Elliptic curve data - 227070.j1

Formats: - HTML - YAML - JSON - 2024-06-18T09:17:12.428912

• 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': '227070bq', 'Clabel': '227070bq2', 'Cnumber': 2, 'abc_quality': 1.055818861759989, 'absD': 46831629708972000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 3480, 'ainvs': [1, -1, 0, -1204890, -508865644], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 29], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 227070, 'degree': 4490640, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1875813492913808871856482263', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 9, 'isogeny_degrees': [1, 3], 'jinv': [-16522921323, 4000], 'lmfdb_iso': '227070.j', 'lmfdb_label': '227070.j1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -159, 813], 'min_quad_twist_disc': -87, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '87.8.0.?', '120.8.0.?', '3480.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.32002578220293839495242171757', 'prec': 107}, 'szpiro_ratio': 4.347657425827896, '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, -1, 0, 1, -1, 0, 2, -1, 0, 1, -3, 0, 5, -2, 0, 1, 3, 0, 4, -1], 'aplist': [-1, 0, -1, 2, -3, 5, 3, 4, -9, 0, -5, 10, 0, 1, -9, -12, 12, -2, -4, 12, 10, 13, 6, 12, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 227070, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '227070.j', 'trace_hash': 1305820322674765511}
• 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': '0.012586094336131794611835114653', 'prec': 107}, 'conductor': 227070, 'gens': [], 'heights': [], 'lmfdb_label': '227070.j1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.072048739111224882125635579043', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9453159560030718173921606341731907995', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 227070.j1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9857990
    {'degree': 2, 'field': [22, -1, 1], 'lmfdb_label': '227070.j1', 'torsion': [3]}
  • id: 9857991
    {'degree': 3, 'field': [-6, 3, 0, 1], 'lmfdb_label': '227070.j1', 'torsion': [2]}
  • id: 9857993
    {'degree': 6, 'field': [-295, -237, 132, 37, -18, -3, 1], 'lmfdb_label': '227070.j1', 'torsion': [3]}
  • id: 9857992
    {'degree': 6, 'field': [30, 0, 21, 0, 12, 0, 1], 'lmfdb_label': '227070.j1', 'torsion': [2, 2]}
  • id: 9857994
    {'degree': 6, 'field': [8416, -2202, 1518, -133, 75, -3, 1], 'lmfdb_label': '227070.j1', 'torsion': [6]}
  • id: 9857995
    {'degree': 12, 'field': [-361283646, -235723194, -2252847411, 297172512, -54998601, 10320984, 1400448, -206712, -1734, -174, 279, 0, 1], 'lmfdb_label': '227070.j1', 'torsion': [4]}
  • id: 9857996
    {'degree': 12, 'field': [47524, 0, -63576, 0, 35520, 0, -8581, 0, 975, 0, -51, 0, 1], 'lmfdb_label': '227070.j1', 'torsion': [3, 3]}
  • id: 9857997
    {'degree': 12, 'field': [29938816, -18981312, 22228632, -6741512, 3996978, -776940, 301905, -37734, 10617, -800, 171, -6, 1], 'lmfdb_label': '227070.j1', 'torsion': [2, 6]}
  • id: 9857999
    {'degree': 18, 'field': [-76569895, -68723331, 85581081, 51346406, -37433832, -18586290, 10346708, 3983484, -1990209, -579347, 270447, 57312, -25268, -3750, 1542, 152, -57, -3, 1], 'lmfdb_label': '227070.j1', 'torsion': [6]}
  • id: 9857998
    {'degree': 18, 'field': [1364821291756, -133552588488, 587657433084, -70946718402, 107325477690, -12115305978, 10939274475, -1030676829, 695798556, -51833320, 29465985, -1694217, 854664, -37065, 16545, -498, 192, -3, 1], 'lmfdb_label': '227070.j1', 'torsion': [9]}
• 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: 5630287
    {'conductor': 227070, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '227070.j1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5630288
    {'conductor': 227070, 'conductor_valuation': 3, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '227070.j1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 5630289
    {'conductor': 227070, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '227070.j1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5630290
    {'conductor': 227070, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '227070.j1', 'prime': 29, 'reduction_type': 0, '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: 3112140
    {'adelic_gens': [[4, 3, 9, 7], [3475, 6, 3474, 7], [1741, 1566, 783, 1219], [697, 1566, 1131, 1219], [871, 1566, 0, 1], [839, 0, 0, 3479], [1, 6, 0, 1], [3, 4, 8, 11], [2754, 2639, 2117, 666], [1, 0, 6, 1]], 'adelic_image': '3480.16.0.?', 'conductor': 227070, 'lmfdb_label': '227070.j1', 'prime': 0}
  • id: 829469
    {'conductor': 227070, 'elladic_image': '3.4.0.1', 'lmfdb_label': '227070.j1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 227070.j does not appear in ec_padic