Elliptic curve data - 1936.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
  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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1936k', 'Clabel': '1936k1', 'Cnumber': 1, 'abc_quality': 0.9461121308337243, 'absD': 59969536, 'adelic_genus': 16, 'adelic_index': 480, 'adelic_level': 88, 'ainvs': [0, 1, 0, -40, 372], 'analytic_rank': 1, 'bad_primes': [2, 11], 'class_deg': 11, 'class_size': 2, 'cm': 0, 'conductor': 1936, 'degree': 384, 'elladic_images': ['8.4.0.2', '11.60.1.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.17518634244426622003229266361', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 11], 'jinv': [-121, 1], 'lmfdb_iso': '1936.b', 'lmfdb_label': '1936.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -2, -7], 'min_quad_twist_disc': -4, 'modell_images': ['11B.10.4'], 'modm_images': ['4.2.0.a.1', '8.4.0-4.a.1.1', '11.60.1.b.1', '22.120.1-11.b.1.1', '44.240.6-44.b.1.2', '88.480.16.?'], 'nonmax_primes': [2, 11], 'nonmax_rad': 22, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.23702021742337972781475335818', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3172592623818026040722539838', 'prec': 103}, 'szpiro_ratio': 3.360263352205102, '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, -2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, -2, 0, -5, 0, -6, 0], 'aplist': [0, -2, 1, 2, 0, 1, -5, -6, -2, 9, 2, -3, -5, 0, -2, 9, -8, 6, -2, -12, -2, 10, -6, -9, -13], 'class_deg': 11, 'class_size': 2, 'conductor': 1936, 'isogeny_matrix': [[1, 11], [11, 1]], 'lmfdb_iso': '1936.b', 'trace_hash': 551826526527420750}
• 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': '0.70442551204895047667652905343', 'prec': 103}, 'conductor': 1936, 'gens': [[-4, 22, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.23702021742337972781475335818', 'prec': 103}], 'lmfdb_label': '1936.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.6911384598331397954566296935', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4050040326561419135900914929259790809', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [-4, 7, 12]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1936.b2'}
• ec_torsion_growth •

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

  
  
  • id: 97827
    {'degree': 3, 'field': [2, 4, -1, 1], 'lmfdb_label': '1936.b2', 'torsion': [2]}
  • id: 97828
    {'degree': 6, 'field': [4, 0, 20, 0, -7, 0, 1], 'lmfdb_label': '1936.b2', 'torsion': [2, 2]}
  • id: 97829
    {'degree': 8, 'field': [-3, 0, -19, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '1936.b2', 'torsion': [3]}
  • id: 97830
    {'degree': 10, 'field': [-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1], 'lmfdb_label': '1936.b2', 'torsion': [11]}
  • id: 97831
    {'degree': 12, 'field': [1, -3, 2, 9, -32, 55, -62, 55, -32, 9, 2, -3, 1], 'lmfdb_label': '1936.b2', 'torsion': [4]}
• 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: 31473
    {'conductor': 1936, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '1936.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 31474
    {'conductor': 1936, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '1936.b2', 'prime': 11, '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

  
  
  • id: 1676589
    {'adelic_gens': [[1, 84, 0, 1], [73, 0, 0, 49], [45, 44, 44, 45], [1, 0, 44, 1], [45, 22, 22, 1], [12, 55, 77, 23], [1, 44, 0, 1], [45, 44, 66, 1], [43, 55, 0, 21]], 'adelic_image': '88.480.16.?', 'conductor': 1936, 'lmfdb_label': '1936.b2', 'prime': 0}
  • id: 9457
    {'conductor': 1936, 'elladic_image': '8.4.0.2', 'lmfdb_label': '1936.b2', 'modell_image': '2G', 'prime': 2}
  • id: 9458
    {'conductor': 1936, 'elladic_image': '11.60.1.4', 'lmfdb_label': '1936.b2', 'modell_image': '11B.10.4', 'prime': 11}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 55777
    {'lmfdb_iso': '1936.b', 'p': 5, 'prec': 20, 'unit': 94604247748039, 'val': -1}
  • id: 55778
    {'lmfdb_iso': '1936.b', 'p': 7, 'prec': 20, 'unit': 2330477726538400, 'val': 1}
  • id: 55783
    {'lmfdb_iso': '1936.b', 'p': 13, 'prec': 20, 'unit': 11396230745605826810655, 'val': -1}
  • id: 55785
    {'lmfdb_iso': '1936.b', 'p': 17, 'prec': 20, 'unit': 88633335411773597311097, 'val': 1}
  • id: 55786
    {'lmfdb_iso': '1936.b', 'p': 19, 'prec': 20, 'unit': 130612028615864012971517, 'val': 1}
  • id: 55790
    {'lmfdb_iso': '1936.b', 'p': 23, 'prec': 20, 'unit': 1982987192055218235446362, 'val': 1}
  • id: 55782
    {'lmfdb_iso': '1936.b', 'p': 29, 'prec': 20, 'unit': 2277899709014438820144292787, 'val': 1}
  • id: 55779
    {'lmfdb_iso': '1936.b', 'p': 31, 'prec': 20, 'unit': 5454180039299376784746358641, 'val': 1}
  • id: 55794
    {'lmfdb_iso': '1936.b', 'p': 37, 'prec': 20, 'unit': 260049750516256854700998984180, 'val': 1}
  • id: 55780
    {'lmfdb_iso': '1936.b', 'p': 41, 'prec': 20, 'unit': 3627221752707702194074276345766, 'val': 1}
  • id: 55792
    {'lmfdb_iso': '1936.b', 'p': 47, 'prec': 20, 'unit': 38301026253482757933865715004424, 'val': 1}
  • id: 55787
    {'lmfdb_iso': '1936.b', 'p': 53, 'prec': 20, 'unit': 478019514105485284265195271537102, 'val': 1}
  • id: 55788
    {'lmfdb_iso': '1936.b', 'p': 59, 'prec': 20, 'unit': 2720576943919174686484016574896611, 'val': 1}
  • id: 55793
    {'lmfdb_iso': '1936.b', 'p': 61, 'prec': 20, 'unit': 2695622825754320782732538011614251, 'val': 1}
  • id: 55776
    {'lmfdb_iso': '1936.b', 'p': 67, 'prec': 20, 'unit': 9661065717945265981584358867895338, 'val': 1}
  • id: 55781
    {'lmfdb_iso': '1936.b', 'p': 71, 'prec': 20, 'unit': 56189575358980127518372961817199070, 'val': 1}
  • id: 55789
    {'lmfdb_iso': '1936.b', 'p': 73, 'prec': 20, 'unit': 173690473362459372308451850630793768, 'val': 1}
  • id: 55784
    {'lmfdb_iso': '1936.b', 'p': 79, 'prec': 20, 'unit': 144758669435165376430705624850959520, 'val': 1}
  • id: 55775
    {'lmfdb_iso': '1936.b', 'p': 83, 'prec': 20, 'unit': 2552103956886695523558270863459245633, 'val': 1}
  • id: 55791
    {'lmfdb_iso': '1936.b', 'p': 89, 'prec': 20, 'unit': 1203676847838672633276077626868753607, 'val': 1}
  • id: 55774
    {'lmfdb_iso': '1936.b', 'p': 97, 'prec': 20, 'unit': 30003239512231793418129879470960619257, 'val': 1}