Elliptic curve data - 155771.z2

Formats: - HTML - YAML - JSON - 2024-06-09T22:02:54.273012

• 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': '155771z', 'Clabel': '155771z1', 'Cnumber': 1, 'abc_quality': 0.8926246805538307, 'absD': 117858594776727343, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 308, 'ainvs': [1, 1, 0, 49269, -15951424], 'analytic_rank': 0, 'bad_primes': [7, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 155771, 'degree': 1419264, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9569685950836434130354461592', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2], 'jinv': [4657463, 41503], 'lmfdb_iso': '155771.z', 'lmfdb_label': '155771.z2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 4, 11], 'min_quad_twist_disc': -119, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '14.6.0.b.1', '44.6.0.b.1', '308.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.43259315147212127964199752146', 'prec': 107}, 'szpiro_ratio': 3.9055938015437643, '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, 1, 2, -1, -2, 2, 0, -3, 1, -2, -1, -2, -4, 0, -4, -1, 0, 1, 0, 2], 'aplist': [1, 2, -2, 0, -1, -4, 0, 0, 4, 6, 10, 6, 4, 12, 10, -6, -2, 0, 8, 12, -8, -8, 0, 6, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 155771, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '155771.z', 'trace_hash': 1588595904511146066}
• 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': '0.019961752922881289147316621339', 'prec': 107}, 'conductor': 155771, 'gens': [], 'heights': [], 'lmfdb_label': '155771.z2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16424483008298415058007011386', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9564069414937147104412620494826447133', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[188, -94, 1]], 'xcoord_integral_points': [188]}
• lmfdb_label 155771.z2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 6985688
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '155771.z2', 'torsion': [2, 2]}
  • id: 6985689
    {'degree': 4, 'field': [-508, -148, -38, -2, 1], 'lmfdb_label': '155771.z2', 'torsion': [4]}
  • id: 6985692
    {'degree': 8, 'field': [-2948399, -815132, -464582, 20523, -5577, 273, -2, -2, 1], 'lmfdb_label': '155771.z2', 'torsion': [6]}
  • id: 6985691
    {'degree': 8, 'field': [13244, 6454, 3045, -1085, 149, 108, -11, -1, 1], 'lmfdb_label': '155771.z2', 'torsion': [2, 4]}
  • id: 6985690
    {'degree': 8, 'field': [51613, 9642, -13162, -256, 1243, -56, -14, -2, 1], 'lmfdb_label': '155771.z2', 'torsion': [2, 4]}
  • id: 6985694
    {'degree': 16, 'field': [39794843, -78791614, 80234893, -47812174, 14671983, -54625, -1900330, 749344, -83112, -27857, 9616, 2, -393, 44, 14, -4, 1], 'lmfdb_label': '155771.z2', 'torsion': [2, 6]}
  • id: 6985693
    {'degree': 16, 'field': [62797541305, -240143471012, 217963585196, 43545103460, -19749080874, -2391114784, 735022612, 53658436, -13979121, 279336, 38812, -48700, 5690, 1092, -136, -8, 1], 'lmfdb_label': '155771.z2', '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: 3853975
    {'conductor': 155771, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '155771.z2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3853976
    {'conductor': 155771, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '155771.z2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3853977
    {'conductor': 155771, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '155771.z2', 'prime': 17, 'reduction_type': 0, '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: 2672895
    {'adelic_gens': [[1, 0, 4, 1], [90, 1, 263, 0], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [81, 232, 76, 231], [57, 4, 114, 9], [305, 4, 304, 5]], 'adelic_image': '308.12.0.?', 'conductor': 155771, 'lmfdb_label': '155771.z2', 'prime': 0}
  • id: 595517
    {'conductor': 155771, 'elladic_image': '2.3.0.1', 'lmfdb_label': '155771.z2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 155771.z does not appear in ec_padic