Elliptic curve data - 1170.f2

Formats: - HTML - YAML - JSON - 2025-10-20T22:34:44.517581

• 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': '1170a', 'Clabel': '1170a1', 'Cnumber': 1, 'abc_quality': 1.0868098531910144, 'absD': 410620354560000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [1, -1, 0, 16806, 493108], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1170, 'degree': 5120, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4920528071580023987033988574', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [19441890357117957, 15208161280000], 'lmfdb_iso': '1170.f', 'lmfdb_label': '1170.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 16806, 493108], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.b.1', '52.6.0.e.1', '78.6.0.?', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 39], [3, 6, 130], [5, 6, 18], [13, 14, 90]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2173997349909749758545875482', 'prec': 100}, 'szpiro_ratio': 5.775433123097694, '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, 0, 1, 1, 0, 2, -1, 0, -1, -4, 0, -1, -2, 0, 1, 4, 0, 6, 1], 'aplist': [-1, 0, 1, 2, -4, -1, 4, 6, 0, 4, 6, -2, -10, 8, 0, 4, -4, 2, 6, 8, 10, -4, 12, 2, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 1170, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1170.f', 'trace_hash': 1869460026762760969}
• 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': '0.050584725577538140594647909118', 'prec': 107}, 'conductor': 1170, 'gens': [], 'heights': [], 'lmfdb_label': '1170.f2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.34171939077949489872800521060', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3668775631179795949120208424151718553', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-28, 14, 1]], 'xcoord_integral_points': [-28]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '1170.f2'}
• ec_torsion_growth •

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

  
  
  • id: 57611
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '1170.f2', 'torsion': [2, 2]}
  • id: 57612
    {'degree': 4, 'field': [-3, -6, -3, 0, 1], 'lmfdb_label': '1170.f2', 'torsion': [4]}
  • id: 57615
    {'degree': 8, 'field': [-10, 35, -20, -29, 13, -1, 5, -4, 1], 'lmfdb_label': '1170.f2', 'torsion': [6]}
  • id: 57614
    {'degree': 8, 'field': [1, 0, 1, 0, 12, 0, 1, 0, 1], 'lmfdb_label': '1170.f2', 'torsion': [2, 4]}
  • id: 57613
    {'degree': 8, 'field': [40, 4, 2, -8, -5, 8, 2, -4, 1], 'lmfdb_label': '1170.f2', 'torsion': [2, 4]}
  • id: 57616
    {'degree': 16, 'field': [-4259, -71136, 110842, -57768, -47248, 59844, -8798, -18024, 7945, 4284, -586, 312, 332, -12, -28, 0, 1], 'lmfdb_label': '1170.f2', 'torsion': [8]}
  • id: 57617
    {'degree': 16, 'field': [25600, 0, -97600, 0, 99760, 0, -4204, 0, 1813, 0, 344, 0, -110, 0, -4, 0, 1], 'lmfdb_label': '1170.f2', 'torsion': [2, 6]}
• 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: 17005
    {'conductor': 1170, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '1170.f2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 17006
    {'conductor': 1170, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1170.f2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 17007
    {'conductor': 1170, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1170.f2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 17008
    {'conductor': 1170, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '1170.f2', 'prime': 13, '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

  
  
  • id: 1671941
    {'adelic_gens': [[1, 2, 2, 5], [134, 1, 11, 0], [3, 4, 8, 11], [153, 4, 152, 5], [56, 1, 103, 0], [121, 40, 116, 39], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 1170, 'lmfdb_label': '1170.f2', 'prime': 0}
  • id: 5580
    {'conductor': 1170, 'elladic_image': '2.3.0.1', 'lmfdb_label': '1170.f2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1170.f does not appear in ec_padic