Elliptic curve data - 18648.u2

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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': '18648z', 'Clabel': '18648z1', 'Cnumber': 1, 'abc_quality': 0.9212770528271738, 'absD': 350529887232, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2072, 'ainvs': [0, 0, 0, 141, 28478], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 18648, 'degree': 20736, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.89422331018891824970001627074', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2], 'jinv': [415292, 469567], 'lmfdb_iso': '18648.u', 'lmfdb_label': '18648.u2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 16, -1060], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '14.6.0.b.1', '296.6.0.?', '2072.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.4926017570135322130009926558', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 63], [3, 6, 296], [7, 8, 2664], [37, 38, 504]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.23270548461175768717863311560', 'prec': 107}, 'szpiro_ratio': 3.4613250578862997, '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, 2, 0, -1, 0, 0, 0, -4, 0, -6, 0, 0, 0, 4, 0, 4, 0], 'aplist': [0, 0, 2, -1, -4, -6, 4, 4, 0, 10, 2, -1, 2, -4, 0, -6, 0, -14, 12, 8, -14, 12, -6, 0, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 18648, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '18648.u', 'trace_hash': 1399216970805956129}
• 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': '0.16721972373312125303616266711', 'prec': 103}, 'conductor': 18648, 'gens': [[259, 4176, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.4926017570135322130009926558', 'prec': 100}], 'lmfdb_label': '18648.u2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.74939093241463268065619202687', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2346481744827105413757669739949133186', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-29, 0, 1]], 'xcoord_integral_points': [-29, 259]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '18648.u2'}
• ec_torsion_growth •

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

  
  
  • id: 955484
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '18648.u2', 'torsion': [2, 2]}
  • id: 955485
    {'degree': 4, 'field': [-182, -44, 45, -2, 1], 'lmfdb_label': '18648.u2', 'torsion': [4]}
  • id: 955488
    {'degree': 8, 'field': [-309, -516, -252, 108, 126, 18, -20, -2, 1], 'lmfdb_label': '18648.u2', 'torsion': [6]}
  • id: 955487
    {'degree': 8, 'field': [88, 1424, 5679, -1440, 243, -52, 29, -4, 1], 'lmfdb_label': '18648.u2', 'torsion': [2, 4]}
  • id: 955486
    {'degree': 8, 'field': [70756, 0, -6356, 0, 1677, 0, 94, 0, 1], 'lmfdb_label': '18648.u2', 'torsion': [2, 4]}
  • id: 955490
    {'degree': 16, 'field': [3528022, -6649628, 3649166, 447538, -867744, -129332, 310734, -61262, -38231, 16868, 1758, -1990, 186, 122, -22, -4, 1], 'lmfdb_label': '18648.u2', 'torsion': [2, 6]}
  • id: 955489
    {'degree': 16, 'field': [9077634712, -13391475968, 13618508192, 949639568, -3928627900, 3990441888, -1076658492, -210562040, 44399673, 5259848, -821568, -121056, 16354, 1736, -228, -8, 1], 'lmfdb_label': '18648.u2', '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: 420461
    {'conductor': 18648, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '18648.u2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 420462
    {'conductor': 18648, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '18648.u2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 420463
    {'conductor': 18648, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '18648.u2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 420464
    {'conductor': 18648, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '18648.u2', 'prime': 37, '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: 1788666
    {'adelic_gens': [[1, 0, 4, 1], [594, 1, 1775, 0], [3, 4, 8, 11], [1037, 4, 2, 9], [1, 2, 2, 5], [1, 4, 0, 1], [1297, 778, 776, 1295], [2069, 4, 2068, 5], [113, 4, 226, 9]], 'adelic_image': '2072.12.0.?', 'conductor': 18648, 'lmfdb_label': '18648.u2', 'prime': 0}
  • id: 87341
    {'conductor': 18648, 'elladic_image': '2.3.0.1', 'lmfdb_label': '18648.u2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 859621
    {'lmfdb_iso': '18648.u', 'p': 5, 'prec': 20, 'unit': 7999629353133, 'val': 1}
  • id: 859628
    {'lmfdb_iso': '18648.u', 'p': 11, 'prec': 20, 'unit': 5887349325466694847, 'val': 1}
  • id: 859626
    {'lmfdb_iso': '18648.u', 'p': 13, 'prec': 20, 'unit': 1245684424432225044257, 'val': 1}
  • id: 859629
    {'lmfdb_iso': '18648.u', 'p': 17, 'prec': 20, 'unit': 138372159968726782325338, 'val': 1}
  • id: 859630
    {'lmfdb_iso': '18648.u', 'p': 19, 'prec': 20, 'unit': 181942449209052327707095, 'val': 1}
  • id: 859625
    {'lmfdb_iso': '18648.u', 'p': 29, 'prec': 20, 'unit': 3849222509102577568768570293, 'val': 1}
  • id: 859634
    {'lmfdb_iso': '18648.u', 'p': 31, 'prec': 20, 'unit': 11813957863000630538399930171, 'val': 1}
  • id: 859623
    {'lmfdb_iso': '18648.u', 'p': 41, 'prec': 20, 'unit': 2702988437315330885689595457481, 'val': 1}
  • id: 859624
    {'lmfdb_iso': '18648.u', 'p': 43, 'prec': 20, 'unit': 9470157994550262769000930735046, 'val': 1}
  • id: 859631
    {'lmfdb_iso': '18648.u', 'p': 53, 'prec': 20, 'unit': 76138200419306365617396463466666, 'val': 1}
  • id: 859633
    {'lmfdb_iso': '18648.u', 'p': 61, 'prec': 20, 'unit': 7137888821258490998670543898540547, 'val': 1}
  • id: 859620
    {'lmfdb_iso': '18648.u', 'p': 67, 'prec': 20, 'unit': 4705205868506188209500265878397535, 'val': 1}
  • id: 859622
    {'lmfdb_iso': '18648.u', 'p': 71, 'prec': 20, 'unit': 127320971560366530679522476165678400, 'val': 1}
  • id: 859632
    {'lmfdb_iso': '18648.u', 'p': 73, 'prec': 20, 'unit': 146706823637639641889581624160911687, 'val': 1}
  • id: 859627
    {'lmfdb_iso': '18648.u', 'p': 79, 'prec': 20, 'unit': 1071344556710728753345235053477027420, 'val': 1}
  • id: 859619
    {'lmfdb_iso': '18648.u', 'p': 83, 'prec': 20, 'unit': 1761577146146119741570911826538889919, 'val': 1}
  • id: 859618
    {'lmfdb_iso': '18648.u', 'p': 97, 'prec': 20, 'unit': 4253212347299635316932389649384034019, 'val': 1}