Elliptic curve data - 28224.be1

Formats: - HTML - YAML - JSON - 2025-10-23T23:08:10.126834

• 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': '28224cm', 'Clabel': '28224cm2', 'Cnumber': 2, 'abc_quality': 0.9079782811805067, 'absD': 963961798754304, 'adelic_genus': 3, 'adelic_index': 72, 'adelic_level': 168, 'ainvs': [0, 0, 0, -127596, -17479280], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 28224, 'degree': 172032, 'elladic_images': ['8.6.0.3', '3.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7297939890941745675506847085', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 30, 'isogeny_degrees': [1, 2], 'jinv': [238328, 1], 'lmfdb_iso': '28224.be', 'lmfdb_label': '28224.be1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -72, -260], 'min_quad_twist_disc': 168, 'modell_images': ['2B', '3Nn'], 'modm_images': ['2.3.0.a.1', '3.3.0.a.1', '6.9.0.a.1', '8.6.0.e.1', '12.18.0.d.1', '24.36.0.be.1', '28.6.0.c.1', '56.12.0.bd.1', '84.36.1.?', '168.72.3.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.9313920083583891903019240857', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 63], [3, 2, 3136], [7, 20, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1453787427312968937474926194', 'prec': 103}, 'szpiro_ratio': 4.574922474621008, '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, -2, 0, 0, 0, 0, 0, -4, 0, 6, 0, 0, 0, -4, 0, -6, 0], 'aplist': [0, 0, -2, 0, -4, 6, -4, -6, -4, -6, -4, 6, 4, 12, 12, 6, 6, -6, 12, 8, 0, 0, 6, -16, 12], 'class_deg': 2, 'class_size': 2, 'conductor': 28224, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '28224.be', 'trace_hash': 1113519841451823463}
• 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': '0.031442714434009915528825395114', 'prec': 107}, 'conductor': 28224, 'gens': [[3712, 6364, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '7.9313920083583891903019240857', 'prec': 100}], 'lmfdb_label': '28224.be1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25266781026824493372596471740', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0080149022619432309560054076166252382', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-196, 0, 1]], 'xcoord_integral_points': [-196]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '28224.be1'}
• ec_torsion_growth •

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

  
  
  • id: 1413662
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '28224.be1', 'torsion': [2, 2]}
  • id: 1413663
    {'degree': 4, 'field': [37, -11, -4, -1, 1], 'lmfdb_label': '28224.be1', 'torsion': [4]}
  • id: 1413666
    {'degree': 8, 'field': [-588, 0, 392, 0, -84, 0, 0, 0, 1], 'lmfdb_label': '28224.be1', 'torsion': [6]}
  • id: 1413665
    {'degree': 8, 'field': [121, -110, 65, -30, 50, -6, 11, -2, 1], 'lmfdb_label': '28224.be1', 'torsion': [2, 4]}
  • id: 1413664
    {'degree': 8, 'field': [169, 0, -116, 0, 20, 0, -4, 0, 1], 'lmfdb_label': '28224.be1', 'torsion': [2, 4]}
  • id: 1413669
    {'degree': 16, 'field': [961, 0, -2020, 0, 2716, 0, -1092, 0, -630, 0, -84, 0, 28, 0, -4, 0, 1], 'lmfdb_label': '28224.be1', 'torsion': [2, 6]}
  • id: 1413667
    {'degree': 16, 'field': [30202, -51000, 79752, -107392, 103672, -85552, 64748, -41764, 23711, -12340, 5470, -2116, 729, -200, 50, -8, 1], 'lmfdb_label': '28224.be1', 'torsion': [8]}
  • id: 1413668
    {'degree': 16, 'field': [345744, 0, 230496, 0, 104272, 0, 32928, 0, 7644, 0, 784, 0, 84, 0, 0, 0, 1], 'lmfdb_label': '28224.be1', 'torsion': [3, 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: 653801
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '28224.be1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 653802
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '28224.be1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 653803
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '28224.be1', 'prime': 7, '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: 1852340
    {'adelic_gens': [[157, 12, 156, 13], [7, 12, 144, 79], [113, 12, 0, 1], [12, 1, 155, 6], [1, 6, 6, 37], [68, 137, 65, 160], [1, 0, 12, 1], [80, 7, 1, 148], [1, 12, 0, 1], [9, 8, 124, 129]], 'adelic_image': '168.72.3.?', 'conductor': 28224, 'lmfdb_label': '28224.be1', 'prime': 0}
  • id: 127432
    {'conductor': 28224, 'elladic_image': '8.6.0.3', 'lmfdb_label': '28224.be1', 'modell_image': '2B', 'prime': 2}
  • id: 127433
    {'conductor': 28224, 'elladic_image': '3.3.0.1', 'lmfdb_label': '28224.be1', 'modell_image': '3Nn', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 1356323
    {'lmfdb_iso': '28224.be', 'p': 5, 'prec': 20, 'unit': 2264002704703, 'val': 2}
  • id: 1356322
    {'lmfdb_iso': '28224.be', 'p': 11, 'prec': 20, 'unit': 5485843610561990958, 'val': 1}
  • id: 1356329
    {'lmfdb_iso': '28224.be', 'p': 13, 'prec': 20, 'unit': 40575551305060251266, 'val': 1}
  • id: 1356331
    {'lmfdb_iso': '28224.be', 'p': 17, 'prec': 20, 'unit': 55245034248151000277330, 'val': 1}
  • id: 1356332
    {'lmfdb_iso': '28224.be', 'p': 19, 'prec': 20, 'unit': 1302734341240654911007947, 'val': 1}
  • id: 1356334
    {'lmfdb_iso': '28224.be', 'p': 23, 'prec': 20, 'unit': 45955826071775835395627008, 'val': 1}
  • id: 1356328
    {'lmfdb_iso': '28224.be', 'p': 29, 'prec': 20, 'unit': 1583157783599009508639372095, 'val': 1}
  • id: 1356325
    {'lmfdb_iso': '28224.be', 'p': 31, 'prec': 20, 'unit': 13390076434629355318760218470, 'val': 1}
  • id: 1356339
    {'lmfdb_iso': '28224.be', 'p': 37, 'prec': 20, 'unit': 80117373238021701294349599231, 'val': 1}
  • id: 1356326
    {'lmfdb_iso': '28224.be', 'p': 41, 'prec': 20, 'unit': 2144369318831517004948348899002, 'val': 1}
  • id: 1356327
    {'lmfdb_iso': '28224.be', 'p': 43, 'prec': 20, 'unit': 9296529677122337385460456215224, 'val': 1}
  • id: 1356330
    {'lmfdb_iso': '28224.be', 'p': 47, 'prec': 20, 'unit': 46034448112657944165259301207991, 'val': 1}
  • id: 1356333
    {'lmfdb_iso': '28224.be', 'p': 53, 'prec': 20, 'unit': 380803433426146608549935355865250, 'val': 1}
  • id: 1356337
    {'lmfdb_iso': '28224.be', 'p': 59, 'prec': 20, 'unit': 4235561393208174681044698240560303, 'val': 1}
  • id: 1356338
    {'lmfdb_iso': '28224.be', 'p': 61, 'prec': 20, 'unit': 550550209146337780778383891880699, 'val': 1}
  • id: 1356321
    {'lmfdb_iso': '28224.be', 'p': 67, 'prec': 20, 'unit': 45358142623006251510267097765683421, 'val': 1}
  • id: 1356324
    {'lmfdb_iso': '28224.be', 'p': 71, 'prec': 20, 'unit': 94521635706342393640136893253566270, 'val': 1}
  • id: 1356335
    {'lmfdb_iso': '28224.be', 'p': 83, 'prec': 20, 'unit': 2890382580150960382303438622145922727, 'val': 1}
  • id: 1356336
    {'lmfdb_iso': '28224.be', 'p': 89, 'prec': 20, 'unit': 4970552782228096775595118447777679550, 'val': 1}
  • id: 1356320
    {'lmfdb_iso': '28224.be', 'p': 97, 'prec': 20, 'unit': 16562786491236824139981813555427767476, 'val': 1}