Elliptic curve data - 187200.pa1

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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': '187200oc', 'Clabel': '187200oc2', 'Cnumber': 2, 'abc_quality': 0.9036561668018798, 'absD': 1768635648000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, 0, 0, -54300, -4430000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 187200, 'degree': 983040, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6621314896160998849331789472', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 390, 'isogeny_degrees': [1, 2], 'jinv': [94875856, 9477], 'lmfdb_iso': '187200.pa', 'lmfdb_label': '187200.pa1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -60, 144], 'min_quad_twist_disc': -120, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '26.6.0.b.1', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 2925], [3, 6, 20800], [5, 14, 7488], [13, 14, 14400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.50056532158827467571826081291', 'prec': 107}, 'szpiro_ratio': 3.650797918206918, '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, 0, 0, 4, 0, 0, 0, -2, 0, -1, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 0, 4, -2, -1, -6, -4, 4, -6, 8, -10, 4, -4, -6, -6, -6, 6, 0, -10, 2, 0, 10, -8, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 187200, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '187200.pa', 'trace_hash': 1841774117717576965}
• 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': '0.035999041019350840678769230151', 'prec': 107}, 'conductor': 187200, 'gens': [], 'heights': [], 'lmfdb_label': '187200.pa1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.31476373659690013658560163673', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2590549463876005463424065469372318668', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-100, 0, 1]], 'xcoord_integral_points': [-100]}
• lmfdb_label 187200.pa1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8255273
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '187200.pa1', 'torsion': [2, 2]}
  • id: 8255274
    {'degree': 4, 'field': [1300, 0, 70, 0, 1], 'lmfdb_label': '187200.pa1', 'torsion': [4]}
  • id: 8255277
    {'degree': 8, 'field': [-1875, 0, 0, 0, 150, 0, -10, 0, 1], 'lmfdb_label': '187200.pa1', 'torsion': [6]}
  • id: 8255275
    {'degree': 8, 'field': [17161, 0, -31974, 0, -773, 0, -6, 0, 1], 'lmfdb_label': '187200.pa1', 'torsion': [2, 4]}
  • id: 8255276
    {'degree': 8, 'field': [90000, 0, -3000, 0, 400, 0, 10, 0, 1], 'lmfdb_label': '187200.pa1', 'torsion': [2, 4]}
  • id: 8255279
    {'degree': 16, 'field': [-2436669, 11073516, -12124344, 2533464, -2332632, 1246296, -375906, -6568, -26077, 8836, 7266, -4168, 88, 252, -16, -8, 1], 'lmfdb_label': '187200.pa1', 'torsion': [2, 6]}
  • id: 8255278
    {'degree': 16, 'field': [900601, 0, 1318960, 0, 681748, 0, 130864, 0, 19054, 0, 1936, 0, 196, 0, 16, 0, 1], 'lmfdb_label': '187200.pa1', 'torsion': [8]}
• 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: 4633604
    {'conductor': 187200, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '187200.pa1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4633605
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '187200.pa1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4633606
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '187200.pa1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4633607
    {'conductor': 187200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '187200.pa1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 2866879
    {'adelic_gens': [[1, 2, 2, 5], [53, 4, 106, 9], [134, 1, 11, 0], [3, 4, 8, 11], [153, 4, 152, 5], [1, 4, 0, 1], [41, 118, 116, 39], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 187200, 'lmfdb_label': '187200.pa1', 'prime': 0}
  • id: 699535
    {'conductor': 187200, 'elladic_image': '2.3.0.1', 'lmfdb_label': '187200.pa1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 187200.pa does not appear in ec_padic