Elliptic curve data - 261612.d1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '261612d', 'Clabel': '261612d1', 'Cnumber': 1, 'abc_quality': 1.0194383844738752, 'absD': 3137480837008128, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 86, 'ainvs': [0, 0, 0, 16224, 2574884], 'analytic_rank': 0, 'bad_primes': [2, 3, 13, 43], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 261612, 'degree': 898560, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6552446284867949922120940513', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1], 'jinv': [524288, 3483], 'lmfdb_iso': '261612.d', 'lmfdb_label': '261612.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 11, -47], 'min_quad_twist_disc': -39, 'modell_images': [], 'modm_images': ['86.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 65403], [3, 8, 29068], [13, 86, 1548], [43, 44, 6084]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.63863431495132509445709370225', 'prec': 107}, 'szpiro_ratio': 3.4506689038096994, '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, 0, 0, -2, 0, -2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 3, 0, 2, 0], 'aplist': [0, 0, -2, -2, -3, 0, 3, 2, 3, 8, -1, 8, 1, 1, 0, 1, 4, 0, -7, 6, -4, 8, 1, -14, 5], 'class_deg': 1, 'class_size': 1, 'conductor': 261612, 'isogeny_matrix': [[1]], 'lmfdb_iso': '261612.d', 'trace_hash': 983960468314291407}
• 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': '0.036498312330851708615587725287', 'prec': 107}, 'conductor': 261612, 'gens': [], 'heights': [], 'lmfdb_label': '261612.d1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.32593981910926408903104799660', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9556389146555845341862879795902749002', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 261612.d1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11212238
    {'degree': 3, 'field': [3, -1, -1, 1], 'lmfdb_label': '261612.d1', 'torsion': [2]}
  • id: 11212239
    {'degree': 6, 'field': [1, -3, 10, -15, 10, -3, 1], 'lmfdb_label': '261612.d1', 'torsion': [2, 2]}
  • id: 11212240
    {'degree': 8, 'field': [-12247, -21991, -14591, -5320, -1252, 160, 65, -1, 1], 'lmfdb_label': '261612.d1', 'torsion': [3]}
  • id: 11212241
    {'degree': 12, 'field': [-6351281075, 2240761816, -244117622, -10507438, 7745337, -913880, 62184, 9624, -5273, 332, 14, -6, 1], 'lmfdb_label': '261612.d1', 'torsion': [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: 6485167
    {'conductor': 261612, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '261612.d1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 6485168
    {'conductor': 261612, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '261612.d1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6485169
    {'conductor': 261612, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '261612.d1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6485170
    {'conductor': 261612, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '261612.d1', 'prime': 43, '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

  
  {'adelic_gens': [[3, 2, 3, 3], [1, 2, 0, 1], [1, 0, 2, 1], [1, 1, 85, 0], [85, 2, 84, 3]], 'adelic_image': '86.2.0.?', 'conductor': 261612, 'lmfdb_label': '261612.d1', 'prime': 0}
• lmfdb_iso 261612.d does not appear in ec_padic