Elliptic curve data - 194688.r2

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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': '194688ci', 'Clabel': '194688ci2', 'Cnumber': 2, 'abc_quality': 0.7935250407803479, 'absD': 9743035524857856, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 624, 'ainvs': [0, 0, 0, -44616, -5975840], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 194688, 'degree': 774144, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7637507535888636025607816402', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2], 'jinv': [-170368, 169], 'lmfdb_iso': '194688.r', 'lmfdb_label': '194688.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -29, 91], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '12.12.0-4.a.1.2', '104.12.0.?', '208.24.0.?', '312.24.0.?', '624.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1521], [3, 2, 21632], [13, 98, 1152]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.87670178012922913881702217408', 'prec': 107}, 'szpiro_ratio': 3.672637494439383, '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, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, -2, -2, 0, 0, -2, 0, -4, -2, -2, 6, -6, -2, 6, 6, 8, 2, 8, -2, 14, 4, -8, -14, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 194688, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '194688.r', 'trace_hash': 1418328088003118837}
• 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': '0.029378225532692490129223541462', 'prec': 107}, 'conductor': 194688, 'gens': [], 'heights': [], 'lmfdb_label': '194688.r2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15791302496241762183528373788', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.63165209984967048734113495152048752679', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[260, 0, 1]], 'xcoord_integral_points': [260]}
• lmfdb_label 194688.r2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8560468
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [2, 2]}
  • id: 8560469
    {'degree': 4, 'field': [-225, 0, -6, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [4]}
  • id: 8560472
    {'degree': 8, 'field': [27, -732, 1512, -1660, 718, -100, 4, -4, 1], 'lmfdb_label': '194688.r2', 'torsion': [6]}
  • id: 8560471
    {'degree': 8, 'field': [841, 0, -716, 0, 362, 0, -4, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [2, 4]}
  • id: 8560470
    {'degree': 8, 'field': [7465, 1108, -1856, -1148, 480, -76, 40, -4, 1], 'lmfdb_label': '194688.r2', 'torsion': [2, 4]}
  • id: 8560473
    {'degree': 16, 'field': [1, 0, 0, 0, -102, 0, 0, 0, 10403, 0, 0, 0, -102, 0, 0, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [4, 4]}
  • id: 8560474
    {'degree': 16, 'field': [47524, 0, 406912, 0, 776656, 0, 553424, 0, 148764, 0, 6880, 0, -248, 0, -40, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [8]}
  • id: 8560475
    {'degree': 16, 'field': [749453, 584624, -17240, 252920, 77796, -30744, 33584, -10640, 5866, -2256, 1528, 152, 124, -40, 0, 0, 1], 'lmfdb_label': '194688.r2', 'torsion': [2, 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

  
  
  • id: 4821251
    {'conductor': 194688, 'conductor_valuation': 7, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '194688.r2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4821252
    {'conductor': 194688, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '194688.r2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4821253
    {'conductor': 194688, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '194688.r2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2913289
    {'adelic_gens': [[155, 414, 0, 623], [3, 8, 10, 27], [1, 0, 8, 1], [1, 8, 0, 1], [479, 414, 0, 623], [77, 204, 351, 623], [415, 0, 0, 623], [5, 8, 48, 77], [617, 8, 616, 9]], 'adelic_image': '624.48.0.?', 'conductor': 194688, 'lmfdb_label': '194688.r2', 'prime': 0}
  • id: 724411
    {'conductor': 194688, 'elladic_image': '4.6.0.5', 'lmfdb_label': '194688.r2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 194688.r does not appear in ec_padic