Elliptic curve data - 177870.ex1

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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
  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': '177870eo', 'Clabel': '177870eo1', 'Cnumber': 1, 'abc_quality': 1.0451539608095972, 'absD': 262835316698325118945312500000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 8, 'ainvs': [1, 1, 1, -1667990871, 8892678420429], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 177870, 'degree': 248371200, 'elladic_images': ['8.2.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.3373730272989706682851072505', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 127, 'isogeny_degrees': [1], 'jinv': [3432365662485529, 1757812500000], 'lmfdb_iso': '177870.ex', 'lmfdb_label': '177870.ex1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -281328, 19456798], 'min_quad_twist_disc': 77, 'modell_images': [], 'modm_images': ['8.2.0.b.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.5713489275272719198164850069', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0418535339301196781632524399', 'prec': 100}, 'szpiro_ratio': 6.230412347698408, '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, -1, 1, -1, -1, 0, 1, 1, -1, 0, -1, 0, 0, 1, 1, -5, 1, -6, -1], 'aplist': [1, -1, -1, 0, 0, 0, -5, -6, 0, 6, -5, 4, -7, -4, 7, 6, -6, 8, 14, -11, -13, -5, 0, -3, 2], 'class_deg': 1, 'class_size': 1, 'conductor': 177870, 'isogeny_matrix': [[1]], 'lmfdb_iso': '177870.ex', 'trace_hash': 1840493799149817782}
• 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': '0.00017084633100233606627419098379', 'prec': 113}, 'conductor': 177870, 'gens': [[1075129, 1113446810, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.5713489275272719198164850069', 'prec': 100}], 'lmfdb_label': '177870.ex1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.027381953972629366006001575648', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.5103479555828225059820295538492486203', 'prec': 130}, 'tamagawa_product': 60, 'torsion_generators': [], 'xcoord_integral_points': [1075129]}
• lmfdb_label 177870.ex1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7880726
    {'degree': 3, 'field': [-97, -51, -1, 1], 'lmfdb_label': '177870.ex1', 'torsion': [2]}
  • id: 7880727
    {'degree': 6, 'field': [-2738, 0, 773, 0, -52, 0, 1], 'lmfdb_label': '177870.ex1', 'torsion': [2, 2]}
  • id: 7880728
    {'degree': 8, 'field': [-29403, 0, -7524, 0, -594, 0, 0, 0, 1], 'lmfdb_label': '177870.ex1', 'torsion': [3]}
  • id: 7880729
    {'degree': 12, 'field': [20492802, 0, 12023891, 0, -4980239, 0, 271282, 0, 4664, 0, -121, 0, 1], 'lmfdb_label': '177870.ex1', '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: 4402695
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '177870.ex1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 4402696
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '177870.ex1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4402697
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '177870.ex1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4402698
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '177870.ex1', 'prime': 7, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
  • id: 4402699
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '177870.ex1', 'prime': 11, '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: 2809606
    {'adelic_gens': [[7, 2, 0, 1], [1, 0, 2, 1], [1, 1, 7, 0], [1, 2, 0, 1], [5, 2, 5, 3], [7, 2, 6, 3]], 'adelic_image': '8.2.0.?', 'conductor': 177870, 'lmfdb_label': '177870.ex1', 'prime': 0}
  • id: 668582
    {'conductor': 177870, 'elladic_image': '8.2.0.2', 'lmfdb_label': '177870.ex1', 'modell_image': '2G', 'prime': 2}
• lmfdb_iso 177870.ex does not appear in ec_padic