Elliptic curve data - 6080.k4

Formats: - HTML - YAML - JSON - 2024-04-20T16:11:13.360285

• 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': '6080c', 'Clabel': '6080c1', 'Cnumber': 1, 'abc_quality': 1.1318614362548602, 'absD': 12160000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 760, 'ainvs': [0, 0, 0, -8, 168], 'analytic_rank': 0, 'bad_primes': [2, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6080, 'degree': 1024, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.038745733330560183730462917821', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [-55296, 11875], 'lmfdb_iso': '6080.k', 'lmfdb_label': '6080.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -2, 21], '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.1.4', '38.6.0.b.1', '40.24.0-40.z.1.11', '76.12.0.?', '152.24.0.?', '760.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.53887691713606090745056385006', 'prec': 107}, 'szpiro_ratio': 2.7283057911305746, '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': '0.92543492141273832469604043388', 'prec': 103}, 'conductor': 6080, 'gens': [], 'heights': [], 'lmfdb_label': '6080.k4', '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': [[-6, 0, 1]], 'xcoord_integral_points': [-6]}
• 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.k4'}
• ec_torsion_growth •

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

  
  
  • id: 316986
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [4]}
  • id: 316985
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '6080.k4', 'torsion': [2, 2]}
  • id: 316987
    {'degree': 2, 'field': [38, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [4]}
  • id: 316988
    {'degree': 4, 'field': [47, -6, 7, -2, 1], 'lmfdb_label': '6080.k4', 'torsion': [2, 4]}
  • id: 316992
    {'degree': 8, 'field': [-48, 0, -2496, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [6]}
  • id: 316989
    {'degree': 8, 'field': [25, 0, -28, 0, 11, 0, 2, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [2, 4]}
  • id: 316990
    {'degree': 8, 'field': [25, 0, -20, 0, -6, 0, -4, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [8]}
  • id: 316991
    {'degree': 8, 'field': [2116, 0, 1592, 0, 484, 0, 48, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [8]}
  • id: 316997
    {'degree': 16, 'field': [400, 0, -1600, 0, 1600, 0, 368, 0, -488, 0, -88, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [12]}
  • id: 316993
    {'degree': 16, 'field': [3969, -8316, 8712, -9348, 7366, -2520, 120, 1060, -1625, 920, -280, 20, 94, -76, 32, -8, 1], 'lmfdb_label': '6080.k4', 'torsion': [4, 4]}
  • id: 316996
    {'degree': 16, 'field': [5625, 0, -36900, 0, 82800, 0, -69480, 0, 19902, 0, -876, 0, 396, 0, 0, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [2, 6]}
  • id: 316994
    {'degree': 16, 'field': [9025, 0, 1140, 9120, 29454, 47912, 41512, 18336, 3191, -152, -64, 64, 50, -8, -12, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [2, 8]}
  • id: 316995
    {'degree': 16, 'field': [390625, 0, 1187500, 0, 1321250, 0, 665000, 0, 178075, 0, 26600, 0, 2114, 0, 76, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [2, 8]}
  • id: 316998
    {'degree': 16, 'field': [70224400, 0, 48107200, 0, 20063200, 0, 4504048, 0, 584392, 0, 47992, 0, 2524, 0, 76, 0, 1], 'lmfdb_label': '6080.k4', 'torsion': [12]}
• 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: 120970
    {'conductor': 6080, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '6080.k4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 120971
    {'conductor': 6080, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6080.k4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 120972
    {'conductor': 6080, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6080.k4', '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: 1703839
    {'adelic_gens': [[457, 8, 308, 33], [1, 0, 8, 1], [753, 8, 752, 9], [7, 6, 754, 755], [1, 8, 0, 1], [168, 3, 485, 2], [1, 4, 4, 17], [661, 662, 462, 85], [289, 288, 678, 295]], 'adelic_image': '760.48.0.?', 'conductor': 6080, 'lmfdb_label': '6080.k4', 'prime': 0}
  • id: 29932
    {'conductor': 6080, 'elladic_image': '8.12.0.8', 'lmfdb_label': '6080.k4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6080.k does not appear in ec_padic