Elliptic curve data - 124215.l1

Formats: - HTML - YAML - JSON - 2025-10-26T20:07:00.960478

• 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': '124215k', 'Clabel': '124215k4', 'Cnumber': 4, 'abc_quality': 0.9536815956308902, 'absD': 290678073388486875, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3640, 'ainvs': [1, 1, 1, -36175721, 83732819204], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 124215, 'degree': 8257536, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8189100385500589736721812576', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 4], 'jinv': [9219915604149769, 511875], 'lmfdb_iso': '124215.l', 'lmfdb_label': '124215.l1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -4369, -111499], 'min_quad_twist_disc': -91, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '28.12.0-4.c.1.1', '40.12.0-4.c.1.3', '52.12.0-4.c.1.2', '280.24.0.?', '364.24.0.?', '520.24.0.?', '3640.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 8281], [3, 4, 41405], [5, 6, 24843], [7, 32, 2535], [13, 98, 735]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56348028529163395309276116510', 'prec': 103}, 'szpiro_ratio': 5.441309044772817, '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, -1, -1, -1, 1, 0, 3, 1, 1, -4, 1, 0, 0, 1, -1, -6, -1, 8, 1], 'aplist': [-1, -1, -1, 0, -4, 0, -6, 8, -4, -2, -4, -10, -2, 8, 8, 6, 8, 10, 12, 8, 6, 8, -4, 6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 124215, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '124215.l', 'trace_hash': 2198576821351889559}
• 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': '0.0035606218332865578861944531960', 'prec': 110}, 'conductor': 124215, 'gens': [], 'heights': [], 'lmfdb_label': '124215.l1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.23136123012026781429944955177', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.92544492048107125719779820709153098424', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[13891, -13895, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': [0, 0], '5': [0, 0], '7': 'a', '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '124215.l1'}
• ec_torsion_growth •

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

  
  
  • id: 5664717
    {'degree': 2, 'field': [-91, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [2, 2]}
  • id: 5664718
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [4]}
  • id: 5664719
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '124215.l1', 'torsion': [4]}
  • id: 5664720
    {'degree': 4, 'field': [9, 20, -19, -2, 1], 'lmfdb_label': '124215.l1', 'torsion': [2, 4]}
  • id: 5664724
    {'degree': 8, 'field': [-2012283, 0, 187551, 0, -4914, 0, 0, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [6]}
  • id: 5664723
    {'degree': 8, 'field': [7056, 0, 784, 0, 147, 0, 21, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [8]}
  • id: 5664722
    {'degree': 8, 'field': [54756, 0, -1259388, 0, 47853, 0, -468, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [8]}
  • id: 5664721
    {'degree': 8, 'field': [669958, -16412, 14798, 3220, -1589, -28, 14, -4, 1], 'lmfdb_label': '124215.l1', 'torsion': [2, 4]}
  • id: 5664729
    {'degree': 16, 'field': [107433225, 0, -554133192, 0, 147899026, 0, 148158, 0, 520563, 0, -25461, 0, 1551, 0, -42, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [12]}
  • id: 5664727
    {'degree': 16, 'field': [196112016, 0, 73160496, 0, 9219868, 0, -164416, 0, -111027, 0, -3962, 0, 567, 0, 38, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [2, 8]}
  • id: 5664730
    {'degree': 16, 'field': [11547006849, 0, -4894264599, 0, -1395344825, 0, -100448922, 0, -1504545, 0, 48818, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [12]}
  • id: 5664728
    {'degree': 16, 'field': [60876186361, 0, -30484258472, 0, 4203184288, 0, -337082469, 0, 18492720, 0, -661659, 0, 14473, 0, -182, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [2, 6]}
  • id: 5664725
    {'degree': 16, 'field': [448843721764, 0, -19558723224, 0, -1804452440, 0, 39556692, 0, 4328205, 0, -10080, 0, -3206, 0, -12, 0, 1], 'lmfdb_label': '124215.l1', 'torsion': [4, 4]}
  • id: 5664726
    {'degree': 16, 'field': [3773132452324, 4241979191432, -3563641360324, -1316113953336, 557835957674, 116970522184, -33554078186, -4549848300, 1001464573, 88989144, -16130990, -897724, 140096, 4368, -604, -8, 1], 'lmfdb_label': '124215.l1', '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: 3059595
    {'conductor': 124215, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '124215.l1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3059596
    {'conductor': 124215, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '124215.l1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3059597
    {'conductor': 124215, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '124215.l1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3059598
    {'conductor': 124215, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '124215.l1', 'prime': 13, 'reduction_type': 0, '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: 2474213
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1457, 8, 2188, 33], [1368, 3193, 1393, 1440], [7, 6, 3634, 3635], [3112, 3637, 1035, 3638], [1396, 3639, 1657, 3634], [459, 458, 1378, 3195], [3633, 8, 3632, 9]], 'adelic_image': '3640.48.0.?', 'conductor': 124215, 'lmfdb_label': '124215.l1', 'prime': 0}
  • id: 486211
    {'conductor': 124215, 'elladic_image': '4.6.0.1', 'lmfdb_label': '124215.l1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 124215.l does not appear in ec_padic