 4]}
  • id: 1577421
    {'degree': 8, 'field': [6400, 0, 1160, 0, -4, 0, -2, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [8]}
  • id: 1577424
    {'degree': 16, 'field': [5625, 0, 1200, 0, 4714, 0, 1820, 0, 1623, 0, 460, 0, 162, 0, 20, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [4, 4]}
  • id: 1577429
    {'degree': 16, 'field': [6400, 0, 6400, 0, 7360, 0, 13984, 0, 5680, 0, 1072, 0, 136, 0, 16, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [12]}
  • id: 1577428
    {'degree': 16, 'field': [210681, 0, 6158592, 0, 3519612, 0, 707616, 0, 66690, 0, 5616, 0, 477, 0, 12, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [12]}
  • id: 1577427
    {'degree': 16, 'field': [1155625, 0, -6061000, 0, -1271900, 0, -372694, 0, 26914, 0, 4076, 0, -227, 0, -10, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [2, 6]}
  • id: 1577426
    {'degree': 16, 'field': [11750905, -5180820, 5910154, -1632896, 1326718, -834564, 688918, -436188, 222187, -88216, 31138, -8276, 2168, -392, 76, -8, 1], 'lmfdb_label': '31680.cs1', 'torsion': [2, 8]}
  • id: 1577425
    {'degree': 16, 'field': [25806400, 0, 4247040, 0, 5160276, 0, -195612, 0, -40351, 0, 2424, 0, -66, 0, -12, 0, 1], 'lmfdb_label': '31680.cs1', 'torsion': [2, 8]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 739335
    {'conductor': 31680, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '31680.cs1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 739336
    {'conductor': 31680, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '31680.cs1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 739337
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '31680.cs1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 739338
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '31680.cs1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1875596
    {'adelic_gens': [[821, 822, 702, 485], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1313, 8, 1312, 9], [439, 0, 0, 1319], [844, 441, 783, 886], [1057, 888, 708, 913], [1048, 393, 633, 1120], [7, 6, 1314, 1315]], 'adelic_image': '1320.48.0.?', 'conductor': 31680, 'lmfdb_label': '31680.cs1', 'prime': 0}
  • id: 141567
    {'conductor': 31680, 'elladic_image': '4.6.0.1', 'lmfdb_label': '31680.cs1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 1540955
    {'lmfdb_iso': '31680.cs', 'p': 13, 'prec': 20, 'unit': 3215674249835094472, 'val': 2}
  • id: 1540957
    {'lmfdb_iso': '31680.cs', 'p': 17, 'prec': 20, 'unit': 186250164500196984088358, 'val': 1}
  • id: 1540958
    {'lmfdb_iso': '31680.cs', 'p': 19, 'prec': 20, 'unit': 471130531346376997589025, 'val': 1}
  • id: 1540962
    {'lmfdb_iso': '31680.cs', 'p': 23, 'prec': 20, 'unit': 47189965134320920533108670, 'val': 1}
  • id: 1540954
    {'lmfdb_iso': '31680.cs', 'p': 29, 'prec': 20, 'unit': 150941066026859026486502528, 'val': 2}
  • id: 1540966
    {'lmfdb_iso': '31680.cs', 'p': 31, 'prec': 20, 'unit': 9910715329942741994431082826, 'val': 1}
  • id: 1540950
    {'lmfdb_iso': '31680.cs', 'p': 37, 'prec': 20, 'unit': 76503584349201167250266291054, 'val': 1}
  • id: 1540952
    {'lmfdb_iso': '31680.cs', 'p': 41, 'prec': 20, 'unit': 1281267778343090857413480265668, 'val': 1}
  • id: 1540953
    {'lmfdb_iso': '31680.cs', 'p': 43, 'prec': 20, 'unit': 248601266094277827945367557811, 'val': 2}
  • id: 1540964
    {'lmfdb_iso': '31680.cs', 'p': 47, 'prec': 20, 'unit': 46911904311930413827209031412886, 'val': 1}
  • id: 1540959
    {'lmfdb_iso': '31680.cs', 'p': 53, 'prec': 20, 'unit': 72284968903281364423191267534689, 'val': 1}
  • id: 1540960
    {'lmfdb_iso': '31680.cs', 'p': 59, 'prec': 20, 'unit': 2576870010390086173151701251513350, 'val': 1}
  • id: 1540965
    {'lmfdb_iso': '31680.cs', 'p': 61, 'prec': 20, 'unit': 260226213615697297443483423789933, 'val': 1}
  • id: 1540949
    {'lmfdb_iso': '31680.cs', 'p': 67, 'prec': 20, 'unit': 13884419353655609351385859918290179, 'val': 1}
  • id: 1540951
    {'lmfdb_iso': '31680.cs', 'p': 71, 'prec': 20, 'unit': 95319237123479373664927041782971192, 'val': 1}
  • id: 1540961
    {'lmfdb_iso': '31680.cs', 'p': 73, 'prec': 20, 'unit': 242978165978838592755919260602149955, 'val': 1}
  • id: 1540956
    {'lmfdb_iso': '31680.cs', 'p': 79, 'prec': 20, 'unit': 554512897576208442008090823672488082, 'val': 1}
  • id: 1540948
    {'lmfdb_iso': '31680.cs', 'p': 83, 'prec': 20, 'unit': 1875566773265769707798388998270923366, 'val': 1}
  • id: 1540963
    {'lmfdb_iso': '31680.cs', 'p': 89, 'prec': 20, 'unit': 457182012121127527560092351666694577, 'val': 1}
  • id: 1540947
    {'lmfdb_iso': '31680.cs', 'p': 97, 'prec': 20, 'unit': 36626139280569399769871895351059317857, 'val': 1}