Elliptic curve data - 17.a2

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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
  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': '17a', 'Clabel': '17a2', 'Cnumber': 2, 'abc_quality': 1.0296285559493121, 'absD': 289, 'adelic_genus': 53, 'adelic_index': 1536, 'adelic_level': 544, 'ainvs': [1, -1, 1, -6, -4], 'analytic_rank': 0, 'bad_primes': [17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 17, 'degree': 2, 'elladic_images': ['16.96.0.13'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.72320971122131613566604906496', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [20346417, 289], 'lmfdb_iso': '17.a', 'lmfdb_label': '17.a2', 'lmfdb_number': 2, 'manin_constant': 2, 'min_quad_twist_ainvs': [1, -1, 1, -6, -4], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.a.1.1', '8.48.0-8.f.1.1', '16.96.0-16.c.2.2', '68.48.0-68.b.1.1', '136.192.3.?', '272.768.21.?', '544.1536.53.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 1, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 2, 1], [17, 18, 1]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.72320971122131613566604906496', 'prec': 107}, 'szpiro_ratio': 5.93969226527156, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, -1, -2, 0, 4, 3, -3, 2, 0, 0, -2, -4, 0, -1, 1, 3, -4, 2], 'aplist': [-1, 0, -2, 4, 0, -2, 1, -4, 4, 6, 4, -2, -6, 4, 0, 6, -12, -10, 4, -4, -6, 12, -4, 10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 17, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '17.a', 'trace_hash': 256041048516234311}
• 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': '4.2478773981299661611114361391', 'prec': 100}, 'conductor': 17, 'gens': [], 'heights': [], 'lmfdb_label': '17.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.0941595071022403464191580099', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.38676993838778004330239475124309554740', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[-1, 0, 1], [3, -2, 1]], 'xcoord_integral_points': [-1, 3]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 1], '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '17.a2'}
• ec_torsion_growth •

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

  
  
  • id: 273
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '17.a2', 'torsion': [2, 4]}
  • id: 272
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '17.a2', 'torsion': [2, 4]}
  • id: 274
    {'degree': 4, 'field': [16, 0, 9, 0, 1], 'lmfdb_label': '17.a2', 'torsion': [4, 4]}
  • id: 277
    {'degree': 8, 'field': [1, -4, 4, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '17.a2', 'torsion': [2, 6]}
  • id: 276
    {'degree': 8, 'field': [1, 0, -4, 0, -11, 0, -4, 0, 1], 'lmfdb_label': '17.a2', 'torsion': [2, 8]}
  • id: 275
    {'degree': 8, 'field': [1, 0, -4, 0, 7, 0, -4, 0, 1], 'lmfdb_label': '17.a2', 'torsion': [2, 8]}
  • id: 280
    {'degree': 16, 'field': [1, 0, 0, 0, 17, 0, 0, 0, -32, 0, 0, 0, 17, 0, 0, 0, 1], 'lmfdb_label': '17.a2', 'torsion': [4, 8]}
  • id: 281
    {'degree': 16, 'field': [1, 0, 8, 0, 16, 0, 11, 0, 28, 0, -7, 0, 1, 0, 2, 0, 1], 'lmfdb_label': '17.a2', 'torsion': [2, 12]}
  • id: 282
    {'degree': 16, 'field': [1, 1, 11, 0, 53, 74, 13, 21, -50, -84, 76, -2, -28, 21, -1, -4, 1], 'lmfdb_label': '17.a2', 'torsion': [2, 12]}
  • id: 279
    {'degree': 16, 'field': [16, 16, -8, -56, 264, -644, 758, -358, -19, 10, 108, -138, 114, -70, 30, -8, 1], 'lmfdb_label': '17.a2', 'torsion': [4, 8]}
  • id: 278
    {'degree': 16, 'field': [256, 0, 0, 0, 528, 0, 0, 0, -40, 0, 0, 0, 33, 0, 0, 0, 1], 'lmfdb_label': '17.a2', 'torsion': [4, 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

  
  {'conductor': 17, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '17.a2', 'prime': 17, '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: 1665906
    {'adelic_gens': [[1, 0, 32, 1], [1, 32, 0, 1], [513, 32, 512, 33], [349, 84, 248, 169], [9, 32, 488, 345], [511, 134, 272, 1], [29, 8, 444, 85], [141, 24, 266, 373]], 'adelic_image': '544.1536.53.?', 'conductor': 17, 'lmfdb_label': '17.a2', 'prime': 0}
  • id: 24
    {'conductor': 17, 'elladic_image': '16.96.0.13', 'lmfdb_label': '17.a2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 17.a does not appear in ec_padic