Elliptic curve data - 186914.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
  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': '186914g', 'Clabel': '186914g4', 'Cnumber': 4, 'abc_quality': 0.9629603875428203, 'absD': 73697803796439368, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 8216, 'ainvs': [1, -1, 0, -375296, -87430056], 'analytic_rank': 1, 'bad_primes': [2, 7, 13, 79], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 186914, 'degree': 1769472, 'elladic_images': ['8.12.0.15'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0458144259155476284402026013', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4], 'jinv': [1211116876909857, 15268431752], 'lmfdb_iso': '186914.b', 'lmfdb_label': '186914.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -2221, -39283], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.k.1', '52.12.0-4.c.1.1', '104.24.0.?', '632.24.0.?', '8216.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '15.607610785006046952671140754', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 169], [3, 2, 93457], [7, 8, 26702], [13, 86, 1106], [79, 80, 2366]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.76333974718477926041345888052', 'prec': 103}, 'szpiro_ratio': 4.129044966503688, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• 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, -1, 0, 1, 2, 0, -1, -1, -3, -2, 4, 0, 0, 1, 0, 1, 2, 3, 4, 2], 'aplist': [-1, 0, 2, -1, 4, 0, 2, 4, 0, -6, 0, 6, -10, -8, 0, 2, 0, -6, 4, -8, -10, -1, -4, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 186914, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '186914.b', 'trace_hash': 1252987396790819694}
• 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': '0.016711990021213918624651587106', 'prec': 107}, 'conductor': 186914, 'gens': [[63349693, 448105926679, 204]], 'heights': [{'__RealLiteral__': 0, 'data': '15.607610785006046952671140754', 'prec': 100}], 'lmfdb_label': '186914.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19303549626788149810028856088', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.0256457868791635907236056028006497322', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-1533, 1533, 2]], 'xcoord_integral_points': []}
• lmfdb_label 186914.b2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8239440
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '186914.b2', 'torsion': [2, 2]}
  • id: 8239441
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '186914.b2', 'torsion': [4]}
  • id: 8239442
    {'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '186914.b2', 'torsion': [4]}
  • id: 8239443
    {'degree': 4, 'field': [49, 0, 12, 0, 1], 'lmfdb_label': '186914.b2', 'torsion': [2, 4]}
  • id: 8239447
    {'degree': 8, 'field': [-296804, 412630, 20191, 8578, -548, 280, 22, -2, 1], 'lmfdb_label': '186914.b2', 'torsion': [6]}
  • id: 8239444
    {'degree': 8, 'field': [6647, 4028, -4170, 296, -177, 32, -6, -4, 1], 'lmfdb_label': '186914.b2', 'torsion': [2, 4]}
  • id: 8239445
    {'degree': 8, 'field': [195350, 57170, -17301, 2498, 1541, -210, 49, -2, 1], 'lmfdb_label': '186914.b2', 'torsion': [8]}
  • id: 8239446
    {'degree': 8, 'field': [2579236, 0, 129968, 0, 3612, 0, 40, 0, 1], 'lmfdb_label': '186914.b2', 'torsion': [8]}
  • id: 8239451
    {'degree': 16, 'field': [-304550454116, -305767766984, 156282046040, 4367587956, 9124719857, 218885756, 177776812, 54453528, 4032400, 912288, 60598, 30148, -2116, 528, 32, -4, 1], 'lmfdb_label': '186914.b2', 'torsion': [2, 6]}
  • id: 8239448
    {'degree': 16, 'field': [2965769, -8581664, 10035816, -7031472, 3622104, 2228128, -2032380, -437696, 375385, 48216, -36176, -1904, 2218, 0, -56, 0, 1], 'lmfdb_label': '186914.b2', 'torsion': [4, 4]}
  • id: 8239449
    {'degree': 16, 'field': [476119588, 51834368, 231949568, 29656032, 50660632, 7965104, 6380528, 1148032, 504104, 81872, 24624, 1904, 532, -72, -24, 0, 1], 'lmfdb_label': '186914.b2', 'torsion': [2, 8]}
  • id: 8239452
    {'degree': 16, 'field': [607721104, 0, 537166796, 0, 156993961, 0, 23881772, 0, 2142724, 0, 124250, 0, 4684, 0, 104, 0, 1], 'lmfdb_label': '186914.b2', 'torsion': [12]}
  • id: 8239450
    {'degree': 16, 'field': [7186287182, 196160492, -1515586102, 143611476, 287624435, -67829836, -8771998, 6059108, -439411, -131804, 37766, -7540, 2665, -420, 46, -4, 1], 'lmfdb_label': '186914.b2', 'torsion': [2, 8]}
  • id: 8239453
    {'degree': 16, 'field': [155576602624, 0, 68757349888, 0, 10047613504, 0, 764216704, 0, 34283584, 0, 994000, 0, 18736, 0, 208, 0, 1], 'lmfdb_label': '186914.b2', 'torsion': [12]}
• 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: 4624383
    {'conductor': 186914, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '186914.b2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4624384
    {'conductor': 186914, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '186914.b2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4624385
    {'conductor': 186914, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '186914.b2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4624386
    {'conductor': 186914, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '186914.b2', 'prime': 79, 'reduction_type': -1, '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: 2864600
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 8210, 8211], [8209, 8, 8208, 9], [5136, 403, 2769, 4694], [3953, 7592, 3172, 5721], [3875, 1976, 2314, 5773], [5055, 0, 0, 8215]], 'adelic_image': '8216.48.0.?', 'conductor': 186914, 'lmfdb_label': '186914.b2', 'prime': 0}
  • id: 698216
    {'conductor': 186914, 'elladic_image': '8.12.0.15', 'lmfdb_label': '186914.b2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 186914.b does not appear in ec_padic