Elliptic curve data - 6080.k1

Formats: - HTML - YAML - JSON - 2026-03-10T02:52:45.421508

• 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': '6080c', 'Clabel': '6080c4', 'Cnumber': 4, 'abc_quality': 0.9624765908615641, 'absD': 6225920, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 760, 'ainvs': [0, 0, 0, -8108, 281008], 'analytic_rank': 0, 'bad_primes': [2, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6080, 'degree': 4096, 'elladic_images': ['8.12.0.12'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.73189291389050549314769503928', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [899466517764, 95], 'lmfdb_iso': '6080.k', 'lmfdb_label': '6080.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -2027, 35126], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.2', '40.24.0-40.z.1.1', '152.24.0.?', '380.12.0.?', '760.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 95], [5, 6, 1216], [19, 20, 320]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.19230332685608825274194778933', 'prec': 107}, 'szpiro_ratio': 4.432053983630564, '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, 0, 0, -1, 0, 0, 0, -3, 0, 4, 0, 6, 0, 0, 0, -6, 0, 1, 0], 'aplist': [0, 0, -1, 0, 4, 6, -6, 1, 8, 2, 0, -2, 2, -4, -8, 6, 4, 2, -8, 8, 2, -8, -4, -14, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 6080, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '6080.k', 'trace_hash': 1939237719846461352}
• 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': '0.23135873035318458117401010847', 'prec': 103}, 'conductor': 6080, 'gens': [], 'heights': [], 'lmfdb_label': '6080.k1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.8393939817983561475914118384', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8393939817983561475914118383736967170', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[52, 0, 1]], 'xcoord_integral_points': [52]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '5': [0, 0], '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '6080.k1'}
• ec_torsion_growth •

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

  
  
  • id: 317021
    {'degree': 2, 'field': [-95, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [2, 2]}
  • id: 317023
    {'degree': 2, 'field': [-38, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [4]}
  • id: 317022
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [4]}
  • id: 317024
    {'degree': 4, 'field': [49, 0, -24, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [2, 4]}
  • id: 317028
    {'degree': 8, 'field': [-48, 0, -2496, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [6]}
  • id: 317025
    {'degree': 8, 'field': [81, 0, 108, 0, -41, 0, 12, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [2, 4]}
  • id: 317026
    {'degree': 8, 'field': [361, 0, -428, 0, 159, 0, -22, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [8]}
  • id: 317027
    {'degree': 8, 'field': [2401, 0, 490, 0, 142, 0, 10, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [8]}
  • id: 317031
    {'degree': 16, 'field': [2201, -71236, 544600, -156460, -1611966, 1270984, 715112, -738540, -92189, 153984, -1528, -14332, 1054, 588, -64, -8, 1], 'lmfdb_label': '6080.k1', 'torsion': [2, 8]}
  • id: 317033
    {'degree': 16, 'field': [4624, 0, -53696, 0, 27040, 0, 112, 0, 520, 0, -968, 0, 172, 0, -20, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [12]}
  • id: 317029
    {'degree': 16, 'field': [6241, 0, 117188, 0, -29130, 0, -14972, 0, 2419, 0, 532, 0, 210, 0, 32, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [4, 4]}
  • id: 317030
    {'degree': 16, 'field': [24010000, 0, 18620000, 0, 5034800, 0, 532000, 0, 25676, 0, 3040, 0, 252, 0, 0, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [2, 8]}
  • id: 317034
    {'degree': 16, 'field': [58354321, 0, -64646476, 0, 21933484, 0, -4306708, 0, 565126, 0, -48148, 0, 2524, 0, -76, 0, 1], 'lmfdb_label': '6080.k1', 'torsion': [12]}
  • id: 317032
    {'degree': 16, 'field': [1593446724, 0, 1470091824, 0, 192160260, 0, -67937328, 0, 1349940, 0, -54228, 0, -288, 0, 0, 0, 1], 'lmfdb_label': '6080.k1', '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: 120979
    {'conductor': 6080, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '6080.k1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 120980
    {'conductor': 6080, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6080.k1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 120981
    {'conductor': 6080, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6080.k1', 'prime': 19, '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: 1703836
    {'adelic_gens': [[753, 8, 752, 9], [1, 0, 8, 1], [7, 6, 754, 755], [1, 8, 0, 1], [1, 4, 4, 17], [661, 662, 462, 85], [84, 1, 103, 6], [288, 673, 313, 360], [616, 3, 5, 2]], 'adelic_image': '760.48.0.?', 'conductor': 6080, 'lmfdb_label': '6080.k1', 'prime': 0}
  • id: 29929
    {'conductor': 6080, 'elladic_image': '8.12.0.12', 'lmfdb_label': '6080.k1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6080.k does not appear in ec_padic