Elliptic curve data - 28224.j2

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• 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': '28224cu', 'Clabel': '28224cu1', 'Cnumber': 1, 'abc_quality': 1.0551964751750895, 'absD': 12910202661888, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 84, 'ainvs': [0, 0, 0, -2352, -178360], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 28224, 'degree': 73728, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1982745918556181189124974841', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2], 'jinv': [-16384, 147], 'lmfdb_iso': '28224.j', 'lmfdb_label': '28224.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1, -2], 'min_quad_twist_disc': 168, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '28.6.0.b.1', '84.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2544536217844248391190869415', 'prec': 100}, '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': '-0.90160927747271447051882827397', 'prec': 107}, 'szpiro_ratio': 3.679403700597661, '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, -4, 0, 0, 0, 0, 0, 2, 0, -6, 0, 0, 0, -4, 0, -4, 0], 'aplist': [0, 0, -4, 0, 2, -6, -4, -4, -2, -2, 0, -2, 0, 4, 12, -6, 8, 6, 8, -14, 2, 12, 4, 0, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 28224, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '28224.j', 'trace_hash': 2100441829276498303}
• 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': '0.091031545042881398946136106302', 'prec': 107}, 'conductor': 28224, 'gens': [[154, 1764, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2544536217844248391190869415', 'prec': 100}], 'lmfdb_label': '28224.j2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.30010828098893714416549875890', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0117753601125604117828935902448751307', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[70, 0, 1]], 'xcoord_integral_points': [70, 154, 217, 5558]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '28224.j2'}
• ec_torsion_growth •

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

  
  
  • id: 1413772
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '28224.j2', 'torsion': [2, 2]}
  • id: 1413773
    {'degree': 4, 'field': [-3, 0, -4, 0, 1], 'lmfdb_label': '28224.j2', 'torsion': [4]}
  • id: 1413776
    {'degree': 8, 'field': [-9408, 0, -840, 0, 252, 0, -14, 0, 1], 'lmfdb_label': '28224.j2', 'torsion': [6]}
  • id: 1413775
    {'degree': 8, 'field': [9, 0, -12, 0, 19, 0, 4, 0, 1], 'lmfdb_label': '28224.j2', 'torsion': [2, 4]}
  • id: 1413774
    {'degree': 8, 'field': [2401, 0, -560, 0, 135, 0, -20, 0, 1], 'lmfdb_label': '28224.j2', 'torsion': [2, 4]}
  • id: 1413777
    {'degree': 16, 'field': [441, 0, -35280, 0, 46144, 0, 69160, 0, 27626, 0, 5680, 0, 656, 0, 40, 0, 1], 'lmfdb_label': '28224.j2', 'torsion': [8]}
  • id: 1413778
    {'degree': 16, 'field': [5531904, 0, 2634240, 0, 859264, 0, 188160, 0, 30576, 0, 2240, 0, 168, 0, 0, 0, 1], 'lmfdb_label': '28224.j2', '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: 653843
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '28224.j2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 653844
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '28224.j2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 653845
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '28224.j2', 'prime': 7, 'reduction_type': 0, '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: 1852600
    {'adelic_gens': [[73, 4, 62, 9], [1, 4, 0, 1], [25, 64, 20, 63], [1, 0, 4, 1], [3, 4, 8, 11], [81, 4, 80, 5], [58, 1, 55, 0], [1, 2, 2, 5]], 'adelic_image': '84.12.0.?', 'conductor': 28224, 'lmfdb_label': '28224.j2', 'prime': 0}
  • id: 127706
    {'conductor': 28224, 'elladic_image': '2.3.0.1', 'lmfdb_label': '28224.j2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1356484
    {'lmfdb_iso': '28224.j', 'p': 5, 'prec': 20, 'unit': 77903953139254, 'val': -1}
  • id: 1356483
    {'lmfdb_iso': '28224.j', 'p': 11, 'prec': 20, 'unit': 19073781653714442180, 'val': 1}
  • id: 1356489
    {'lmfdb_iso': '28224.j', 'p': 13, 'prec': 20, 'unit': 795905812851735230405, 'val': 1}
  • id: 1356491
    {'lmfdb_iso': '28224.j', 'p': 17, 'prec': 20, 'unit': 111548649560026090671127, 'val': 1}
  • id: 1356492
    {'lmfdb_iso': '28224.j', 'p': 19, 'prec': 20, 'unit': 444655996209113212627023, 'val': 1}
  • id: 1356495
    {'lmfdb_iso': '28224.j', 'p': 23, 'prec': 20, 'unit': 47511468298113108915019402, 'val': 1}
  • id: 1356488
    {'lmfdb_iso': '28224.j', 'p': 29, 'prec': 20, 'unit': 5910934681252815594901546843, 'val': 1}
  • id: 1356499
    {'lmfdb_iso': '28224.j', 'p': 37, 'prec': 20, 'unit': 46146129727862536487945949571, 'val': 1}
  • id: 1356487
    {'lmfdb_iso': '28224.j', 'p': 43, 'prec': 20, 'unit': 2346948123219419634640586328501, 'val': 1}
  • id: 1356497
    {'lmfdb_iso': '28224.j', 'p': 47, 'prec': 20, 'unit': 29365404265561986062392495931033, 'val': 1}
  • id: 1356493
    {'lmfdb_iso': '28224.j', 'p': 53, 'prec': 20, 'unit': 185529814103323676398745971850299, 'val': 1}
  • id: 1356494
    {'lmfdb_iso': '28224.j', 'p': 59, 'prec': 20, 'unit': 524879897707452960894322900296690, 'val': 1}
  • id: 1356498
    {'lmfdb_iso': '28224.j', 'p': 61, 'prec': 20, 'unit': 6914025096427299182851595506828366, 'val': 1}
  • id: 1356482
    {'lmfdb_iso': '28224.j', 'p': 67, 'prec': 20, 'unit': 40382681460136596256136547733254044, 'val': 1}
  • id: 1356485
    {'lmfdb_iso': '28224.j', 'p': 71, 'prec': 20, 'unit': 136658273031001449680869299026463002, 'val': 1}
  • id: 1356486
    {'lmfdb_iso': '28224.j', 'p': 73, 'prec': 20, 'unit': 159504856593797606888569837254825819, 'val': 1}
  • id: 1356490
    {'lmfdb_iso': '28224.j', 'p': 79, 'prec': 20, 'unit': 357870376586084124757694987430767129, 'val': 1}
  • id: 1356496
    {'lmfdb_iso': '28224.j', 'p': 83, 'prec': 20, 'unit': 357695707462482320185089663895980400, 'val': 1}
  • id: 1356481
    {'lmfdb_iso': '28224.j', 'p': 97, 'prec': 20, 'unit': 5652760083921430195563698272555385253, 'val': 1}