Elliptic curve data - 15075.l2

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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': '15075i', 'Clabel': '15075i2', 'Cnumber': 2, 'abc_quality': 0.9578467147857307, 'absD': 377415489392578125, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4020, 'ainvs': [1, -1, 0, 73683, 28518966], 'analytic_rank': 1, 'bad_primes': [3, 5, 67], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 15075, 'degree': 138240, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0540191447465308251264652825', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2], 'jinv': [3883959939959, 33133870125], 'lmfdb_iso': '15075.l', 'lmfdb_label': '15075.l2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 328, -8319], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.a.1', '804.6.0.?', '4020.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.1012048133498278246076341150', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 225], [3, 8, 1675], [5, 18, 603], [67, 68, 225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.69999404419542579212846299743', 'prec': 103}, 'szpiro_ratio': 4.974288151787057, '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, 1, 0, -1, 0, 0, 0, -3, 0, 0, 0, 0, -4, 0, 0, -1, -4, 0, 4, 0], 'aplist': [1, 0, 0, 0, 0, -4, -4, 4, 8, 2, 2, -6, -6, 0, 12, -2, 6, 14, 1, -14, -2, -10, -16, 18, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 15075, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '15075.l', 'trace_hash': 564443591876084166}
• 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': '0.016439993421716839101936555165', 'prec': 107}, 'conductor': 15075, 'gens': [[6213, 675597, 4]], 'heights': [{'__RealLiteral__': 0, 'data': '6.1012048133498278246076341150', 'prec': 100}], 'lmfdb_label': '15075.l2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.22033001516034102729417353225', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.3771141960868528493915402730282460170', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-909, 909, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 1], '3': 'a', '5': 'a', '7': [1, 1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0], '67': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '15075.l2'}
• ec_torsion_growth •

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

  
  
  • id: 775384
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '15075.l2', 'torsion': [2, 2]}
  • id: 775385
    {'degree': 4, 'field': [-5, 0, -28, 0, 1], 'lmfdb_label': '15075.l2', 'torsion': [4]}
  • id: 775388
    {'degree': 8, 'field': [-6929, -4111, 3802, 617, -305, -7, 7, -4, 1], 'lmfdb_label': '15075.l2', 'torsion': [6]}
  • id: 775387
    {'degree': 8, 'field': [2025, 0, -1500, 0, 355, 0, -20, 0, 1], 'lmfdb_label': '15075.l2', 'torsion': [2, 4]}
  • id: 775386
    {'degree': 8, 'field': [87904, -6432, 6910, -962, 497, -22, 12, -4, 1], 'lmfdb_label': '15075.l2', 'torsion': [2, 4]}
  • id: 775390
    {'degree': 16, 'field': [169, 0, 709, 0, 448, 0, 5521, 0, 2065, 0, 103, 0, 19, 0, 10, 0, 1], 'lmfdb_label': '15075.l2', 'torsion': [2, 6]}
  • id: 775389
    {'degree': 16, 'field': [100000000, 0, -336750000, 0, 218531875, 0, 34848375, 0, 1754775, 0, 30150, 0, -395, 0, 15, 0, 1], 'lmfdb_label': '15075.l2', '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: 333025
    {'conductor': 15075, 'conductor_valuation': 2, 'discriminant_valuation': 16, 'j_denominator_valuation': 10, 'kodaira_symbol': -14, 'lmfdb_label': '15075.l2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 333026
    {'conductor': 15075, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '15075.l2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 333027
    {'conductor': 15075, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '15075.l2', 'prime': 67, 'reduction_type': 1, '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: 1764364
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1141, 4, 2282, 9], [1, 2, 2, 5], [1, 4, 0, 1], [2414, 1, 803, 0], [3016, 1009, 1005, 3016], [4017, 4, 4016, 5], [2681, 4, 1342, 9]], 'adelic_image': '4020.12.0.?', 'conductor': 15075, 'lmfdb_label': '15075.l2', 'prime': 0}
  • id: 71231
    {'conductor': 15075, 'elladic_image': '2.3.0.1', 'lmfdb_label': '15075.l2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 676583
    {'lmfdb_iso': '15075.l', 'p': 13, 'prec': 20, 'unit': 883857803946315591739, 'val': 1}
  • id: 676585
    {'lmfdb_iso': '15075.l', 'p': 17, 'prec': 20, 'unit': 77708010356495202053887, 'val': 1}
  • id: 676575
    {'lmfdb_iso': '15075.l', 'p': 19, 'prec': 20, 'unit': 290271977030115643677942, 'val': 1}
  • id: 676581
    {'lmfdb_iso': '15075.l', 'p': 23, 'prec': 20, 'unit': 37724148900425457754546305, 'val': 1}
  • id: 676582
    {'lmfdb_iso': '15075.l', 'p': 29, 'prec': 20, 'unit': 3452930478173508056167385741, 'val': 1}
  • id: 676592
    {'lmfdb_iso': '15075.l', 'p': 31, 'prec': 20, 'unit': 8197369434141905079804898040, 'val': 1}
  • id: 676578
    {'lmfdb_iso': '15075.l', 'p': 37, 'prec': 20, 'unit': 430242424794883134857239223162, 'val': 1}
  • id: 676580
    {'lmfdb_iso': '15075.l', 'p': 41, 'prec': 20, 'unit': 922544587968065381320028768510, 'val': 1}
  • id: 676590
    {'lmfdb_iso': '15075.l', 'p': 47, 'prec': 20, 'unit': 38106514078529313293882187788915, 'val': 1}
  • id: 676587
    {'lmfdb_iso': '15075.l', 'p': 53, 'prec': 20, 'unit': 101657962001113593583136131378791, 'val': 1}
  • id: 676577
    {'lmfdb_iso': '15075.l', 'p': 59, 'prec': 20, 'unit': 3800838742909205754153959086180384, 'val': 1}
  • id: 676591
    {'lmfdb_iso': '15075.l', 'p': 61, 'prec': 20, 'unit': 7486856098474402760591868451216460, 'val': 1}
  • id: 676579
    {'lmfdb_iso': '15075.l', 'p': 71, 'prec': 20, 'unit': 114623354410491107256605138126126217, 'val': 1}
  • id: 676588
    {'lmfdb_iso': '15075.l', 'p': 73, 'prec': 20, 'unit': 9146227687133693897840010570845329, 'val': 1}
  • id: 676584
    {'lmfdb_iso': '15075.l', 'p': 79, 'prec': 20, 'unit': 809921778544447797474140514666447542, 'val': 1}
  • id: 676586
    {'lmfdb_iso': '15075.l', 'p': 83, 'prec': 20, 'unit': 1871827776891175487655363552883206447, 'val': 1}
  • id: 676589
    {'lmfdb_iso': '15075.l', 'p': 89, 'prec': 20, 'unit': 8509445787834859830889728633289557227, 'val': 1}
  • id: 676576
    {'lmfdb_iso': '15075.l', 'p': 97, 'prec': 20, 'unit': 17616156684121165404015425883283541494, 'val': 1}