Elliptic curve data - 28224.x2

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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': '28224ec', 'Clabel': '28224ec2', 'Cnumber': 2, 'abc_quality': 1.3265882735428125, 'absD': 129448569470976, 'adelic_genus': 2, 'adelic_index': 144, 'adelic_level': 504, 'ainvs': [0, 0, 0, 756, 547344], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 28224, 'degree': 82944, 'elladic_images': ['9.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3868061373380671067431750360', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 23, 'isogeny_degrees': [1, 3], 'jinv': [189, 512], 'lmfdb_iso': '28224.x', 'lmfdb_label': '28224.x2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 12, -1072], 'min_quad_twist_disc': -8, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.b.1', '24.8.0.d.1', '63.36.0.i.1', '72.24.0.?', '84.8.0.?', '168.16.0.?', '252.72.0.?', '504.144.2.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2729935696976960148229418735', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 147], [3, 2, 3136], [7, 14, 576]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.80119220817881867677999919779', 'prec': 107}, 'szpiro_ratio': 3.8982330121094138, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -3, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 6, 0, -2, 0], 'aplist': [0, 0, -3, 0, 3, 2, 6, -2, -6, 9, -7, 10, 0, -4, -12, -3, -3, -4, 2, 0, -2, -5, 9, -6, 13], 'class_deg': 3, 'class_size': 2, 'conductor': 28224, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '28224.x', 'trace_hash': 487266020962951665}
• 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': '0.062436060700922831803631176465', 'prec': 107}, 'conductor': 28224, 'gens': [[-62, 512, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2729935696976960148229418735', 'prec': 100}], 'lmfdb_label': '28224.x2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.45970943896105662660020644463', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6816572778140845651721343571605802622', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [-62, 268]}
• 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': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '28224.x2'}
• ec_torsion_growth •

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

  
  
  • id: 1414288
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '28224.x2', 'torsion': [3]}
  • id: 1414289
    {'degree': 3, 'field': [-6, -2, -1, 1], 'lmfdb_label': '28224.x2', 'torsion': [2]}
  • id: 1414291
    {'degree': 6, 'field': [-56, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '28224.x2', 'torsion': [3]}
  • id: 1414290
    {'degree': 6, 'field': [6, 0, 13, 0, 16, 0, 1], 'lmfdb_label': '28224.x2', 'torsion': [2, 2]}
  • id: 1414292
    {'degree': 6, 'field': [43, -74, 65, -8, 11, -2, 1], 'lmfdb_label': '28224.x2', 'torsion': [6]}
  • id: 1414293
    {'degree': 12, 'field': [64, 779, 3569, 6939, 5077, 1324, 916, 124, 148, -9, 5, -1, 1], 'lmfdb_label': '28224.x2', 'torsion': [4]}
  • id: 1414295
    {'degree': 12, 'field': [378, 252, 798, 0, 217, -196, -146, -44, 32, -8, 16, -4, 1], 'lmfdb_label': '28224.x2', 'torsion': [2, 6]}
  • id: 1414294
    {'degree': 12, 'field': [3025, 330, 861, -2290, 930, 210, 29, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '28224.x2', 'torsion': [3, 3]}
  • id: 1414297
    {'degree': 18, 'field': [8, 0, 0, 16112, 0, 0, 32596, 0, 0, -13644, 0, 0, 1535, 0, 0, -46, 0, 0, 1], 'lmfdb_label': '28224.x2', 'torsion': [6]}
  • id: 1414296
    {'degree': 18, 'field': [8429568, 0, -6322176, 0, 7507584, 0, 3988992, 0, 1270080, 0, 317520, 0, 25032, 0, 168, 0, 0, 0, 1], 'lmfdb_label': '28224.x2', 'torsion': [9]}
• 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: 654020
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 27, 'j_denominator_valuation': 9, 'kodaira_symbol': -21, 'lmfdb_label': '28224.x2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 654021
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '28224.x2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 654022
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '28224.x2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1852623
    {'adelic_gens': [[1, 18, 0, 1], [1, 18, 12, 217], [377, 486, 0, 503], [251, 486, 243, 341], [10, 9, 81, 73], [299, 18, 270, 239], [487, 18, 486, 19], [121, 234, 333, 59], [1, 0, 18, 1], [13, 12, 440, 445]], 'adelic_image': '504.144.2.?', 'conductor': 28224, 'lmfdb_label': '28224.x2', 'prime': 0}
  • id: 127728
    {'conductor': 28224, 'elladic_image': '9.12.0.2', 'lmfdb_label': '28224.x2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1356868
    {'lmfdb_iso': '28224.x', 'p': 5, 'prec': 20, 'unit': 14695739168597, 'val': 1}
  • id: 1356867
    {'lmfdb_iso': '28224.x', 'p': 11, 'prec': 20, 'unit': 12193873516202575056, 'val': 1}
  • id: 1356873
    {'lmfdb_iso': '28224.x', 'p': 13, 'prec': 20, 'unit': 2696371876380936664, 'val': 3}
  • id: 1356875
    {'lmfdb_iso': '28224.x', 'p': 17, 'prec': 20, 'unit': 68554758246679508727834, 'val': 1}
  • id: 1356876
    {'lmfdb_iso': '28224.x', 'p': 19, 'prec': 20, 'unit': 213124638046438239369140, 'val': 1}
  • id: 1356879
    {'lmfdb_iso': '28224.x', 'p': 23, 'prec': 20, 'unit': 41729263187280568925946341, 'val': 1}
  • id: 1356872
    {'lmfdb_iso': '28224.x', 'p': 29, 'prec': 20, 'unit': 1320862459553255852518747672, 'val': 1}
  • id: 1356869
    {'lmfdb_iso': '28224.x', 'p': 31, 'prec': 20, 'unit': 21035256075941716730730979595, 'val': 1}
  • id: 1356884
    {'lmfdb_iso': '28224.x', 'p': 37, 'prec': 20, 'unit': 369346116708468524369472959308, 'val': 1}
  • id: 1356871
    {'lmfdb_iso': '28224.x', 'p': 43, 'prec': 20, 'unit': 5871184738658994735301903730902, 'val': 1}
  • id: 1356882
    {'lmfdb_iso': '28224.x', 'p': 47, 'prec': 20, 'unit': 34818913797053252813571277734136, 'val': 1}
  • id: 1356877
    {'lmfdb_iso': '28224.x', 'p': 53, 'prec': 20, 'unit': 193256546362640696037023889152425, 'val': 1}
  • id: 1356878
    {'lmfdb_iso': '28224.x', 'p': 59, 'prec': 20, 'unit': 2671134686944354510691519887487294, 'val': 1}
  • id: 1356883
    {'lmfdb_iso': '28224.x', 'p': 61, 'prec': 20, 'unit': 5364447596675167686300165780907877, 'val': 1}
  • id: 1356866
    {'lmfdb_iso': '28224.x', 'p': 67, 'prec': 20, 'unit': 29954630717615684596664871550085103, 'val': 1}
  • id: 1356870
    {'lmfdb_iso': '28224.x', 'p': 73, 'prec': 20, 'unit': 170548324014161945008401217075443422, 'val': 1}
  • id: 1356874
    {'lmfdb_iso': '28224.x', 'p': 79, 'prec': 20, 'unit': 621026020413866695591370223670043522, 'val': 1}
  • id: 1356880
    {'lmfdb_iso': '28224.x', 'p': 83, 'prec': 20, 'unit': 2216974270390207104966465281561264124, 'val': 1}
  • id: 1356881
    {'lmfdb_iso': '28224.x', 'p': 89, 'prec': 20, 'unit': 8621187116053664897573432269160799857, 'val': 1}
  • id: 1356865
    {'lmfdb_iso': '28224.x', 'p': 97, 'prec': 20, 'unit': 50813722144288196990029779823523604190, 'val': 1}