Elliptic curve data - 38720.cs1

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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': '38720df', 'Clabel': '38720df1', 'Cnumber': 1, 'abc_quality': 0.93814512349847, 'absD': 204337798184960, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 1320, 'ainvs': [0, 1, 0, -7905, 736415], 'analytic_rank': 0, 'bad_primes': [2, 5, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 38720, 'degree': 92160, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4315629366431188013095402490', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 70, 'isogeny_degrees': [1, 3], 'jinv': [-117649, 440], 'lmfdb_iso': '38720.cs', 'lmfdb_label': '38720.cs1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1, 1], 'min_quad_twist_disc': 88, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '60.8.0-3.a.1.4', '264.8.0.?', '440.2.0.?', '1320.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 605], [5, 6, 7744], [11, 72, 320]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.80710547059598443484727972217', 'prec': 107}, 'szpiro_ratio': 3.8384096279627813, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 1, 0, -1, 0, -2, 0, 0, 0, 2, 0, 1, 0, 3, 0, 1, 0], 'aplist': [0, 1, 1, -1, 0, 2, 3, 1, -6, -9, -5, -5, 6, -8, -6, -9, 6, 5, 8, 9, 10, 14, 6, -15, 8], 'class_deg': 3, 'class_size': 2, 'conductor': 38720, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '38720.cs', 'trace_hash': 479979843163536699}
• 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': '0.057090024875244898363850093895', 'prec': 107}, 'conductor': 38720, 'gens': [], 'heights': [], 'lmfdb_label': '38720.cs1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.49273265627567441588268880841', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9709306251026976635307552336585790397', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [3, 0], '7': [0, 0], '11': 'a', '13': [0, 0], '17': [0, 0], '19': [4, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '38720.cs1'}
• ec_torsion_growth •

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

  
  
  • id: 1909773
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '38720.cs1', 'torsion': [3]}
  • id: 1909774
    {'degree': 3, 'field': [-8, 2, 0, 1], 'lmfdb_label': '38720.cs1', 'torsion': [2]}
  • id: 1909777
    {'degree': 6, 'field': [4, -16, -6, -4, 8, 0, 1], 'lmfdb_label': '38720.cs1', 'torsion': [6]}
  • id: 1909775
    {'degree': 6, 'field': [16, -32, 118, 16, -7, -2, 1], 'lmfdb_label': '38720.cs1', 'torsion': [2, 2]}
  • id: 1909776
    {'degree': 6, 'field': [4224, 0, -572, 0, 22, 0, 1], 'lmfdb_label': '38720.cs1', 'torsion': [3]}
  • id: 1909778
    {'degree': 12, 'field': [-146, -630, -775, 7, 393, 48, -252, -228, -174, -46, -7, -1, 1], 'lmfdb_label': '38720.cs1', 'torsion': [4]}
  • id: 1909780
    {'degree': 12, 'field': [4225, 0, 590, 0, -829, 0, -4, 0, 67, 0, 14, 0, 1], 'lmfdb_label': '38720.cs1', 'torsion': [2, 6]}
  • id: 1909779
    {'degree': 12, 'field': [17842176, 0, 2416128, 0, 234256, 0, 21032, 0, 1056, 0, -22, 0, 1], 'lmfdb_label': '38720.cs1', 'torsion': [3, 3]}
  • id: 1909781
    {'degree': 18, 'field': [-20614528, 0, 669035136, 0, -60949152, 0, -20095680, 0, 3278616, 0, 328152, 0, -34694, 0, -792, 0, 0, 0, 1], 'lmfdb_label': '38720.cs1', 'torsion': [9]}
  • id: 1909782
    {'degree': 18, 'field': [5940000, 0, 1188000, 0, 3121800, 0, 676, 0, -272916, 0, -13835, 0, 5530, 0, 595, 0, 14, 0, 1], 'lmfdb_label': '38720.cs1', 'torsion': [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: 914375
    {'conductor': 38720, 'conductor_valuation': 6, 'discriminant_valuation': 21, 'j_denominator_valuation': 3, 'kodaira_symbol': -15, 'lmfdb_label': '38720.cs1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 914376
    {'conductor': 38720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '38720.cs1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 914377
    {'conductor': 38720, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '38720.cs1', 'prime': 11, 'reduction_type': 0, '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: 1922355
    {'adelic_gens': [[659, 1314, 657, 1301], [4, 3, 9, 7], [1057, 6, 531, 19], [606, 721, 385, 771], [329, 1314, 0, 1319], [1315, 6, 1314, 7], [1, 6, 0, 1], [3, 4, 8, 11], [119, 1314, 357, 1301], [1, 0, 6, 1]], 'adelic_image': '1320.16.0.?', 'conductor': 38720, 'lmfdb_label': '38720.cs1', 'prime': 0}
  • id: 170333
    {'conductor': 38720, 'elladic_image': '3.4.0.1', 'lmfdb_label': '38720.cs1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 38720.cs does not appear in ec_padic