Elliptic curve data - 1089.g2

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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': '1089e', 'Clabel': '1089e1', 'Cnumber': 1, 'abc_quality': 1.0251241218312794, 'absD': 970299, 'ainvs': [0, 0, 1, -66, -212], 'analytic_rank': 0, 'bad_primes': [3, 11], 'class_deg': 11, 'class_size': 2, 'cm': -11, 'conductor': 1089, 'degree': 120, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.073766679995419603973548741678', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 6, 'isogeny_degrees': [1, 11], 'jinv': [-32768, 1], 'lmfdb_iso': '1089.g', 'lmfdb_label': '1089.g2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -7, 10], 'min_quad_twist_disc': -3, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 99], [3, 2, 121], [11, 42, 9]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2225466425290670856866572546', 'prec': 103}, 'szpiro_ratio': 3.465451994405012, '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, 0, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -6], 'aplist': [0, 0, 3, 0, 0, 0, 0, 0, 9, 0, -5, 7, 0, 0, 12, -6, 15, 0, 13, 3, 0, 0, 0, 9, 17], 'class_deg': 11, 'class_size': 2, 'conductor': 1089, 'isogeny_matrix': [[1, 11], [11, 1]], 'lmfdb_iso': '1089.g', 'trace_hash': 996847679136073904}
• 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': '1.1589719474784053852647317196', 'prec': 100}, 'conductor': 1089, 'gens': [], 'heights': [], 'lmfdb_label': '1089.g2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.83599424664542189612256810638', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6719884932908437922451362127504359485', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': 'a', '5': [0, 0], '7': [0, 0, 0], '11': 'a', '13': [0, 0, 0], '17': [0, 0, 0], '19': [0, 0, 0], '23': [0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '1089.g2'}
• ec_torsion_growth •

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

  
  
  • id: 53508
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '1089.g2', 'torsion': [2]}
  • id: 53509
    {'degree': 4, 'field': [-2, 5, -4, -2, 1], 'lmfdb_label': '1089.g2', 'torsion': [3]}
  • id: 53510
    {'degree': 4, 'field': [4, 2, -1, -1, 1], 'lmfdb_label': '1089.g2', 'torsion': [3]}
  • id: 53511
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '1089.g2', 'torsion': [2, 2]}
  • id: 53512
    {'degree': 8, 'field': [16, 8, 8, 6, -1, -3, 2, -1, 1], 'lmfdb_label': '1089.g2', 'torsion': [3, 3]}
  • id: 53513
    {'degree': 8, 'field': [201, -60, 112, -49, -26, 29, -4, -3, 1], 'lmfdb_label': '1089.g2', 'torsion': [5]}
  • id: 53514
    {'degree': 10, 'field': [1, -3, 12, 1, 20, -7, 16, -2, 5, -1, 1], 'lmfdb_label': '1089.g2', 'torsion': [11]}
  • id: 53515
    {'degree': 12, 'field': [-9851, 21118, -17696, 3238, 4415, -2792, 596, 172, -193, 34, 4, -2, 1], 'lmfdb_label': '1089.g2', 'torsion': [4]}
  • id: 53517
    {'degree': 12, 'field': [1, -1, -7, -14, -15, -9, 4, 13, -1, -8, 9, -5, 1], 'lmfdb_label': '1089.g2', 'torsion': [6]}
  • id: 53518
    {'degree': 12, 'field': [47, -180, 291, -312, 296, -240, 175, -124, 72, -36, 15, -4, 1], 'lmfdb_label': '1089.g2', 'torsion': [2, 6]}
  • id: 53516
    {'degree': 12, 'field': [113, 40, 174, 124, 141, -22, 45, -14, 22, -8, 5, -2, 1], 'lmfdb_label': '1089.g2', 'torsion': [9]}
  • id: 53519
    {'degree': 16, 'field': [-70319, 16025, 68823, -28857, -7467, 19258, -8965, -1650, 3296, -1693, -90, 374, -125, 15, 12, -7, 1], 'lmfdb_label': '1089.g2', 'torsion': [5]}
  • id: 53520
    {'degree': 16, 'field': [9, -36, 153, -345, 721, -1008, 1298, -1155, 1068, -420, 76, 45, -51, 12, 2, -3, 1], 'lmfdb_label': '1089.g2', '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: 15525
    {'conductor': 1089, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1089.g2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 15526
    {'conductor': 1089, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1089.g2', 'prime': 11, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• lmfdb_label 1089.g2 does not appear in ec_galrep
• lmfdb_iso 1089.g does not appear in ec_padic