Elliptic curve data - 28224.dw3

Formats: - HTML - YAML - JSON - 2023-06-04T10:26:34.737243

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '28224bn', 'Clabel': '28224bn2', 'Cnumber': 2, 'absD': 65548320768, 'ainvs': [0, 0, 0, -21420, 1206576], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 14, 'class_size': 4, 'cm': -28, 'conductor': 28224, 'degree': 32768, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1364621163983230474077751517', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 100, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [16581375, 1], 'lmfdb_iso': '28224.dw', 'lmfdb_label': '28224.dw3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -37, -78], 'min_quad_twist_disc': -24, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.69190873220748374292040284330', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.93904233603947808869203383481', 'prec': 107}, '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, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, 0, 0, 4, 0, 0, 0, -8, 2, 0, 6, 0, 12, 0, -10, 0, 0, -4, -16, 0, 8, 0, 0, 0], 'class_deg': 14, 'class_size': 4, 'conductor': 28224, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '28224.dw', 'trace_hash': 1474547690586168832}
• 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': '0.10301051250588639034371243684', 'prec': 103}, 'conductor': 28224, 'gens': [[70, 224, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.69190873220748374292040284330', 'prec': 103}], 'lmfdb_label': '28224.dw3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0441076544415988952242884345', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.7794176277825297904209902354670756865', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[84, 0, 1]], 'xcoord_integral_points': [-168, 70, 84, 85, 102]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 1, 0], '7': 'a', '11': [1, 0], '13': [1, 1, 0], '17': [1, 1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [3, 1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '28224.dw3'}
• ec_torsion_growth •

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

  
  
  • id: 1412851
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [2, 2]}
  • id: 1412852
    {'degree': 4, 'field': [252, 0, 0, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [4]}
  • id: 1412853
    {'degree': 6, 'field': [-1512, 0, 504, 0, -42, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [14]}
  • id: 1412858
    {'degree': 8, 'field': [-2352, 0, 1176, 0, -168, 0, 0, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [6]}
  • id: 1412855
    {'degree': 8, 'field': [36, 0, -60, 0, 13, 0, -4, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [2, 4]}
  • id: 1412857
    {'degree': 8, 'field': [616, -560, -28, -140, 207, -18, -9, -2, 1], 'lmfdb_label': '28224.dw3', 'torsion': [8]}
  • id: 1412856
    {'degree': 8, 'field': [2809, 0, 1334, 0, 290, 0, 22, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [8]}
  • id: 1412854
    {'degree': 8, 'field': [3844, 0, 760, 0, -120, 0, 4, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [2, 4]}
  • id: 1412859
    {'degree': 12, 'field': [729, 0, -5832, 0, 6966, 0, -2808, 0, 477, 0, -36, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [2, 14]}
  • id: 1412860
    {'degree': 16, 'field': [256, 0, 1088, 0, 1892, 0, 2004, 0, 1601, 0, 144, 0, -34, 0, -4, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [4, 4]}
  • id: 1412861
    {'degree': 16, 'field': [14641, 0, 0, 0, -9159, 0, 0, 0, 4016, 0, 0, 0, 9, 0, 0, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [2, 8]}
  • id: 1412865
    {'degree': 16, 'field': [21609, 0, 86436, 0, 108045, 0, 24696, 0, -26754, 0, -7644, 0, -588, 0, 0, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [2, 6]}
  • id: 1412862
    {'degree': 16, 'field': [2920681, 0, -2421226, 0, 1421667, 0, -443766, 0, 86718, 0, -11290, 0, 947, 0, -46, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [16]}
  • id: 1412863
    {'degree': 16, 'field': [2920681, 0, 2421226, 0, 1421667, 0, 443766, 0, 86718, 0, 11290, 0, 947, 0, 46, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [16]}
  • id: 1412864
    {'degree': 16, 'field': [5531904, 0, 2765952, 0, 987840, 0, 197568, 0, 30576, 0, 2352, 0, 168, 0, 0, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [3, 6]}
  • id: 1412866
    {'degree': 20, 'field': [11178805220352, 0, 0, 0, 88720676352, 0, 0, 0, 176033088, 0, 5334336, 0, 508032, 0, -21168, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '28224.dw3', 'torsion': [22]}
• 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: 653585
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '28224.dw3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 653586
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '28224.dw3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 653587
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '28224.dw3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 28224.dw3 does not appear in ec_galrep
• ec_padic •

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

  
  
  • id: 1355720
    {'lmfdb_iso': '28224.dw', 'p': 11, 'prec': 20, 'unit': 23118271525123948600, 'val': 1}
  • id: 1355722
    {'lmfdb_iso': '28224.dw', 'p': 23, 'prec': 20, 'unit': 47182559341393938990168790, 'val': 1}
  • id: 1355723
    {'lmfdb_iso': '28224.dw', 'p': 29, 'prec': 20, 'unit': 2654029789028616400024441928, 'val': 1}
  • id: 1355716
    {'lmfdb_iso': '28224.dw', 'p': 37, 'prec': 20, 'unit': 131363061787541770633752059273, 'val': 1}
  • id: 1355718
    {'lmfdb_iso': '28224.dw', 'p': 43, 'prec': 20, 'unit': 3423856732980331609752329273281, 'val': 1}
  • id: 1355721
    {'lmfdb_iso': '28224.dw', 'p': 53, 'prec': 20, 'unit': 518238792975634317295157824453098, 'val': 1}
  • id: 1355715
    {'lmfdb_iso': '28224.dw', 'p': 67, 'prec': 20, 'unit': 41398326286636266625700261051880427, 'val': 1}
  • id: 1355717
    {'lmfdb_iso': '28224.dw', 'p': 71, 'prec': 20, 'unit': 60290780260925184606475819820288347, 'val': 1}
  • id: 1355719
    {'lmfdb_iso': '28224.dw', 'p': 79, 'prec': 20, 'unit': 546005011508201776841323459225127141, 'val': 1}