Elliptic curve data - 243.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': '243b', 'Clabel': '243b1', 'Cnumber': 1, 'absD': 2187, 'ainvs': [0, 0, 1, 0, 2], 'analytic_rank': 0, 'bad_primes': [3], 'class_deg': 3, 'class_size': 2, 'cm': -3, 'conductor': 243, 'degree': 9, 'elladic_images': ['27.1944.55.43'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.68026026003830726167597614098', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [0, 1], 'lmfdb_iso': '243.b', 'lmfdb_label': '243.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 2], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.1'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 1, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 8, 1]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 2.757115704285749, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, 8, 0], 'aplist': [0, 0, 0, 5, 0, 2, 0, 8, 0, 0, -7, -1, 0, -13, 0, 0, 0, -1, 5, 0, -7, -4, 0, 0, 14], 'class_deg': 3, 'class_size': 2, 'conductor': 243, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '243.b', 'trace_hash': 1284796781524546439}
• 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': '3.8982218765423093654349707236', 'prec': 100}, 'conductor': 243, 'gens': [], 'heights': [], 'lmfdb_label': '243.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.6747566856453969085122985176', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2249188952151323028374328391842014656', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [[0, 1, 1]], 'xcoord_integral_points': [0]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 3, 0], '3': 'a'}, 'iwp0': 5, 'lmfdb_label': '243.b2'}
• ec_torsion_growth •

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

  
  
  • id: 10615
    {'degree': 3, 'field': [-12, 0, 0, 1], 'lmfdb_label': '243.b2', 'torsion': [6]}
  • id: 10617
    {'degree': 6, 'field': [3, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '243.b2', 'torsion': [3, 3]}
  • id: 10616
    {'degree': 6, 'field': [12, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '243.b2', 'torsion': [2, 6]}
  • id: 10618
    {'degree': 9, 'field': [-1, 0, 0, -6, 0, 0, -3, 0, 0, 1], 'lmfdb_label': '243.b2', 'torsion': [9]}
  • id: 10619
    {'degree': 12, 'field': [-12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '243.b2', 'torsion': [12]}
  • id: 10620
    {'degree': 12, 'field': [63, 0, 0, 0, 0, 0, 24, 0, 0, -9, 0, 0, 1], 'lmfdb_label': '243.b2', 'torsion': [21]}
  • id: 10621
    {'degree': 18, 'field': [1, 0, 0, 6, 0, 0, 33, 0, 0, 20, 0, 0, 15, 0, 0, -3, 0, 0, 1], 'lmfdb_label': '243.b2', 'torsion': [9, 9]}
  • id: 10622
    {'degree': 18, 'field': [27, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '243.b2', 'torsion': [6, 6]}
• 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': 243, 'conductor_valuation': 5, 'discriminant_valuation': 7, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '243.b2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  {'conductor': 243, 'elladic_image': '27.1944.55.43', 'lmfdb_label': '243.b2', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 243.b does not appear in ec_padic