Elliptic curve data - 11.a3

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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': '11a', 'Clabel': '11a3', 'Cnumber': 3, 'abc_quality': 0.8254556483942886, 'absD': 11, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 550, 'ainvs': [0, -1, 1, 0, 0], 'analytic_rank': 0, 'bad_primes': [11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 11, 'degree': 5, 'elladic_images': ['25.120.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-1.1127287973354532519893939281', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 5, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5, 25], 'jinv': [-4096, 11], 'lmfdb_iso': '11.a', 'lmfdb_label': '11.a3', 'lmfdb_number': 3, 'manin_constant': 5, 'min_quad_twist_ainvs': [0, -1, 1, 0, 0], 'min_quad_twist_disc': 1, 'modell_images': ['5B.1.1'], 'modm_images': ['5.24.0-5.a.1.2', '22.2.0.a.1', '25.120.0-25.a.1.2', '110.48.1.?', '275.600.12.?', '550.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 1, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[11, 12, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1127287973354532519893939281', 'prec': 103}, 'szpiro_ratio': 4.190241815676422, 'torsion': 5, 'torsion_primes': [5], 'torsion_structure': [5]}
• 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, -1, 2, 1, 2, -2, 0, -2, -2, 1, -2, 4, 4, -1, -4, -2, 4, 0, 2], 'aplist': [-2, -1, 1, -2, 1, 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': 11, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '11.a', 'trace_hash': 1428752966040989219}
• 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': '9.2577181172797965885400335591', 'prec': 100}, 'conductor': 11, 'gens': [], 'heights': [], 'lmfdb_label': '11.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '6.3460465213977671084439730838', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.25384186085591068433775892335043887465', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0, 1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 1, 0], '3': [0, 0], '5': [0, 0], '11': [1, 0]}, 'iwp0': 7, 'lmfdb_label': '11.a3'}
• ec_torsion_growth •

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

  
  
  • id: 17
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '11.a3', 'torsion': [10]}
  • id: 18
    {'degree': 5, 'field': [-1, 3, 3, -4, -1, 1], 'lmfdb_label': '11.a3', 'torsion': [25]}
  • id: 19
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '11.a3', 'torsion': [2, 10]}
  • id: 20
    {'degree': 8, 'field': [-1, 1, 2, -7, 7, -7, 7, -4, 1], 'lmfdb_label': '11.a3', 'torsion': [15]}
  • id: 21
    {'degree': 12, 'field': [-1, 6, -10, 4, -3, 12, -8, -4, 5, -2, 6, -4, 1], 'lmfdb_label': '11.a3', 'torsion': [20]}
  • id: 22
    {'degree': 15, 'field': [-1, -3, -8, -2, 22, 1, 4, -17, -13, 14, 1, 8, -5, -3, 0, 1], 'lmfdb_label': '11.a3', 'torsion': [50]}
  • id: 24
    {'degree': 20, 'field': [1, -10, 46, -108, 101, 108, -325, 44, 749, -1227, 768, 136, -595, 403, 14, -252, 244, -134, 47, -10, 1], 'lmfdb_label': '11.a3', 'torsion': [25]}
  • id: 23
    {'degree': 20, 'field': [1, 4, 14, 54, 214, -88, -424, -114, 346, -894, -466, 1348, 1538, -782, 58, 88, -32, 18, -2, -2, 1], 'lmfdb_label': '11.a3', 'torsion': [5, 5]}
• 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

  
  {'conductor': 11, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '11.a3', 'prime': 11, '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: 1665890
    {'adelic_gens': [[316, 545, 377, 287], [38, 41, 191, 539], [1, 0, 50, 1], [1, 50, 0, 1], [501, 50, 500, 51], [516, 5, 35, 186]], 'adelic_image': '550.1200.37.?', 'conductor': 11, 'lmfdb_label': '11.a3', 'prime': 0}
  • id: 2
    {'conductor': 11, 'elladic_image': '25.120.0.1', 'lmfdb_label': '11.a3', 'modell_image': '5B.1.1', 'prime': 5}
• lmfdb_iso 11.a does not appear in ec_padic