Elliptic curve data - 40768.co1

Formats: - HTML - YAML - JSON - 2025-10-28T23:38:26.351734

• 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': '40768cq', 'Clabel': '40768cq1', 'Cnumber': 1, 'abc_quality': 0.7942083638864892, 'absD': 8479744, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 728, 'ainvs': [0, 1, 0, -177, 839], 'analytic_rank': 1, 'bad_primes': [2, 7, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 40768, 'degree': 9216, 'elladic_images': ['2.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.13528688971512566266476226543', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 66, 'isogeny_degrees': [1], 'jinv': [12291328, 169], 'lmfdb_iso': '40768.co', 'lmfdb_label': '40768.co1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -44, -127], 'min_quad_twist_disc': -8, 'modell_images': ['2Cn'], 'modm_images': ['2.2.0.a.1', '14.6.0.a.1', '728.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.84863851875370614040747957180', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 49], [7, 14, 832], [13, 14, 3136]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.76665411892738097936715662636', 'prec': 107}, 'szpiro_ratio': 2.5573271189611204, '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, -3, 0, 0, 0, -2, 0, -3, 0, -1, 0, -3, 0, -7, 0, 1, 0], 'aplist': [0, 1, -3, 0, -3, -1, -7, 1, -1, 2, 9, 3, -10, 4, 3, 1, 11, -1, -7, -8, 7, 11, 4, -1, -2], 'class_deg': 1, 'class_size': 1, 'conductor': 40768, 'isogeny_matrix': [[1]], 'lmfdb_iso': '40768.co', 'trace_hash': 1821728347932138508}
• 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': '0.76294160852247708584344499684', 'prec': 103}, 'conductor': 40768, 'gens': [[10, 13, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.84863851875370614040747957180', 'prec': 103}], 'lmfdb_label': '40768.co1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.3307081308126171680268462748', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9558573915600771977335370140940575865', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [10]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': 'a', '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': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '40768.co1'}
• ec_torsion_growth •

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

  
  
  • id: 2005293
    {'degree': 3, 'field': [1, -2, -1, 1], 'lmfdb_label': '40768.co1', 'torsion': [2, 2]}
  • id: 2005294
    {'degree': 8, 'field': [-583443, 0, -11662, 0, -2646, 0, 0, 0, 1], 'lmfdb_label': '40768.co1', 'torsion': [3]}
  • id: 2005295
    {'degree': 12, 'field': [49, 0, 1078, 0, -686, 0, -196, 0, -175, 0, 0, 0, 1], 'lmfdb_label': '40768.co1', 'torsion': [2, 4]}
• 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: 965966
    {'conductor': 40768, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '40768.co1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 965967
    {'conductor': 40768, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '40768.co1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 965968
    {'conductor': 40768, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '40768.co1', 'prime': 13, '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: 1936109
    {'adelic_gens': [[464, 727, 621, 727], [1, 2, 2, 5], [3, 2, 720, 723], [725, 4, 724, 5], [1, 4, 0, 1], [185, 4, 190, 11], [363, 0, 0, 727], [367, 724, 368, 723], [227, 4, 120, 11], [725, 726, 372, 369], [1, 0, 4, 1]], 'adelic_image': '728.12.0.?', 'conductor': 40768, 'lmfdb_label': '40768.co1', 'prime': 0}
  • id: 178627
    {'conductor': 40768, 'elladic_image': '2.2.0.1', 'lmfdb_label': '40768.co1', 'modell_image': '2Cn', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2023002
    {'lmfdb_iso': '40768.co', 'p': 5, 'prec': 20, 'unit': 2956364364952, 'val': 1}
  • id: 2023009
    {'lmfdb_iso': '40768.co', 'p': 11, 'prec': 20, 'unit': 59870549776873596298, 'val': 1}
  • id: 2023010
    {'lmfdb_iso': '40768.co', 'p': 17, 'prec': 20, 'unit': 83130403329679984363890, 'val': 1}
  • id: 2023011
    {'lmfdb_iso': '40768.co', 'p': 19, 'prec': 20, 'unit': 3385111628070527670728993, 'val': -1}
  • id: 2023015
    {'lmfdb_iso': '40768.co', 'p': 23, 'prec': 20, 'unit': 73364635386028467199260602, 'val': 1}
  • id: 2023007
    {'lmfdb_iso': '40768.co', 'p': 29, 'prec': 20, 'unit': 5348245005939586840958905635, 'val': 1}
  • id: 2023004
    {'lmfdb_iso': '40768.co', 'p': 31, 'prec': 20, 'unit': 15144993950842291855019328164, 'val': 1}
  • id: 2023019
    {'lmfdb_iso': '40768.co', 'p': 37, 'prec': 20, 'unit': 170526059155697575799789724844, 'val': 1}
  • id: 2023005
    {'lmfdb_iso': '40768.co', 'p': 41, 'prec': 20, 'unit': 1627085445042527189732931225363, 'val': 1}
  • id: 2023006
    {'lmfdb_iso': '40768.co', 'p': 43, 'prec': 20, 'unit': 10574766669896473398772332258684, 'val': 1}
  • id: 2023017
    {'lmfdb_iso': '40768.co', 'p': 47, 'prec': 20, 'unit': 3060230893410748036763752336334, 'val': 1}
  • id: 2023012
    {'lmfdb_iso': '40768.co', 'p': 53, 'prec': 20, 'unit': 24241952281532238769359612524095230, 'val': -1}
  • id: 2023013
    {'lmfdb_iso': '40768.co', 'p': 59, 'prec': 20, 'unit': 1765012324316632545242999815071934, 'val': 1}
  • id: 2023018
    {'lmfdb_iso': '40768.co', 'p': 61, 'prec': 20, 'unit': 8125572541411569784339693869587845, 'val': 1}
  • id: 2023001
    {'lmfdb_iso': '40768.co', 'p': 67, 'prec': 20, 'unit': 24004144393585403534426862104419370, 'val': 1}
  • id: 2023003
    {'lmfdb_iso': '40768.co', 'p': 71, 'prec': 20, 'unit': 137455799165973604967626299331371684, 'val': 1}
  • id: 2023014
    {'lmfdb_iso': '40768.co', 'p': 73, 'prec': 20, 'unit': 113199526892317112123657270155864052, 'val': 1}
  • id: 2023008
    {'lmfdb_iso': '40768.co', 'p': 79, 'prec': 20, 'unit': 951284720398328734887482670495008202, 'val': 1}
  • id: 2023000
    {'lmfdb_iso': '40768.co', 'p': 83, 'prec': 20, 'unit': 715260659603297265910556850168279107, 'val': 1}
  • id: 2023016
    {'lmfdb_iso': '40768.co', 'p': 89, 'prec': 20, 'unit': 39946141734550821482029259573707842, 'val': 2}
  • id: 2022999
    {'lmfdb_iso': '40768.co', 'p': 97, 'prec': 20, 'unit': 3162567246963490463407196018922194675, 'val': 1}