Elliptic curve data - 233289.b1

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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': '233289b', 'Clabel': '233289b2', 'Cnumber': 2, 'abc_quality': 1.1059237401535138, 'absD': 991870961644560484651563, 'adelic_genus': 9, 'adelic_index': 336, 'adelic_level': 12558, 'ainvs': [0, 0, 1, -212837331, -1196103024090], 'analytic_rank': 1, 'bad_primes': [3, 7, 23], 'class_deg': 13, 'class_size': 2, 'cm': 0, 'conductor': 233289, 'degree': 55351296, 'elladic_images': ['13.28.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5273954891380024096554339749', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 13, 'iso_nlabel': 1, 'isogeny_degrees': [1, 13], 'jinv': [-1713910976512, 1594323], 'lmfdb_iso': '233289.b', 'lmfdb_label': '233289.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -912, 10919], 'min_quad_twist_disc': -483, 'modell_images': ['13B.4.2'], 'modm_images': ['6.2.0.a.1', '13.28.0.a.2', '78.56.1.?', '91.84.2.?', '546.168.9.?', '598.56.0.?', '897.56.0.?', '1794.112.1.?', '4186.168.2.?', '6279.168.2.?', '12558.336.9.?'], 'nonmax_primes': [13], 'nonmax_rad': 13, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.864897410103845559490777085', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 8, 25921], [7, 26, 4761], [23, 266, 441]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.11306880413583051515086644490', 'prec': 103}, 'szpiro_ratio': 5.594105099484086, '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, -2, 0, 0, 0, 0, 4, -2, 0, 1, 0, 0, -4, 0, 0, -1, -4], 'aplist': [-2, 0, -2, 0, -2, 1, 0, -1, 0, -4, 9, -3, 10, -5, 6, 12, 12, -10, 5, 6, -3, 1, 6, 16, 6], 'class_deg': 13, 'class_size': 2, 'conductor': 233289, 'isogeny_matrix': [[1, 13], [13, 1]], 'lmfdb_iso': '233289.b', 'trace_hash': 439091993717558242}
• 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': '0.00086326315898102682377996494355', 'prec': 113}, 'conductor': 233289, 'gens': [[42367311, 275291737235, 13]], 'heights': [{'__RealLiteral__': 0, 'data': '11.864897410103845559490777085', 'prec': 100}], 'lmfdb_label': '233289.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.019762113203036042283517387935', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8137053491305761991437435091047711152', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 233289.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10096495
    {'degree': 3, 'field': [1, 5, -1, 1], 'lmfdb_label': '233289.b1', 'torsion': [2]}
  • id: 10096496
    {'degree': 6, 'field': [27, 9, -8, -3, 4, -3, 1], 'lmfdb_label': '233289.b1', 'torsion': [2, 2]}
  • id: 10096497
    {'degree': 8, 'field': [-36787, 3522, 7171, -4337, 945, -64, 5, -3, 1], 'lmfdb_label': '233289.b1', 'torsion': [3]}
  • id: 10096498
    {'degree': 12, 'field': [-5251149, 9393624, -8140662, 2038182, 767719, -526484, 107640, -8224, 379, -28, -6, -2, 1], 'lmfdb_label': '233289.b1', 'torsion': [4]}
  • id: 10096499
    {'degree': 12, 'field': [179464251513, 19516208802, 14214525469, 180812345, 524789682, 10354993, 15436370, 18576, 147941, -170, 612, -1, 1], 'lmfdb_label': '233289.b1', 'torsion': [13]}
• 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: 5781144
    {'conductor': 233289, 'conductor_valuation': 2, 'discriminant_valuation': 19, 'j_denominator_valuation': 13, 'kodaira_symbol': -17, 'lmfdb_label': '233289.b1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5781145
    {'conductor': 233289, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '233289.b1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
  • id: 5781146
    {'conductor': 233289, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '233289.b1', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 3149141
    {'adelic_gens': [[14, 23, 871, 1431], [8371, 5980, 5083, 2391], [8735, 0, 0, 12557], [12533, 26, 12532, 27], [1, 0, 26, 1], [9889, 5980, 10764, 7543], [5475, 6578, 7774, 9569], [1, 26, 0, 1]], 'adelic_image': '12558.336.9.?', 'conductor': 233289, 'lmfdb_label': '233289.b1', 'prime': 0}
  • id: 848591
    {'conductor': 233289, 'elladic_image': '13.28.0.2', 'lmfdb_label': '233289.b1', 'modell_image': '13B.4.2', 'prime': 13}
• lmfdb_iso 233289.b does not appear in ec_padic