Elliptic curve data - 1089.e1

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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': '1089b', 'Clabel': '1089b1', 'Cnumber': 1, 'absD': 700310464227, 'ainvs': [0, 0, 1, 0, -40263], 'analytic_rank': 0, 'bad_primes': [3, 11], 'class_deg': 3, 'class_size': 2, 'cm': -3, 'conductor': 1089, 'degree': 1232, 'elladic_images': ['11.165.5.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.95178170440429829457722842835', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 3], 'jinv': [0, 1], 'lmfdb_iso': '1089.e', 'lmfdb_label': '1089.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 30], 'min_quad_twist_disc': -11, 'modell_images': ['11Nn.1.4'], 'nonmax_primes': [11], 'nonmax_rad': 11, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 363], [3, 6, 121], [11, 22, 9]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 4.9663140909648185, '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, 0, 0, -5, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 7, 0], 'aplist': [0, 0, 0, -5, 0, -2, 0, 7, 0, 0, 11, 11, 0, -8, 0, 0, 0, 1, 11, 0, -17, 13, 0, 0, 5], 'class_deg': 3, 'class_size': 2, 'conductor': 1089, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '1089.e', 'trace_hash': 1847930099670751024}
• 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': '0.14903659356283523404200766441', 'prec': 103}, 'conductor': 1089, 'gens': [], 'heights': [], 'lmfdb_label': '1089.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.41484049323229710182617593147', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.82968098646459420365235186293204928033', 'prec': 133}, '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, 0], '7': [0, 0], '11': 'a', '13': [0, 0], '17': [0, 0, 0], '19': [0, 0], '23': [0, 0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '1089.e1'}
• ec_torsion_growth •

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

  
  
  • id: 53458
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '1089.e1', 'torsion': [3]}
  • id: 53459
    {'degree': 3, 'field': [13, -7, -1, 1], 'lmfdb_label': '1089.e1', 'torsion': [2]}
  • id: 53461
    {'degree': 6, 'field': [-297, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1089.e1', 'torsion': [3]}
  • id: 53462
    {'degree': 6, 'field': [15, -6, 23, -4, 9, -2, 1], 'lmfdb_label': '1089.e1', 'torsion': [6]}
  • id: 53460
    {'degree': 6, 'field': [75, 0, -29, 0, 1, 0, 1], 'lmfdb_label': '1089.e1', 'torsion': [2, 2]}
  • id: 53463
    {'degree': 12, 'field': [-1623, -1698, 3762, -1056, 1111, 836, 220, 176, 121, -22, 22, -4, 1], 'lmfdb_label': '1089.e1', 'torsion': [4]}
  • id: 53466
    {'degree': 12, 'field': [36, -36, -12, -12, 52, -18, 23, -39, 18, -9, 8, -3, 1], 'lmfdb_label': '1089.e1', 'torsion': [2, 6]}
  • id: 53464
    {'degree': 12, 'field': [144, -72, -144, 390, -75, -192, 163, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '1089.e1', 'torsion': [3, 3]}
  • id: 53465
    {'degree': 12, 'field': [1237, 614, 1957, 1335, 997, 1064, 267, 248, 94, -10, 17, -2, 1], 'lmfdb_label': '1089.e1', 'torsion': [7]}
  • id: 53468
    {'degree': 18, 'field': [-8, 0, 0, -148, 0, 0, -490, 0, 0, 3983, 0, 0, 245, 0, 0, -37, 0, 0, 1], 'lmfdb_label': '1089.e1', 'torsion': [6]}
  • id: 53467
    {'degree': 18, 'field': [213, 936, 1962, -3801, -2151, 6030, -5829, -1257, 6084, -3994, 2589, -954, 411, -156, 126, -9, 12, 0, 1], 'lmfdb_label': '1089.e1', 'torsion': [9]}
• 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: 15513
    {'conductor': 1089, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1089.e1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 15514
    {'conductor': 1089, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '1089.e1', 'prime': 11, 'reduction_type': 0, '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

  
  {'conductor': 1089, 'elladic_image': '11.165.5.1', 'lmfdb_label': '1089.e1', 'modell_image': '11Nn.1.4', 'prime': 11}
• lmfdb_iso 1089.e does not appear in ec_padic