Elliptic curve data - 12240.cf3

Formats: - HTML - YAML - JSON - 2024-06-15T14:26:58.984693

• 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': '12240z', 'Clabel': '12240z2', 'Cnumber': 2, 'abc_quality': 1.0333686215042301, 'absD': 4659515519294736000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 0, 0, -15215907, 22607897906], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 12240, 'degree': 860160, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9690955611063052753086291409', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 57, 'isogeny_degrees': [1, 2], 'jinv': [521902963282042184836, 6241849278890625], 'lmfdb_iso': '12240.cf', 'lmfdb_label': '12240.cf3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1690656, 836766000], 'min_quad_twist_disc': 12, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '24.24.0-24.b.1.1', '40.24.0-40.a.1.6', '60.24.0-60.b.1.4', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8421667663056293384299797546', 'prec': 100}, 'szpiro_ratio': 6.504901933314226, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, -4, 0], 'aplist': [0, 0, 1, 4, 0, 2, 1, -4, 8, 6, 0, -6, -2, -4, 8, -10, 8, 6, -4, -8, 10, 0, 12, 14, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 12240, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '12240.cf', 'trace_hash': 814523790988543203}
• 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': '0.0026367949796338514805700995852', 'prec': 110}, 'conductor': 12240, 'gens': [], 'heights': [], 'lmfdb_label': '12240.cf3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.13787871598540120400165951504', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3090891836496288960398283609164178677', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[2062, 0, 1], [2437, 0, 1]], 'xcoord_integral_points': [-4499, 2062, 2437]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '17': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '12240.cf3'}
• ec_torsion_growth •

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

  
  
  • id: 631797
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '12240.cf3', 'torsion': [2, 4]}
  • id: 631798
    {'degree': 4, 'field': [1, 0, -8, 0, 1], 'lmfdb_label': '12240.cf3', 'torsion': [2, 4]}
  • id: 631799
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '12240.cf3', 'torsion': [2, 4]}
  • id: 631802
    {'degree': 8, 'field': [-1323, 0, -948, 0, -126, 0, 0, 0, 1], 'lmfdb_label': '12240.cf3', 'torsion': [2, 6]}
  • id: 631800
    {'degree': 8, 'field': [16, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '12240.cf3', 'torsion': [4, 4]}
  • id: 631801
    {'degree': 8, 'field': [135, -270, 270, -150, 16, 22, -6, -2, 1], 'lmfdb_label': '12240.cf3', 'torsion': [2, 8]}
  • id: 631805
    {'degree': 16, 'field': [36864, 0, 33792, 0, 140032, 0, -8448, 0, 2100, 0, 484, 0, -84, 0, 0, 0, 1], 'lmfdb_label': '12240.cf3', 'torsion': [2, 12]}
  • id: 631803
    {'degree': 16, 'field': [6975757441, 0, -8206773460, 0, 1544804416, 0, -283971400, 0, 32656711, 0, -982600, 0, 18496, 0, -340, 0, 1], 'lmfdb_label': '12240.cf3', 'torsion': [2, 8]}
  • id: 631804
    {'degree': 16, 'field': [6975757441, 0, 0, 0, 386201104, 0, 0, 0, -2505630, 0, 0, 0, 4624, 0, 0, 0, 1], 'lmfdb_label': '12240.cf3', 'torsion': [2, 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: 264364
    {'conductor': 12240, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '12240.cf3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 264365
    {'conductor': 12240, 'conductor_valuation': 2, 'discriminant_valuation': 20, 'j_denominator_valuation': 14, 'kodaira_symbol': -18, 'lmfdb_label': '12240.cf3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 264366
    {'conductor': 12240, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '12240.cf3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 264367
    {'conductor': 12240, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12240.cf3', 'prime': 17, '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: 1745214
    {'adelic_gens': [[61, 2, 0, 1], [79, 116, 38, 111], [51, 2, 46, 119], [117, 4, 116, 5], [89, 116, 0, 119], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '120.48.0.?', 'conductor': 12240, 'lmfdb_label': '12240.cf3', 'prime': 0}
  • id: 58369
    {'conductor': 12240, 'elladic_image': '4.12.0.1', 'lmfdb_label': '12240.cf3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 12240.cf does not appear in ec_padic