Elliptic curve data - 28224.cd2

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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': '28224fo', 'Clabel': '28224fo1', 'Cnumber': 1, 'abc_quality': 1.1169180726528216, 'absD': 56184274944, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 168, 'ainvs': [0, 0, 0, -588, -12656], 'analytic_rank': 2, 'bad_primes': [2, 3, 7], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 28224, 'degree': 18432, 'elladic_images': ['7.24.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.75054840413297012813350813518', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 55, 'isogeny_degrees': [1, 7], 'jinv': [-2401, 6], 'lmfdb_iso': '28224.cd', 'lmfdb_label': '28224.cd2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1, -1], 'min_quad_twist_disc': 24, 'modell_images': ['7B.6.3'], 'modm_images': ['7.24.0.a.2', '24.2.0.b.1', '28.48.0-7.a.2.3', '168.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 3, 'num_int_pts': 16, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.0527683063496217456731598788', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 441], [3, 8, 3136], [7, 2, 576]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1627968692168882325408547894', 'prec': 103}, 'szpiro_ratio': 3.1630705297618085, '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, -1, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -4, 0, -8, 0], 'aplist': [0, 0, -1, 0, -5, 0, -4, -8, -4, -5, 3, 4, 0, 2, 6, -9, -11, -6, -2, 2, -10, -3, -7, -6, -7], 'class_deg': 7, 'class_size': 2, 'conductor': 28224, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '28224.cd', 'trace_hash': 2159156335299194889}
• 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': '0.22288556330683789426380818345', 'prec': 103}, 'conductor': 28224, 'gens': [[50, 288, 1], [32, 36, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.58051130247051423675967813635', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.8322343383571941232506707344', 'prec': 100}], 'lmfdb_label': '28224.cd2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.45153585589139499629915251852', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.6058022122065725504241429962658759484', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [], 'xcoord_integral_points': [32, 44, 50, 114, 149, 242, 365, 6962]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': 'a', '11': [2, 0], '13': [2, 2, 0], '17': [2, 0], '19': [2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '28224.cd2'}
• ec_torsion_growth •

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

  
  
  • id: 1414780
    {'degree': 3, 'field': [-6, -2, -1, 1], 'lmfdb_label': '28224.cd2', 'torsion': [2]}
  • id: 1414781
    {'degree': 6, 'field': [6, 0, 13, 0, 16, 0, 1], 'lmfdb_label': '28224.cd2', 'torsion': [2, 2]}
  • id: 1414782
    {'degree': 6, 'field': [1512, 0, 504, 0, 42, 0, 1], 'lmfdb_label': '28224.cd2', 'torsion': [7]}
  • id: 1414783
    {'degree': 8, 'field': [-9408, 0, 840, 0, 252, 0, 14, 0, 1], 'lmfdb_label': '28224.cd2', 'torsion': [3]}
  • id: 1414784
    {'degree': 12, 'field': [-48, 66, -326, 446, -458, 178, -134, 130, -94, 9, 17, -3, 1], 'lmfdb_label': '28224.cd2', 'torsion': [4]}
  • id: 1414785
    {'degree': 14, 'field': [-864, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '28224.cd2', 'torsion': [7]}
  • id: 1414786
    {'degree': 18, 'field': [17851, -54474, 112877, -124430, 146017, -123990, 110878, -85698, 65630, -42600, 25573, -13076, 5951, -2306, 777, -214, 50, -8, 1], 'lmfdb_label': '28224.cd2', 'torsion': [14]}
• 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: 654197
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '28224.cd2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 654198
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '28224.cd2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 654199
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '28224.cd2', '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: 1852401
    {'adelic_gens': [[160, 161, 91, 6], [1, 0, 14, 1], [104, 161, 119, 6], [129, 80, 70, 113], [8, 5, 91, 57], [155, 14, 154, 15], [41, 154, 0, 167], [1, 14, 0, 1]], 'adelic_image': '168.96.2.?', 'conductor': 28224, 'lmfdb_label': '28224.cd2', 'prime': 0}
  • id: 127497
    {'conductor': 28224, 'elladic_image': '7.24.0.2', 'lmfdb_label': '28224.cd2', 'modell_image': '7B.6.3', 'prime': 7}
• ec_padic •

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

  
  
  • id: 1357414
    {'lmfdb_iso': '28224.cd', 'p': 5, 'prec': 20, 'unit': 2548097934851, 'val': 2}
  • id: 1357421
    {'lmfdb_iso': '28224.cd', 'p': 11, 'prec': 20, 'unit': 35384662616723371163, 'val': 2}
  • id: 1357422
    {'lmfdb_iso': '28224.cd', 'p': 17, 'prec': 20, 'unit': 80966266537231956646663, 'val': 2}
  • id: 1357423
    {'lmfdb_iso': '28224.cd', 'p': 19, 'prec': 20, 'unit': 163402300143208696373910, 'val': 2}
  • id: 1357426
    {'lmfdb_iso': '28224.cd', 'p': 23, 'prec': 20, 'unit': 35651930079633406836308553, 'val': 2}
  • id: 1357419
    {'lmfdb_iso': '28224.cd', 'p': 29, 'prec': 20, 'unit': 1503729979193374775341507719, 'val': 2}
  • id: 1357416
    {'lmfdb_iso': '28224.cd', 'p': 31, 'prec': 20, 'unit': 2289728480210082439444753610, 'val': 2}
  • id: 1357430
    {'lmfdb_iso': '28224.cd', 'p': 37, 'prec': 20, 'unit': 296352470596796467828076197221, 'val': 2}
  • id: 1357418
    {'lmfdb_iso': '28224.cd', 'p': 43, 'prec': 20, 'unit': 785573437979229946300793835094, 'val': 2}
  • id: 1357428
    {'lmfdb_iso': '28224.cd', 'p': 47, 'prec': 20, 'unit': 12817815226254620662158833000708, 'val': 2}
  • id: 1357424
    {'lmfdb_iso': '28224.cd', 'p': 53, 'prec': 20, 'unit': 444460192124985944701378466538577, 'val': 2}
  • id: 1357425
    {'lmfdb_iso': '28224.cd', 'p': 59, 'prec': 20, 'unit': 3556538214913744515797856384264280, 'val': 2}
  • id: 1357429
    {'lmfdb_iso': '28224.cd', 'p': 61, 'prec': 20, 'unit': 7813720661453084119370247886572771, 'val': 2}
  • id: 1357413
    {'lmfdb_iso': '28224.cd', 'p': 67, 'prec': 20, 'unit': 49194420347272983306612822313636000, 'val': 2}
  • id: 1357415
    {'lmfdb_iso': '28224.cd', 'p': 71, 'prec': 20, 'unit': 63686526368343830984352231505739570, 'val': 2}
  • id: 1357417
    {'lmfdb_iso': '28224.cd', 'p': 73, 'prec': 20, 'unit': 220619766492011695396420245581947248, 'val': 2}
  • id: 1357420
    {'lmfdb_iso': '28224.cd', 'p': 79, 'prec': 20, 'unit': 256571770419918550220488733102150398, 'val': 2}
  • id: 1357412
    {'lmfdb_iso': '28224.cd', 'p': 83, 'prec': 20, 'unit': 240425215426344507902721215160497293, 'val': 2}
  • id: 1357427
    {'lmfdb_iso': '28224.cd', 'p': 89, 'prec': 20, 'unit': 1326588586807729113025160122097288882, 'val': 2}
  • id: 1357411
    {'lmfdb_iso': '28224.cd', 'p': 97, 'prec': 20, 'unit': 13651139616766417669486890630819280582, 'val': 2}