Elliptic curve data - 24.a6

Formats: - HTML - YAML - JSON - 2025-03-07T10:22:36.679636

• 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': '24a', 'Clabel': '24a6', 'Cnumber': 6, 'abc_quality': 1.1597991410868231, 'absD': 13436928, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 48, 'ainvs': [0, -1, 0, 16, -180], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 24, 'degree': 4, 'elladic_images': ['8.96.0.166'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.047794894480088036758221444632', 'prec': 107}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [207646, 6561], 'lmfdb_iso': '24.a', 'lmfdb_label': '24.a6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 16, -180], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.96.0-8.m.1.2', '48.192.1-48.w.2.4'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1], [3, 4, 8]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.58759002103319516354090800004', 'prec': 107}, 'szpiro_ratio': 7.504514900845317, '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, -2, 0, 0, 0, 1, 0, 4, 0, -2, 0, 2, 0, 2, 0, -4, 0], 'aplist': [0, -1, -2, 0, 4, -2, 2, -4, -8, 6, 8, 6, -6, 4, 0, -2, 4, -2, -4, 8, 10, -8, -4, -6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 24, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '24.a', 'trace_hash': 906478665263567321}
• 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': '0.90883675448285972014062333356', 'prec': 103}, 'conductor': 24, 'gens': [], 'heights': [], 'lmfdb_label': '24.a6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0782578237498216177193374994', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.53912891187491080885966874970005048289', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[5, 0, 1]], 'xcoord_integral_points': [5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '24.a6'}
• ec_torsion_growth •

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

  
  
  • id: 566
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [4]}
  • id: 567
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [8]}
  • id: 565
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [2, 2]}
  • id: 570
    {'degree': 4, 'field': [-2, 0, 0, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [8]}
  • id: 569
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [2, 8]}
  • id: 568
    {'degree': 4, 'field': [2, 0, 0, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [2, 4]}
  • id: 573
    {'degree': 8, 'field': [-3, 0, 4, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [6]}
  • id: 571
    {'degree': 8, 'field': [1, 0, -4, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [4, 8]}
  • id: 572
    {'degree': 8, 'field': [4, 0, -12, 0, 14, 0, -6, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [16]}
  • id: 580
    {'degree': 16, 'field': [1, -4, 6, -10, 28, -30, 24, -36, 60, -36, 24, -30, 28, -10, 6, -4, 1], 'lmfdb_label': '24.a6', 'torsion': [24]}
  • id: 574
    {'degree': 16, 'field': [1, 0, -8, 0, 52, 0, -168, 0, 264, 0, -168, 0, 52, 0, -8, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [8, 8]}
  • id: 575
    {'degree': 16, 'field': [1, 0, -4, 0, 8, 0, 36, 0, 62, 0, 36, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [2, 16]}
  • id: 576
    {'degree': 16, 'field': [1, 0, 0, 0, -4, 0, 0, 0, 15, 0, 0, 0, -4, 0, 0, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [2, 16]}
  • id: 579
    {'degree': 16, 'field': [4, 0, -40, 0, 28, 0, -32, 0, 56, 0, -20, 0, -8, 0, 2, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [12]}
  • id: 577
    {'degree': 16, 'field': [4, 0, 0, 0, 64, 0, 0, 0, 36, 0, 0, 0, -32, 0, 0, 0, 1], 'lmfdb_label': '24.a6', 'torsion': [16]}
  • id: 578
    {'degree': 16, 'field': [4, 0, 40, 0, 28, 0, 32, 0, 56, 0, 20, 0, -8, 0, -2, 0, 1], 'lmfdb_label': '24.a6', '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: 68
    {'conductor': 24, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '24.a6', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 69
    {'conductor': 24, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '24.a6', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1665927
    {'adelic_gens': [[1, 0, 16, 1], [1, 16, 0, 1], [22, 37, 9, 34], [15, 2, 46, 35], [5, 4, 44, 45], [33, 16, 32, 17], [44, 41, 27, 26], [17, 16, 40, 33]], 'adelic_image': '48.192.1.?', 'conductor': 24, 'lmfdb_label': '24.a6', 'prime': 0}
  • id: 49
    {'conductor': 24, 'elladic_image': '8.96.0.166', 'lmfdb_label': '24.a6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 24.a does not appear in ec_padic