Elliptic curve data - 5160.k2

Formats: - HTML - YAML - JSON - 2025-10-11T22:30:25.521385

• 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': '5160l', 'Clabel': '5160l1', 'Cnumber': 1, 'abc_quality': 0.9861336388010359, 'absD': 325005696000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 5160, 'ainvs': [0, 1, 0, 1144, -22656], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 43], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 5160, 'degree': 4800, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.89344264390985839389454822779', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [161555647964, 317388375], 'lmfdb_iso': '5160.k', 'lmfdb_label': '5160.k2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 1144, -22656], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.d.1', '430.6.0.?', '5160.12.0.?'], '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, 2, 215], [3, 4, 344], [5, 6, 344], [43, 44, 120]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.31581999344323730271352145991', 'prec': 103}, 'szpiro_ratio': 3.9319327913577813, '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, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, 4, 0, -1, 0, 4, 0, 0, 0], 'aplist': [0, 1, -1, 0, 0, 4, 4, 0, 4, -2, 4, -6, 2, 1, 0, -10, -8, 8, 8, 12, -10, 8, -14, 12, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 5160, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '5160.k', 'trace_hash': 1082363060048319652}
• 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': '0.16748101325898739386988902597', 'prec': 103}, 'conductor': 5160, 'gens': [], 'heights': [], 'lmfdb_label': '5160.k2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.50329856255498103736342012052', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5164928127749051868171006025922785676', 'prec': 130}, 'tamagawa_product': 20, 'torsion_generators': [[16, 0, 1]], 'xcoord_integral_points': [16]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [2, 0], '43': [1, 0]}, 'iwp0': 7, 'lmfdb_label': '5160.k2'}
• ec_torsion_growth •

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

  
  
  • id: 269372
    {'degree': 2, 'field': [54, -1, 1], 'lmfdb_label': '5160.k2', 'torsion': [2, 2]}
  • id: 269373
    {'degree': 4, 'field': [-18, -24, -17, -2, 1], 'lmfdb_label': '5160.k2', 'torsion': [4]}
  • id: 269376
    {'degree': 8, 'field': [-3, 0, -508, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '5160.k2', 'torsion': [6]}
  • id: 269375
    {'degree': 8, 'field': [16824, 4728, -3650, -2152, 1067, 8, 2, -4, 1], 'lmfdb_label': '5160.k2', 'torsion': [2, 4]}
  • id: 269374
    {'degree': 8, 'field': [38416, 79136, 131154, 16662, 49, 324, 36, -2, 1], 'lmfdb_label': '5160.k2', 'torsion': [2, 4]}
  • id: 269377
    {'degree': 16, 'field': [50140561, 0, -92065400, 0, -206248976, 0, -17490440, 0, 513586, 0, 205000, 0, 8944, 0, -200, 0, 1], 'lmfdb_label': '5160.k2', 'torsion': [8]}
  • id: 269378
    {'degree': 16, 'field': [105789415000, 34470071000, 61988752200, 4458803720, 9755390956, -757528776, 584914258, -144588070, 19649469, -2519650, 282424, -2790, 3334, -430, -42, -4, 1], 'lmfdb_label': '5160.k2', '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: 100236
    {'conductor': 5160, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '5160.k2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 100237
    {'conductor': 5160, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '5160.k2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 100238
    {'conductor': 5160, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5160.k2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 100239
    {'conductor': 5160, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5160.k2', '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

  
  
  • id: 1697620
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [2581, 4, 2, 9], [1, 2, 2, 5], [1, 4, 0, 1], [1034, 1, 2063, 0], [3962, 1, 599, 0], [5157, 4, 5156, 5], [649, 4516, 3224, 1935], [1721, 4, 3442, 9]], 'adelic_image': '5160.12.0.?', 'conductor': 5160, 'lmfdb_label': '5160.k2', 'prime': 0}
  • id: 25559
    {'conductor': 5160, 'elladic_image': '2.3.0.1', 'lmfdb_label': '5160.k2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 5160.k does not appear in ec_padic