Elliptic curve data - 187200.in1

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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': '187200mi', 'Clabel': '187200mi3', 'Cnumber': 3, 'abc_quality': 1.052193877800105, 'absD': 29113344000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -749100, 249550000], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 187200, 'degree': 1048576, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9037240153337966660166156864', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 221, 'isogeny_degrees': [1, 2, 4], 'jinv': [62275269892, 39], 'lmfdb_iso': '187200.in', 'lmfdb_label': '187200.in1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -832, -9520], 'min_quad_twist_disc': -120, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.z.1', '40.12.0-4.c.1.2', '104.12.0.?', '120.24.0.?', '156.12.0.?', '312.24.0.?', '520.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.90467044046711282405178946454', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 2925], [3, 8, 20800], [5, 14, 7488], [13, 14, 14400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37449732596390211287102942729', 'prec': 107}, 'szpiro_ratio': 4.299322492341188, '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, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, 0, 0, 0, 1, 2, 4, 0, 6, 0, -2, -6, -12, -4, -6, -8, 2, 4, 12, 14, 0, -8, 18, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 187200, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '187200.in', 'trace_hash': 1694691627376561802}
• 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': '0.022204772612426742011555190739', 'prec': 107}, 'conductor': 187200, 'gens': [[510, 400, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.90467044046711282405178946454', 'prec': 103}], 'lmfdb_label': '187200.in1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.54732048073291918802635460950', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.9223145661011510357245097997898582837', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[500, 0, 1]], 'xcoord_integral_points': [500, 501, 510, 590, 1400]}
• lmfdb_label 187200.in1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8254222
    {'degree': 2, 'field': [-390, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [4]}
  • id: 8254221
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [2, 2]}
  • id: 8254223
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [4]}
  • id: 8254224
    {'degree': 4, 'field': [841, 0, -98, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [2, 4]}
  • id: 8254228
    {'degree': 8, 'field': [-16875, 0, -8250, 0, 450, 0, 0, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [6]}
  • id: 8254227
    {'degree': 8, 'field': [961, 0, 92, 0, 63, 0, 2, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [8]}
  • id: 8254226
    {'degree': 8, 'field': [16641, 0, -8532, 0, 1423, 0, -82, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [8]}
  • id: 8254225
    {'degree': 8, 'field': [27556, -13280, 14588, -2696, 1549, -244, 86, -4, 1], 'lmfdb_label': '187200.in1', 'torsion': [2, 4]}
  • id: 8254232
    {'degree': 16, 'field': [-5076961191, 5736946356, -1898050104, 653304348, -51214500, -122453748, 835944, 14385396, -1709298, 106236, -135720, -684, 4876, -220, -72, -4, 1], 'lmfdb_label': '187200.in1', 'torsion': [2, 6]}
  • id: 8254230
    {'degree': 16, 'field': [3136, 0, -81024, 0, 577984, 0, -1090944, 0, 359376, 0, -48816, 0, 3184, 0, -96, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [2, 8]}
  • id: 8254233
    {'degree': 16, 'field': [1004004, 0, -4752888, 0, -37446764, 0, -2860752, 0, -32100, 0, -181756, 0, 744, 0, 0, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [12]}
  • id: 8254231
    {'degree': 16, 'field': [1500625, 0, 710500, 0, 182050, 0, 4480, 0, -1589, 0, 2368, 0, 658, 0, 28, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [2, 8]}
  • id: 8254229
    {'degree': 16, 'field': [48012136, 62471600, 39782008, 8229920, 2027148, 3267920, 456040, -333360, 112846, 60780, -15610, -2640, 1523, -20, -58, 0, 1], 'lmfdb_label': '187200.in1', 'torsion': [4, 4]}
  • id: 8254234
    {'degree': 16, 'field': [51127824, 430141888, -247757536, -132248512, 74854864, 18567072, -9206688, -1724144, 736136, 109760, -39512, -5184, 1512, 184, -52, -4, 1], 'lmfdb_label': '187200.in1', '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: 4633192
    {'conductor': 187200, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '187200.in1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4633193
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '187200.in1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4633194
    {'conductor': 187200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '187200.in1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4633195
    {'conductor': 187200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '187200.in1', '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: 2866569
    {'adelic_gens': [[269, 270, 1430, 29], [1, 0, 8, 1], [824, 1245, 515, 934], [1, 8, 0, 1], [1, 4, 4, 17], [623, 0, 0, 1559], [1516, 625, 215, 6], [1056, 905, 145, 816], [1553, 8, 1552, 9], [7, 6, 1554, 1555]], 'adelic_image': '1560.48.0.?', 'conductor': 187200, 'lmfdb_label': '187200.in1', 'prime': 0}
  • id: 699284
    {'conductor': 187200, 'elladic_image': '4.6.0.1', 'lmfdb_label': '187200.in1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 187200.in does not appear in ec_padic