Elliptic curve data - 22848.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': '22848cw', 'Clabel': '22848cw4', 'Cnumber': 4, 'abc_quality': 1.108049552899778, 'absD': 557160726528, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 952, 'ainvs': [0, 1, 0, -725469697, -7521266762497], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 22848, 'degree': 2211840, 'elladic_images': ['8.24.0.60'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2375808957870659341773094754', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 70, 'isogeny_degrees': [1, 2, 4], 'jinv': [322159999717985454060440834, 4250799], 'lmfdb_iso': '22848.cs', 'lmfdb_label': '22848.cs1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -181367424, 940067661600], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.p.1.3', '952.48.0.?'], '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': '7.3320180936646660990614490198', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 119], [3, 4, 1088], [7, 8, 3264], [17, 18, 1344]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2556223899938100791695639700', 'prec': 100}, 'szpiro_ratio': 7.255490478967511, '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, 1, 0, 2, 0, 1, 0, 1, 0, 0, 0, -2, 0, 2, 0, 1, 0, 0, 0], 'aplist': [0, 1, 2, 1, 0, -2, 1, 0, 0, -2, -8, 6, -6, 4, 0, -14, -8, -14, 4, -8, 10, -8, -16, 2, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 22848, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '22848.cs', 'trace_hash': 1635299008906240504}
• 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': '0.0015412495559837992432887566662', 'prec': 110}, 'conductor': 22848, 'gens': [[32849, 2023560, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '7.3320180936646660990614490198', 'prec': 100}], 'lmfdb_label': '22848.cs1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.029090067935623746770854549591', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.6784005601973954914601404783593846401', 'prec': 130}, 'tamagawa_product': 36, 'torsion_generators': [[-15551, 0, 1]], 'xcoord_integral_points': [-15551, 32849]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [2, 0], '11': [1, 1, 0], '13': [3, 0], '17': [2, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [3, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '22848.cs1'}
• ec_torsion_growth •

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

  
  
  • id: 1159224
    {'degree': 2, 'field': [-238, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [2, 2]}
  • id: 1159226
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [4]}
  • id: 1159225
    {'degree': 2, 'field': [238, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [4]}
  • id: 1159228
    {'degree': 4, 'field': [-104958, 0, 0, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [2, 4]}
  • id: 1159227
    {'degree': 4, 'field': [14161, 0, 0, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [2, 4]}
  • id: 1159232
    {'degree': 8, 'field': [-3, 0, 2, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [6]}
  • id: 1159230
    {'degree': 8, 'field': [22878, 768, 5813, -6402, 2169, -212, 83, -2, 1], 'lmfdb_label': '22848.cs1', 'torsion': [8]}
  • id: 1159231
    {'degree': 8, 'field': [1147041, 0, 12852, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [8]}
  • id: 1159229
    {'degree': 8, 'field': [11015971849, 0, 1259500, 0, -209910, 0, 4, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [4, 4]}
  • id: 1159238
    {'degree': 16, 'field': [4, 0, 536, 0, -332, 0, 0, 0, -156, 0, 36, 0, 40, 0, 8, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [12]}
  • id: 1159234
    {'degree': 16, 'field': [54700816, 0, 0, 0, -19946895, 0, 0, 0, 3692083, 0, 0, 0, 3795, 0, 0, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [2, 8]}
  • id: 1159236
    {'degree': 16, 'field': [3027420484, 0, -2692602248, 0, -173205956, 0, -50843096, 0, 1350304, 0, 99316, 0, 2836, 0, -110, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [2, 6]}
  • id: 1159237
    {'degree': 16, 'field': [18423467791, 15571499092, 2518091912, 541189352, -174735608, -146216760, 68937850, -15503708, 8709752, -3271120, 501052, -44976, 8938, -1508, 86, -4, 1], 'lmfdb_label': '22848.cs1', 'torsion': [12]}
  • id: 1159233
    {'degree': 16, 'field': [41006250000, 0, -9841500000, 0, 1180980000, 0, -144779400, 0, 11353041, 0, -321732, 0, 5832, 0, -108, 0, 1], 'lmfdb_label': '22848.cs1', 'torsion': [2, 8]}
  • id: 1159235
    {'degree': 16, 'field': [2489307684516, 0, -8676056502432, 0, 345627895536, 0, -13884417792, 0, 435861468, 0, -8411760, 0, 92232, 0, -480, 0, 1], 'lmfdb_label': '22848.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: 522788
    {'conductor': 22848, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '22848.cs1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 522789
    {'conductor': 22848, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '22848.cs1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 522790
    {'conductor': 22848, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '22848.cs1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 522791
    {'conductor': 22848, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '22848.cs1', 'prime': 17, '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: 1816783
    {'adelic_gens': [[945, 8, 944, 9], [568, 3, 117, 2], [416, 3, 141, 2], [1, 0, 8, 1], [1, 8, 0, 1], [832, 349, 829, 800], [1, 4, 4, 17], [7, 6, 946, 947], [592, 111, 365, 378]], 'adelic_image': '952.48.0.?', 'conductor': 22848, 'lmfdb_label': '22848.cs1', 'prime': 0}
  • id: 105318
    {'conductor': 22848, 'elladic_image': '8.24.0.60', 'lmfdb_label': '22848.cs1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1077968
    {'lmfdb_iso': '22848.cs', 'p': 5, 'prec': 20, 'unit': 1368880310772, 'val': 1}
  • id: 1077960
    {'lmfdb_iso': '22848.cs', 'p': 13, 'prec': 20, 'unit': 38461790773270428159, 'val': 2}
  • id: 1077959
    {'lmfdb_iso': '22848.cs', 'p': 29, 'prec': 20, 'unit': 2011322881299124641800428472, 'val': 1}
  • id: 1077956
    {'lmfdb_iso': '22848.cs', 'p': 31, 'prec': 20, 'unit': 17608437585301056766366511945, 'val': 1}
  • id: 1077954
    {'lmfdb_iso': '22848.cs', 'p': 37, 'prec': 20, 'unit': 16761265513919757104828618220, 'val': 2}
  • id: 1077957
    {'lmfdb_iso': '22848.cs', 'p': 41, 'prec': 20, 'unit': 380566742937081024803754446699, 'val': 1}
  • id: 1077958
    {'lmfdb_iso': '22848.cs', 'p': 43, 'prec': 20, 'unit': 6145668531431848182646684944711, 'val': 1}
  • id: 1077963
    {'lmfdb_iso': '22848.cs', 'p': 53, 'prec': 20, 'unit': 381002392544320772175950003943849, 'val': 1}
  • id: 1077966
    {'lmfdb_iso': '22848.cs', 'p': 59, 'prec': 20, 'unit': 3376543814927932095879939078181945, 'val': 1}
  • id: 1077967
    {'lmfdb_iso': '22848.cs', 'p': 61, 'prec': 20, 'unit': 5679271101290123799522870536943499, 'val': 1}
  • id: 1077953
    {'lmfdb_iso': '22848.cs', 'p': 67, 'prec': 20, 'unit': 4949018459335643750046095769851762, 'val': 1}
  • id: 1077955
    {'lmfdb_iso': '22848.cs', 'p': 71, 'prec': 20, 'unit': 67186242138940127328273478770406520, 'val': 1}
  • id: 1077964
    {'lmfdb_iso': '22848.cs', 'p': 73, 'prec': 20, 'unit': 83187535308979500705791869022161921, 'val': 1}
  • id: 1077961
    {'lmfdb_iso': '22848.cs', 'p': 79, 'prec': 20, 'unit': 571399927077540808054211251437865070, 'val': 1}
  • id: 1077962
    {'lmfdb_iso': '22848.cs', 'p': 83, 'prec': 20, 'unit': 1198035778414115269136385748908970787, 'val': 1}
  • id: 1077965
    {'lmfdb_iso': '22848.cs', 'p': 89, 'prec': 20, 'unit': 5433731645190517941908949438619555782, 'val': 1}
  • id: 1077952
    {'lmfdb_iso': '22848.cs', 'p': 97, 'prec': 20, 'unit': 51294468820901478154716409769082945880, 'val': 1}