Elliptic curve data - 235200.cj4

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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': '235200cj', 'Clabel': '235200cj1', 'Cnumber': 1, 'abc_quality': 0.9605836908258326, 'absD': 988251600000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, -1, 0, -859133, 306788637], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 235200, 'degree': 2359296, 'elladic_images': ['8.24.0.94'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0174419239634375752570602703', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 61, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [37256083456, 525], 'lmfdb_iso': '235200.cj', 'lmfdb_label': '235200.cj4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -175, 952], 'min_quad_twist_disc': 280, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.3', '42.6.0.a.1', '48.48.0-48.e.2.16', '80.48.0.?', '84.12.0.?', '112.48.0.?', '120.48.0.?', '168.48.0.?', '240.96.0.?', '280.48.0.?', '336.96.0.?', '560.96.0.?', '840.96.0.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9516750008139415920999030140', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3675], [3, 4, 78400], [5, 18, 9408], [7, 32, 4800]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33785475724789035577702253592', 'prec': 107}, 'szpiro_ratio': 4.253220147704425, '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, -1, 0, 0, 0, 0, 0, 1, 0, -4, 0, 2, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, -1, 0, 0, -4, 2, 2, 4, 0, 10, 0, 6, 6, 4, 8, 6, 4, -10, -4, 16, -14, -8, -4, -10, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 235200, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '235200.cj', 'trace_hash': 1316399584937204650}
• 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': '0.017687734460895272600562152739', 'prec': 107}, 'conductor': 235200, 'gens': [[532, 125, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9516750008139415920999030140', 'prec': 100}], 'lmfdb_label': '235200.cj4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.45117748761459078978021616099', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.0444145880595088178636614138567979920', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[537, 0, 1]], 'xcoord_integral_points': [-443, 532, 537]}
• lmfdb_label 235200.cj4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10170406
    {'degree': 2, 'field': [-70, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [4]}
  • id: 10170407
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [4]}
  • id: 10170405
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '235200.cj4', 'torsion': [2, 2]}
  • id: 10170410
    {'degree': 4, 'field': [49, 0, -56, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [8]}
  • id: 10170408
    {'degree': 4, 'field': [100, 0, -50, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [2, 4]}
  • id: 10170409
    {'degree': 4, 'field': [289, 0, -36, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [8]}
  • id: 10170414
    {'degree': 8, 'field': [-132300, 0, 92680, 0, 7140, 0, 210, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [6]}
  • id: 10170411
    {'degree': 8, 'field': [1, 0, 46, 0, 6, 0, 46, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [2, 4]}
  • id: 10170413
    {'degree': 8, 'field': [1225, 0, -1260, 0, 359, 0, -36, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [2, 8]}
  • id: 10170412
    {'degree': 8, 'field': [15814, 7024, 8228, 964, 124, -100, 38, -4, 1], 'lmfdb_label': '235200.cj4', 'torsion': [8]}
  • id: 10170415
    {'degree': 16, 'field': [7056, 0, 0, 0, -9744, 0, 25200, 0, 36796, 0, 14200, 0, 2616, 0, 100, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [4, 4]}
  • id: 10170421
    {'degree': 16, 'field': [275625, 0, -1947750, 0, 2812600, 0, -3281250, 0, 691950, 0, 113750, 0, 5280, 0, 90, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [12]}
  • id: 10170419
    {'degree': 16, 'field': [2480625, 0, 393750, 0, -1370900, 0, -493950, 0, -42150, 0, 25850, 0, 1500, 0, 150, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [2, 6]}
  • id: 10170420
    {'degree': 16, 'field': [150062500, 0, 111475000, 0, 9677500, 0, -5488000, 0, -254800, 0, 980, 0, 2800, 0, 70, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [12]}
  • id: 10170417
    {'degree': 16, 'field': [167987521, 0, -264649816, 0, 125225632, 0, -27781488, 0, 3307010, 0, -219352, 0, 7952, 0, -144, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [16]}
  • id: 10170416
    {'degree': 16, 'field': [431363521, 1337277060, 1783728642, 1316690340, 568305034, 127594320, -571062, -9586080, -2651301, -163380, 80358, 20160, 892, -420, -60, 0, 1], 'lmfdb_label': '235200.cj4', 'torsion': [2, 8]}
  • id: 10170418
    {'degree': 16, 'field': [1445346826, -244111336, -445611040, 44865240, 71488694, -2409716, -8064308, 158520, 545011, 11004, -25628, -2512, 1154, 48, -4, -8, 1], 'lmfdb_label': '235200.cj4', 'torsion': [16]}
• 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: 5828075
    {'conductor': 235200, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '235200.cj4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5828076
    {'conductor': 235200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '235200.cj4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5828077
    {'conductor': 235200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '235200.cj4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 5828078
    {'conductor': 235200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '235200.cj4', 'prime': 7, '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: 3160693
    {'adelic_gens': [[5, 4, 1676, 1677], [1679, 1664, 1260, 1259], [1, 16, 0, 1], [1665, 16, 1664, 17], [1184, 1675, 765, 14], [15, 2, 1582, 1667], [568, 1, 1199, 10], [1, 0, 16, 1], [659, 1664, 592, 315], [195, 1664, 526, 309]], 'adelic_image': '1680.192.1.?', 'conductor': 235200, 'lmfdb_label': '235200.cj4', 'prime': 0}
  • id: 854670
    {'conductor': 235200, 'elladic_image': '8.24.0.94', 'lmfdb_label': '235200.cj4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 235200.cj does not appear in ec_padic