Elliptic curve data - 80586.k1

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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': '80586l', 'Clabel': '80586l1', 'Cnumber': 1, 'abc_quality': 0.9869944369461394, 'absD': 301854042633377482915392, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 264, 'ainvs': [1, -1, 0, -40233672, 94613889024], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 80586, 'degree': 12165120, 'elladic_images': ['8.6.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2701460885335135401736881892', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [5577108481460841625, 233729407061568], 'lmfdb_iso': '80586.k', 'lmfdb_label': '80586.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -36946, 2629412], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.d.1', '66.6.0.a.1', '264.12.0.?'], '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, 1089], [3, 8, 4477], [11, 72, 666], [37, 38, 2178]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5218923078002734224450937818', 'prec': 100}, 'szpiro_ratio': 5.677949192558976, '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, 0, 0, 2, -1, 0, 0, 0, 0, -4, -2, 0, 1, 2, 0, 8, 0], 'aplist': [-1, 0, 0, 2, 0, -4, 2, 8, 2, -2, -8, 1, 6, -12, 10, -12, 4, 0, -12, 14, 14, 10, 12, -6, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 80586, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '80586.k', 'trace_hash': 1058404827406040622}
• 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': '0.0014440665142576822337015247622', 'prec': 110}, 'conductor': 80586, 'gens': [], 'heights': [], 'lmfdb_label': '80586.k1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.096110940326808353703246851102', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5377750452289336592519496176371299540', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[3072, -1536, 1]], 'xcoord_integral_points': [3072]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '11': 'a', '37': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '80586.k1'}
• ec_torsion_growth •

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

  
  
  • id: 3790638
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '80586.k1', 'torsion': [2, 2]}
  • id: 3790639
    {'degree': 4, 'field': [1, -2, 5, -2, 1], 'lmfdb_label': '80586.k1', 'torsion': [4]}
  • id: 3790642
    {'degree': 8, 'field': [-120240, 10194, 2091, -2943, -108, 153, -12, -1, 1], 'lmfdb_label': '80586.k1', 'torsion': [6]}
  • id: 3790641
    {'degree': 8, 'field': [4, 0, -79, 0, -45, 0, 23, 0, 1], 'lmfdb_label': '80586.k1', 'torsion': [2, 4]}
  • id: 3790640
    {'degree': 8, 'field': [187, 88, -40, -92, 37, 8, 2, -4, 1], 'lmfdb_label': '80586.k1', 'torsion': [2, 4]}
  • id: 3790644
    {'degree': 16, 'field': [63872064, 0, -7622592, 0, 679024, 0, -1342113, 0, 269946, 0, -30017, 0, 1977, 0, -66, 0, 1], 'lmfdb_label': '80586.k1', 'torsion': [2, 6]}
  • id: 3790643
    {'degree': 16, 'field': [50598787776, -95752521984, 87590924800, -29262057152, 8180424072, 409364896, -4836424, 45543192, -112247, 956284, 47230, -4704, 855, -560, 66, -4, 1], 'lmfdb_label': '80586.k1', 'torsion': [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

  
  
  • id: 1960162
    {'conductor': 80586, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '80586.k1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1960163
    {'conductor': 80586, 'conductor_valuation': 2, 'discriminant_valuation': 17, 'j_denominator_valuation': 11, 'kodaira_symbol': -15, 'lmfdb_label': '80586.k1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1960164
    {'conductor': 80586, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '80586.k1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1960165
    {'conductor': 80586, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '80586.k1', 'prime': 37, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2195177
    {'adelic_gens': [[178, 1, 175, 0], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [26, 1, 119, 0], [261, 4, 260, 5], [169, 100, 32, 231], [133, 4, 2, 9]], 'adelic_image': '264.12.0.?', 'conductor': 80586, 'lmfdb_label': '80586.k1', 'prime': 0}
  • id: 330645
    {'conductor': 80586, 'elladic_image': '8.6.0.4', 'lmfdb_label': '80586.k1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 80586.k does not appear in ec_padic