Elliptic curve data - 5025.b2

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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': '5025e', 'Clabel': '5025e2', 'Cnumber': 2, 'abc_quality': 0.9578467147857307, 'absD': 517716720703125, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4020, 'ainvs': [1, 0, 0, 8187, -1056258], 'analytic_rank': 1, 'bad_primes': [3, 5, 67], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 5025, 'degree': 17280, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5047130004124759794288426640', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [3883959939959, 33133870125], 'lmfdb_iso': '5025.b', 'lmfdb_label': '5025.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 328, -8319], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.a.1', '804.6.0.?', '4020.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.55676341365513254955816722866', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 1675], [5, 18, 67], [67, 68, 75]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.69999404419542579212846299739', 'prec': 103}, 'szpiro_ratio': 4.842061474555799, '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, -1, 1, -1, 0, -1, 0, 3, 1, 0, 0, -1, -4, 0, 0, -1, 4, -1, 4, 0], 'aplist': [-1, 1, 0, 0, 0, -4, 4, 4, -8, -2, 2, -6, 6, 0, -12, 2, -6, 14, 1, 14, -2, -10, 16, -18, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 5025, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '5025.b', 'trace_hash': 1227860549647654237}
• 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': '0.049319980265150517305809665495', 'prec': 107}, 'conductor': 5025, 'gens': [[87, 519, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.55676341365513254955816722866', 'prec': 103}], 'lmfdb_label': '5025.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25847503220829540957701404691', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8781888255382177199216238026372887689', 'prec': 130}, 'tamagawa_product': 80, 'torsion_generators': [[303, -303, 2]], 'xcoord_integral_points': [87, 126, 582, 2337]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 1], '3': [2, 0], '5': 'a', '7': [1, 1, 0], '11': [1, 3, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [5, 0], '43': [1, 1, 0], '47': [1, 0], '67': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '5025.b2'}
• ec_torsion_growth •

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

  
  
  • id: 262318
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '5025.b2', 'torsion': [2, 2]}
  • id: 262319
    {'degree': 4, 'field': [-20, 0, -11, 0, 1], 'lmfdb_label': '5025.b2', 'torsion': [4]}
  • id: 262320
    {'degree': 8, 'field': [726, 132, -118, -40, 51, -40, 18, -4, 1], 'lmfdb_label': '5025.b2', 'torsion': [2, 4]}
  • id: 262322
    {'degree': 8, 'field': [1625, 425, 2171, -3231, 627, 138, -35, -2, 1], 'lmfdb_label': '5025.b2', 'torsion': [6]}
  • id: 262321
    {'degree': 8, 'field': [3600, 0, 3900, 0, 121, 0, -2, 0, 1], 'lmfdb_label': '5025.b2', 'torsion': [2, 4]}
  • id: 262324
    {'degree': 16, 'field': [178929, 0, -246564, 0, 12960, 0, 51743, 0, 7100, 0, 413, 0, -83, 0, 10, 0, 1], 'lmfdb_label': '5025.b2', 'torsion': [2, 6]}
  • id: 262323
    {'degree': 16, 'field': [2342560000, 0, 1901152000, 0, 523741600, 0, -82522400, 0, -1827815, 0, 216295, 0, -1106, 0, -59, 0, 1], 'lmfdb_label': '5025.b2', 'torsion': [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: 97334
    {'conductor': 5025, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '5025.b2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 97335
    {'conductor': 5025, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '5025.b2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 97336
    {'conductor': 5025, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5025.b2', 'prime': 67, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1696760
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1141, 4, 2282, 9], [1, 2, 2, 5], [1, 4, 0, 1], [2414, 1, 803, 0], [3016, 1009, 1005, 3016], [4017, 4, 4016, 5], [2681, 4, 1342, 9]], 'adelic_image': '4020.12.0.?', 'conductor': 5025, 'lmfdb_label': '5025.b2', 'prime': 0}
  • id: 24896
    {'conductor': 5025, 'elladic_image': '2.3.0.1', 'lmfdb_label': '5025.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 184658
    {'lmfdb_iso': '5025.b', 'p': 13, 'prec': 20, 'unit': 22429123082067951702, 'val': 2}
  • id: 184660
    {'lmfdb_iso': '5025.b', 'p': 17, 'prec': 20, 'unit': 47638599507017577545083, 'val': 1}
  • id: 184650
    {'lmfdb_iso': '5025.b', 'p': 19, 'prec': 20, 'unit': 1076040289967857246075973, 'val': 1}
  • id: 184656
    {'lmfdb_iso': '5025.b', 'p': 23, 'prec': 20, 'unit': 43963211026255357345178312, 'val': 1}
  • id: 184657
    {'lmfdb_iso': '5025.b', 'p': 29, 'prec': 20, 'unit': 4931094428485467095487772892, 'val': 1}
  • id: 184667
    {'lmfdb_iso': '5025.b', 'p': 31, 'prec': 20, 'unit': 254221961339030480533132427, 'val': 2}
  • id: 184653
    {'lmfdb_iso': '5025.b', 'p': 37, 'prec': 20, 'unit': 7291643627453031451412866962, 'val': 1}
  • id: 184655
    {'lmfdb_iso': '5025.b', 'p': 41, 'prec': 20, 'unit': 51013516463732523481934114151, 'val': 2}
  • id: 184665
    {'lmfdb_iso': '5025.b', 'p': 47, 'prec': 20, 'unit': 822413808461957604650079560022, 'val': 1}
  • id: 184662
    {'lmfdb_iso': '5025.b', 'p': 53, 'prec': 20, 'unit': 323622263172626650479687837307202, 'val': 1}
  • id: 184652
    {'lmfdb_iso': '5025.b', 'p': 59, 'prec': 20, 'unit': 4015297252823887505910908742565752, 'val': 1}
  • id: 184666
    {'lmfdb_iso': '5025.b', 'p': 61, 'prec': 20, 'unit': 5334644308896003729162030420447597, 'val': 1}
  • id: 184654
    {'lmfdb_iso': '5025.b', 'p': 71, 'prec': 20, 'unit': 104186236693116690974811101651415854, 'val': 1}
  • id: 184663
    {'lmfdb_iso': '5025.b', 'p': 73, 'prec': 20, 'unit': 218949722517976525277969027428429438, 'val': 1}
  • id: 184659
    {'lmfdb_iso': '5025.b', 'p': 79, 'prec': 20, 'unit': 454893437433136278218308157243019271, 'val': 1}
  • id: 184661
    {'lmfdb_iso': '5025.b', 'p': 83, 'prec': 20, 'unit': 2572156422704321390998593187385726399, 'val': 1}
  • id: 184664
    {'lmfdb_iso': '5025.b', 'p': 89, 'prec': 20, 'unit': 3897329510208586901110480452034918005, 'val': 1}
  • id: 184651
    {'lmfdb_iso': '5025.b', 'p': 97, 'prec': 20, 'unit': 23247284939088479095942347825825505213, 'val': 1}