Elliptic curve data - 28224.es1

Formats: - HTML - YAML - JSON - 2025-01-18T08:11:34.778116

• 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': '28224fw', 'Clabel': '28224fw6', 'Cnumber': 6, 'abc_quality': 1.0508747826837916, 'absD': 3305011881443328, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [0, 0, 0, -22128204, 40065204368], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 28224, 'degree': 786432, 'elladic_images': ['16.48.0.95'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6361873730925692331344130270', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 122, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [53297461115137, 147], 'lmfdb_iso': '28224.es', 'lmfdb_label': '28224.es1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -784, -8515], 'min_quad_twist_disc': -168, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.1', '12.12.0.h.1', '16.48.0-16.e.2.15', '24.48.0-24.bl.1.4', '48.96.0-48.y.1.15', '56.48.0-56.bu.1.15', '112.96.0.?', '168.96.0.?', '336.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 441], [3, 8, 3136], [7, 32, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854628', 'prec': 107}, 'szpiro_ratio': 6.084224434359162, '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, -2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 2, 0, -4, -2, -6, -4, 0, -2, 0, -6, 2, -4, 0, 6, 12, -2, 4, 0, 6, 16, -12, -14, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 28224, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '28224.es', 'trace_hash': 1210649544045141312}
• 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': '0.0051314102954590891704533170660', 'prec': 110}, 'conductor': 28224, 'gens': [], 'heights': [], 'lmfdb_label': '28224.es1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29487212491333079155708746451', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1794884996533231662283498580268883419', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[2716, 0, 1]], 'xcoord_integral_points': [2716]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '28224.es1'}
• ec_torsion_growth •

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

  
  
  • id: 1415201
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [8]}
  • id: 1415202
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [4]}
  • id: 1415200
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [2, 2]}
  • id: 1415203
    {'degree': 4, 'field': [49, 0, -28, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [2, 8]}
  • id: 1415207
    {'degree': 8, 'field': [-2352, 0, 1680, 0, 252, 0, 28, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [6]}
  • id: 1415204
    {'degree': 8, 'field': [1521, 468, 498, -264, 184, -40, 18, -4, 1], 'lmfdb_label': '28224.es1', 'torsion': [2, 4]}
  • id: 1415205
    {'degree': 8, 'field': [2401, 0, 1372, 0, 147, 0, -14, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [8]}
  • id: 1415206
    {'degree': 8, 'field': [345744, 0, 49392, 0, 2898, 0, 84, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [16]}
  • id: 1415209
    {'degree': 16, 'field': [2401, 0, -38416, 0, 122108, 0, -120736, 0, 52087, 0, -10976, 0, 1148, 0, -56, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [2, 16]}
  • id: 1415211
    {'degree': 16, 'field': [5203, -9548, 18960, -4936, 20066, -7428, -1388, -3416, -156, 868, 664, -360, -70, 44, 12, -8, 1], 'lmfdb_label': '28224.es1', 'torsion': [16]}
  • id: 1415212
    {'degree': 16, 'field': [21609, 0, 94668, 0, 112357, 0, 27048, 0, -26754, 0, -8372, 0, -588, 0, 0, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [2, 6]}
  • id: 1415208
    {'degree': 16, 'field': [133921, -1090268, 2836206, -1439824, 1486194, -403368, 335254, -61048, 53319, -7844, 6022, -672, 504, -68, 36, -4, 1], 'lmfdb_label': '28224.es1', 'torsion': [4, 8]}
  • id: 1415213
    {'degree': 16, 'field': [4108729, 0, -15984310, 0, -4546127, 0, -497152, 0, 41806, 0, 13190, 0, 1024, 0, 56, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [24]}
  • id: 1415214
    {'degree': 16, 'field': [5531904, 0, -5707520, 0, 2976064, 0, -907872, 0, 166208, 0, -18760, 0, 1344, 0, -56, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [12]}
  • id: 1415210
    {'degree': 16, 'field': [94128804, 0, 43563744, 0, 12113388, 0, 889056, 0, 55125, 0, 3528, 0, 504, 0, 0, 0, 1], 'lmfdb_label': '28224.es1', 'torsion': [2, 16]}
• 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: 654293
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '28224.es1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 654294
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '28224.es1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 654295
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '28224.es1', '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: 1852492
    {'adelic_gens': [[5, 4, 332, 333], [208, 331, 45, 14], [1, 16, 0, 1], [323, 320, 172, 231], [15, 2, 238, 323], [202, 247, 123, 166], [227, 320, 208, 315], [321, 16, 320, 17], [1, 0, 16, 1]], 'adelic_image': '336.192.1.?', 'conductor': 28224, 'lmfdb_label': '28224.es1', 'prime': 0}
  • id: 127599
    {'conductor': 28224, 'elladic_image': '16.48.0.95', 'lmfdb_label': '28224.es1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 28224.es does not appear in ec_padic