Elliptic curve data - 1089.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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1089j', 'Clabel': '1089j2', 'Cnumber': 2, 'abc_quality': 1.012998630378065, 'absD': 207992207875419, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 1650, 'ainvs': [0, 0, 1, -11253, -832208], 'analytic_rank': 1, 'bad_primes': [3, 11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 1089, 'degree': 3600, 'elladic_images': ['5.60.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4402439396148370530395801460', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 5, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 5], 'jinv': [-122023936, 161051], 'lmfdb_iso': '1089.b', 'lmfdb_label': '1089.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -10, -20], 'min_quad_twist_disc': 33, 'modell_images': ['5Cs.4.1'], 'modm_images': ['5.60.0.a.1', '22.2.0.a.1', '30.120.0-5.a.1.1', '110.120.5.?', '165.120.0.?', '275.300.12.?', '330.240.5.?', '550.600.37.?', '825.600.12.?', '1650.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5311503328197968916248120549', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 6, 121], [11, 72, 9]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.30800984111840306468901426144', 'prec': 107}, 'szpiro_ratio': 5.832508524135334, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, 0, 2, -1, 0, 2, 0, 0, 2, 0, 0, -4, -4, 0, -4, -2, 0, 0, -2], 'aplist': [-2, 0, -1, 2, 0, -4, -2, 0, 1, 0, 7, 3, -8, 6, -8, 6, -5, -12, -7, 3, -4, 10, -6, -15, -7], 'class_deg': 25, 'class_size': 3, 'conductor': 1089, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '1089.b', 'trace_hash': 21587110522507335}
• 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': '0.056107382528968464172969900358', 'prec': 107}, 'conductor': 1089, 'gens': [[737, 14637, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5311503328197968916248120549', 'prec': 100}], 'lmfdb_label': '1089.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.22094098060614671238928457184', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3531754239545353161960741752893349376', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': 'a', '5': [1, 1], '7': [1, 0], '11': 'a', '13': [3, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1089.b2'}
• ec_torsion_growth •

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

  
  
  • id: 53616
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '1089.b2', 'torsion': [5]}
  • id: 53617
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '1089.b2', 'torsion': [2]}
  • id: 53618
    {'degree': 4, 'field': [361, -41, 41, -1, 1], 'lmfdb_label': '1089.b2', 'torsion': [5]}
  • id: 53620
    {'degree': 6, 'field': [-2, -6, -2, 7, 1, -1, 1], 'lmfdb_label': '1089.b2', 'torsion': [10]}
  • id: 53619
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '1089.b2', 'torsion': [2, 2]}
  • id: 53621
    {'degree': 8, 'field': [-13, 11, -14, -8, 19, 5, -7, -1, 1], 'lmfdb_label': '1089.b2', 'torsion': [3]}
  • id: 53622
    {'degree': 8, 'field': [4096, 512, 576, 136, 89, -17, 9, -1, 1], 'lmfdb_label': '1089.b2', 'torsion': [5, 5]}
  • id: 53623
    {'degree': 12, 'field': [-149, 152, 374, -618, 151, 100, 48, -24, -1, -16, 6, -2, 1], 'lmfdb_label': '1089.b2', 'torsion': [4]}
  • id: 53625
    {'degree': 12, 'field': [1, -1, -1, 4, -1, -3, 6, -3, -1, 4, -1, -1, 1], 'lmfdb_label': '1089.b2', 'torsion': [2, 10]}
  • id: 53624
    {'degree': 12, 'field': [10201, -3927, 4620, -3286, 485, -284, 77, 32, 29, -4, 8, -1, 1], 'lmfdb_label': '1089.b2', 'torsion': [10]}
  • id: 53626
    {'degree': 16, 'field': [9, -9, -9, 54, -261, 270, -306, 198, -15, -69, 108, -75, 37, -25, 14, -5, 1], 'lmfdb_label': '1089.b2', 'torsion': [15]}
• 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: 15549
    {'conductor': 1089, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1089.b2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 15550
    {'conductor': 1089, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '1089.b2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1671428
    {'adelic_gens': [[719, 1050, 315, 1079], [16, 35, 115, 561], [1, 0, 50, 1], [1, 50, 0, 1], [1201, 600, 204, 277], [1099, 0, 0, 1649], [1, 50, 10, 501], [1601, 50, 1600, 51]], 'adelic_image': '1650.1200.37.?', 'conductor': 1089, 'lmfdb_label': '1089.b2', 'prime': 0}
  • id: 5152
    {'conductor': 1089, 'elladic_image': '5.60.0.1', 'lmfdb_label': '1089.b2', 'modell_image': '5Cs.4.1', 'prime': 5}
• ec_padic •

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

  
  
  • id: 25542
    {'lmfdb_iso': '1089.b', 'p': 5, 'prec': 20, 'unit': 17593173471146, 'val': 1}
  • id: 25543
    {'lmfdb_iso': '1089.b', 'p': 7, 'prec': 20, 'unit': 2144761564919296, 'val': 1}
  • id: 25547
    {'lmfdb_iso': '1089.b', 'p': 13, 'prec': 20, 'unit': 6575516224189098838, 'val': 2}
  • id: 25549
    {'lmfdb_iso': '1089.b', 'p': 17, 'prec': 20, 'unit': 178197817291887529506181, 'val': 1}
  • id: 25554
    {'lmfdb_iso': '1089.b', 'p': 23, 'prec': 20, 'unit': 930418934492365077403630735, 'val': -1}
  • id: 25544
    {'lmfdb_iso': '1089.b', 'p': 31, 'prec': 20, 'unit': 13491765967816241401959480384, 'val': 1}
  • id: 25559
    {'lmfdb_iso': '1089.b', 'p': 37, 'prec': 20, 'unit': 174039849304140453390373918815, 'val': 1}
  • id: 25545
    {'lmfdb_iso': '1089.b', 'p': 41, 'prec': 20, 'unit': 90094605734085580230517362849, 'val': 2}
  • id: 25546
    {'lmfdb_iso': '1089.b', 'p': 43, 'prec': 20, 'unit': 8198357998205040974750884074792, 'val': 1}
  • id: 25557
    {'lmfdb_iso': '1089.b', 'p': 47, 'prec': 20, 'unit': 6899560007313402568165014023794, 'val': 1}
  • id: 25551
    {'lmfdb_iso': '1089.b', 'p': 53, 'prec': 20, 'unit': 216655849091997160687919646086945, 'val': 1}
  • id: 25552
    {'lmfdb_iso': '1089.b', 'p': 59, 'prec': 20, 'unit': 1665297281805027276974909658776442, 'val': 1}
  • id: 25558
    {'lmfdb_iso': '1089.b', 'p': 61, 'prec': 20, 'unit': 2807634808765918870543088611627868, 'val': 1}
  • id: 25541
    {'lmfdb_iso': '1089.b', 'p': 67, 'prec': 20, 'unit': 43737103863456653104386030454396734, 'val': 1}
  • id: 25556
    {'lmfdb_iso': '1089.b', 'p': 71, 'prec': 20, 'unit': 91401817117020758610774267795910529, 'val': 1}
  • id: 25553
    {'lmfdb_iso': '1089.b', 'p': 73, 'prec': 20, 'unit': 17492731126981219980085233852819892, 'val': 1}
  • id: 25548
    {'lmfdb_iso': '1089.b', 'p': 79, 'prec': 20, 'unit': 860408975343884263539884917002592547, 'val': 1}
  • id: 25550
    {'lmfdb_iso': '1089.b', 'p': 83, 'prec': 20, 'unit': 2166216169089781270564566595440451847, 'val': 1}
  • id: 25555
    {'lmfdb_iso': '1089.b', 'p': 89, 'prec': 20, 'unit': 7863582323778578677443421360659834210, 'val': 1}
  • id: 25540
    {'lmfdb_iso': '1089.b', 'p': 97, 'prec': 20, 'unit': 11058309287174139372109210763174358829, 'val': 1}