Elliptic curve data - 1008.e4

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '1008g', 'Clabel': '1008g4', 'Cnumber': 4, 'abc_quality': 1.0121470066906046, 'absD': 5377010688, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 0, 0, 429, 866], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1008, 'degree': 512, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.55626513940314938919857294812', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [11696828, 7203], 'lmfdb_iso': '1008.e', 'lmfdb_label': '1008.e4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 48, 48], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '6.6.0.a.1', '12.24.0-12.g.1.2', '56.24.0-56.ba.1.13', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 15, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.68815432164241278023671161100', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.57066365539752654768007643822', 'prec': 107}, 'szpiro_ratio': 4.308728365273921, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 0, 0, -2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, -2, 1, 0, -2, -6, 4, -4, -6, 8, -10, 10, -12, -8, -6, 4, -10, -12, 4, 2, -8, 4, -6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 1008, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1008.e', 'trace_hash': 652906082165316733}
• 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': '0.32872613910078235029576516593', 'prec': 103}, 'conductor': 1008, 'gens': [[1, 36, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.68815432164241278023671161100', 'prec': 103}], 'lmfdb_label': '1008.e4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.83788672024673682221895262987', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3063814703383170713476282544500528762', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[19, 126, 1]], 'xcoord_integral_points': [-2, 1, 5, 19, 34, 61, 145, 523]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [2, 0], '11': [3, 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, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1008.e4'}
• ec_torsion_growth •

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

  
  
  • id: 49022
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '1008.e4', 'torsion': [2, 4]}
  • id: 49023
    {'degree': 4, 'field': [-12, 0, 6, 0, 1], 'lmfdb_label': '1008.e4', 'torsion': [8]}
  • id: 49027
    {'degree': 8, 'field': [-14, -52, 34, 16, -4, -2, 4, -4, 1], 'lmfdb_label': '1008.e4', 'torsion': [12]}
  • id: 49025
    {'degree': 8, 'field': [1, -2, 8, 12, 11, 12, 8, -2, 1], 'lmfdb_label': '1008.e4', 'torsion': [2, 8]}
  • id: 49024
    {'degree': 8, 'field': [9, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '1008.e4', 'torsion': [4, 4]}
  • id: 49026
    {'degree': 8, 'field': [144, 0, 72, 0, 48, 0, -6, 0, 1], 'lmfdb_label': '1008.e4', 'torsion': [2, 8]}
  • id: 49029
    {'degree': 16, 'field': [9, 0, -60, 0, 382, 0, -120, 0, 39, 0, -40, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '1008.e4', 'torsion': [2, 12]}
  • id: 49028
    {'degree': 16, 'field': [441, 0, -1764, 0, 1386, 0, -252, 0, 102, 0, -60, 0, -30, 0, 12, 0, 1], 'lmfdb_label': '1008.e4', '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: 14062
    {'conductor': 1008, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '1008.e4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 14063
    {'conductor': 1008, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1008.e4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 14064
    {'conductor': 1008, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1008.e4', 'prime': 7, 'reduction_type': 1, '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: 1670924
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [7, 6, 162, 163], [161, 8, 160, 9], [52, 167, 89, 162], [1, 4, 4, 17], [73, 8, 124, 33], [101, 104, 166, 99], [67, 66, 34, 115]], 'adelic_image': '168.48.0.?', 'conductor': 1008, 'lmfdb_label': '1008.e4', 'prime': 0}
  • id: 4736
    {'conductor': 1008, 'elladic_image': '4.12.0.7', 'lmfdb_label': '1008.e4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 22875
    {'lmfdb_iso': '1008.e', 'p': 5, 'prec': 20, 'unit': 18872719838522, 'val': 1}
  • id: 22881
    {'lmfdb_iso': '1008.e', 'p': 13, 'prec': 20, 'unit': 697119403126556401101, 'val': 1}
  • id: 22883
    {'lmfdb_iso': '1008.e', 'p': 17, 'prec': 20, 'unit': 201334395111438506865396, 'val': 1}
  • id: 22884
    {'lmfdb_iso': '1008.e', 'p': 19, 'prec': 20, 'unit': 1874973675550472849848899, 'val': 1}
  • id: 22888
    {'lmfdb_iso': '1008.e', 'p': 23, 'prec': 20, 'unit': 39484888743794637035322071, 'val': 1}
  • id: 22880
    {'lmfdb_iso': '1008.e', 'p': 29, 'prec': 20, 'unit': 4507444447523242855047338495, 'val': 1}
  • id: 22877
    {'lmfdb_iso': '1008.e', 'p': 31, 'prec': 20, 'unit': 10692631964751845824077791791, 'val': 1}
  • id: 22892
    {'lmfdb_iso': '1008.e', 'p': 37, 'prec': 20, 'unit': 25599895147510965858816121124, 'val': 1}
  • id: 22878
    {'lmfdb_iso': '1008.e', 'p': 41, 'prec': 20, 'unit': 4129157835892298889967898898497, 'val': 1}
  • id: 22879
    {'lmfdb_iso': '1008.e', 'p': 43, 'prec': 20, 'unit': 3175230173623921218843314846861, 'val': 1}
  • id: 22890
    {'lmfdb_iso': '1008.e', 'p': 47, 'prec': 20, 'unit': 22177558065981800445001095314223, 'val': 1}
  • id: 22885
    {'lmfdb_iso': '1008.e', 'p': 53, 'prec': 20, 'unit': 37147780274570626310679678503170, 'val': 1}
  • id: 22886
    {'lmfdb_iso': '1008.e', 'p': 59, 'prec': 20, 'unit': 1699473820255431029853673158181737, 'val': 1}
  • id: 22891
    {'lmfdb_iso': '1008.e', 'p': 61, 'prec': 20, 'unit': 2348436309483231451012623028655240, 'val': 1}
  • id: 22874
    {'lmfdb_iso': '1008.e', 'p': 67, 'prec': 20, 'unit': 34556847858784221782843135242359467, 'val': 1}
  • id: 22876
    {'lmfdb_iso': '1008.e', 'p': 71, 'prec': 20, 'unit': 87362083667956365248321653248055185, 'val': 1}
  • id: 22887
    {'lmfdb_iso': '1008.e', 'p': 73, 'prec': 20, 'unit': 54367249009206355861700576846220860, 'val': 1}
  • id: 22882
    {'lmfdb_iso': '1008.e', 'p': 79, 'prec': 20, 'unit': 890069900888161504932527390248087479, 'val': 1}
  • id: 22873
    {'lmfdb_iso': '1008.e', 'p': 83, 'prec': 20, 'unit': 603622344714985044148357223132864198, 'val': 1}
  • id: 22889
    {'lmfdb_iso': '1008.e', 'p': 89, 'prec': 20, 'unit': 8649975947341649284696999538920417691, 'val': 1}
  • id: 22872
    {'lmfdb_iso': '1008.e', 'p': 97, 'prec': 20, 'unit': 26216358918062589859259066611681734238, 'val': 1}