Elliptic curve data - 1008.i1

Formats: - HTML - YAML - JSON - 2024-06-10T10:41:59.976613

• 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': '1008a', 'Clabel': '1008a1', 'Cnumber': 1, 'abc_quality': 0.8157560984175539, 'absD': 2204496, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 84, 'ainvs': [0, 0, 0, -54, 135], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1008, 'degree': 192, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.053615324079199163246489902159', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2], 'jinv': [55296, 7], 'lmfdb_iso': '1008.i', 'lmfdb_label': '1008.i1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -6, 5], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '28.6.0.d.1', '42.6.0.a.1', '84.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0261077295249786437937411684', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1086236007669298682653345370', 'prec': 103}, 'szpiro_ratio': 3.4097018695973604, '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, -6, 0, -6, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, 2, -1, -6, -6, -2, -4, -2, 8, -4, -6, 10, 4, 4, -4, 12, -2, -12, -6, -2, 8, 0, -14, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 1008, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1008.i', 'trace_hash': 1355073422499928431}
• 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': '1.1131909803210728609661462118', 'prec': 100}, 'conductor': 1008, 'gens': [[7, 10, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0261077295249786437937411684', 'prec': 100}], 'lmfdb_label': '1008.i1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.5074269992406519338677696261', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5401586121905538198407262110392917883', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[3, 0, 1]], 'xcoord_integral_points': [3, 7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1008.i1'}
• ec_torsion_growth •

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

  
  
  • id: 48866
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '1008.i1', 'torsion': [2, 2]}
  • id: 48867
    {'degree': 4, 'field': [21, 0, -9, 0, 1], 'lmfdb_label': '1008.i1', 'torsion': [4]}
  • id: 48870
    {'degree': 8, 'field': [-12, 0, 20, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '1008.i1', 'torsion': [6]}
  • id: 48869
    {'degree': 8, 'field': [9, 0, 9, 0, 12, 0, -3, 0, 1], 'lmfdb_label': '1008.i1', 'torsion': [2, 4]}
  • id: 48868
    {'degree': 8, 'field': [49, 0, -98, 0, 0, 0, 7, 0, 1], 'lmfdb_label': '1008.i1', 'torsion': [2, 4]}
  • id: 48871
    {'degree': 16, 'field': [1, 2, 0, 6, 11, 18, 32, 8, 45, -8, 32, -18, 11, -6, 0, -2, 1], 'lmfdb_label': '1008.i1', 'torsion': [8]}
  • id: 48872
    {'degree': 16, 'field': [441, 0, 4452, 0, -5480, 0, 5652, 0, -474, 0, -596, 0, -24, 0, 12, 0, 1], 'lmfdb_label': '1008.i1', 'torsion': [2, 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: 14011
    {'conductor': 1008, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '1008.i1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 14012
    {'conductor': 1008, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '1008.i1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 14013
    {'conductor': 1008, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1008.i1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1670937
    {'adelic_gens': [[1, 2, 2, 5], [62, 1, 11, 0], [81, 4, 80, 5], [3, 4, 8, 11], [32, 1, 55, 0], [1, 4, 0, 1], [65, 22, 20, 63], [1, 0, 4, 1]], 'adelic_image': '84.12.0.?', 'conductor': 1008, 'lmfdb_label': '1008.i1', 'prime': 0}
  • id: 4759
    {'conductor': 1008, 'elladic_image': '2.3.0.1', 'lmfdb_label': '1008.i1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 22811
    {'lmfdb_iso': '1008.i', 'p': 5, 'prec': 20, 'unit': 2016106521372, 'val': 2}
  • id: 22810
    {'lmfdb_iso': '1008.i', 'p': 11, 'prec': 20, 'unit': 12114179480392260624, 'val': 1}
  • id: 22817
    {'lmfdb_iso': '1008.i', 'p': 13, 'prec': 20, 'unit': 175902408946058803659, 'val': 1}
  • id: 22819
    {'lmfdb_iso': '1008.i', 'p': 17, 'prec': 20, 'unit': 99963972575050855307324, 'val': 1}
  • id: 22820
    {'lmfdb_iso': '1008.i', 'p': 19, 'prec': 20, 'unit': 2387843041621410546484, 'val': 1}
  • id: 22824
    {'lmfdb_iso': '1008.i', 'p': 23, 'prec': 20, 'unit': 60179005231593474267471528, 'val': 1}
  • id: 22816
    {'lmfdb_iso': '1008.i', 'p': 29, 'prec': 20, 'unit': 1803241493600579367285176524, 'val': 1}
  • id: 22813
    {'lmfdb_iso': '1008.i', 'p': 31, 'prec': 20, 'unit': 1429832211523516639955952149, 'val': 1}
  • id: 22828
    {'lmfdb_iso': '1008.i', 'p': 37, 'prec': 20, 'unit': 159064025088828279577119153492, 'val': 1}
  • id: 22814
    {'lmfdb_iso': '1008.i', 'p': 41, 'prec': 20, 'unit': 22088072306386143675884402032, 'val': 2}
  • id: 22815
    {'lmfdb_iso': '1008.i', 'p': 43, 'prec': 20, 'unit': 1639734389267083517231028610300, 'val': 1}
  • id: 22826
    {'lmfdb_iso': '1008.i', 'p': 47, 'prec': 20, 'unit': 6917656939060082412683157153063, 'val': 1}
  • id: 22821
    {'lmfdb_iso': '1008.i', 'p': 53, 'prec': 20, 'unit': 460421028701444412867948245189185, 'val': 1}
  • id: 22822
    {'lmfdb_iso': '1008.i', 'p': 59, 'prec': 20, 'unit': 156474620790869830455639654629935, 'val': 1}
  • id: 22827
    {'lmfdb_iso': '1008.i', 'p': 61, 'prec': 20, 'unit': 7518330056488951610019634188083409, 'val': 1}
  • id: 22809
    {'lmfdb_iso': '1008.i', 'p': 67, 'prec': 20, 'unit': 40252565650999001925526329182725765, 'val': 1}
  • id: 22812
    {'lmfdb_iso': '1008.i', 'p': 71, 'prec': 20, 'unit': 22898643217469809725840861643085988, 'val': 1}
  • id: 22823
    {'lmfdb_iso': '1008.i', 'p': 73, 'prec': 20, 'unit': 246615511562831732234027453923942041, 'val': 1}
  • id: 22818
    {'lmfdb_iso': '1008.i', 'p': 79, 'prec': 20, 'unit': 472990144302267195952380125008841172, 'val': 1}
  • id: 22825
    {'lmfdb_iso': '1008.i', 'p': 89, 'prec': 20, 'unit': 1605486991039833353545155147543554986, 'val': 1}
  • id: 22808
    {'lmfdb_iso': '1008.i', 'p': 97, 'prec': 20, 'unit': 28097976648614061875495470320992343961, 'val': 1}