Elliptic curve data - 84672.fx3

Formats: - HTML - YAML - JSON - 2024-05-03T03:13:57.783132

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '84672r', 'Clabel': '84672r3', 'Cnumber': 3, 'abc_quality': 1.014071361016312, 'absD': 2175642107098693632, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 504, 'ainvs': [0, 0, 0, 291060, 37192176], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 84672, 'degree': 995328, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2065597030639027467475863507', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 153, 'isogeny_degrees': [1, 3, 9], 'jinv': [4492125, 3584], 'lmfdb_iso': '84672.fx', 'lmfdb_label': '84672.fx3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 93, -235], 'min_quad_twist_disc': -56, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '12.8.0-3.a.1.3', '36.24.0-9.a.1.4', '63.36.0.d.1', '168.16.0.?', '252.72.0.?', '504.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.63007535880475413847737213090', 'prec': 107}, 'szpiro_ratio': 4.350000624649526, '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, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 3, 0, 2, 0], 'aplist': [0, 0, 0, 0, 0, 5, 3, 2, 9, -3, -5, -2, -6, 1, -6, 3, 3, -10, 13, -9, -2, -10, 12, 15, -8], 'class_deg': 9, 'class_size': 3, 'conductor': 84672, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '84672.fx', 'trace_hash': 1641478620249507999}
• 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': '0.012117320469866942858718411938', 'prec': 107}, 'conductor': 84672, 'gens': [], 'heights': [], 'lmfdb_label': '84672.fx3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16762797668611310315085670810', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6820476269778096504137073296100260003', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0, 0], '7': 'a', '11': [0, 0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [2, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '84672.fx3'}
• ec_torsion_growth •

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

  
  
  • id: 3969760
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '84672.fx3', 'torsion': [3]}
  • id: 3969761
    {'degree': 3, 'field': [-16, -6, 0, 1], 'lmfdb_label': '84672.fx3', 'torsion': [2]}
  • id: 3969764
    {'degree': 6, 'field': [-10752, 0, 1764, 0, -84, 0, 1], 'lmfdb_label': '84672.fx3', 'torsion': [9]}
  • id: 3969765
    {'degree': 6, 'field': [22, -120, 9, -40, 6, 0, 1], 'lmfdb_label': '84672.fx3', 'torsion': [6]}
  • id: 3969762
    {'degree': 6, 'field': [42, 0, 141, 0, 12, 0, 1], 'lmfdb_label': '84672.fx3', 'torsion': [2, 2]}
  • id: 3969763
    {'degree': 6, 'field': [56, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '84672.fx3', 'torsion': [3]}
  • id: 3969766
    {'degree': 12, 'field': [256, 288, 768, 788, -252, 0, 384, -36, -36, 56, 0, -3, 1], 'lmfdb_label': '84672.fx3', 'torsion': [4]}
  • id: 3969769
    {'degree': 12, 'field': [484, 0, 14004, 0, -9255, 0, 1448, 0, 54, 0, -12, 0, 1], 'lmfdb_label': '84672.fx3', 'torsion': [2, 6]}
  • id: 3969767
    {'degree': 12, 'field': [3249, -342, -819, 2190, -750, -462, 253, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '84672.fx3', 'torsion': [3, 3]}
  • id: 3969768
    {'degree': 12, 'field': [153664, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '84672.fx3', 'torsion': [9]}
  • id: 3969771
    {'degree': 18, 'field': [-47993148, 501046560, -647502660, 298652508, -112245021, -4491774, 11826837, -6160212, 1950129, -345186, 21303, 41796, -14967, 1206, 351, -12, -9, -6, 1], 'lmfdb_label': '84672.fx3', 'torsion': [18]}
  • id: 3969770
    {'degree': 18, 'field': [11239424, 0, 0, 0, 0, 0, -67767, 0, 0, 0, 0, 0, 1050, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '84672.fx3', 'torsion': [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: 2063853
    {'conductor': 84672, 'conductor_valuation': 6, 'discriminant_valuation': 27, 'j_denominator_valuation': 9, 'kodaira_symbol': -21, 'lmfdb_label': '84672.fx3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2063854
    {'conductor': 84672, 'conductor_valuation': 3, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '84672.fx3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2063855
    {'conductor': 84672, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '84672.fx3', '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: 2221717
    {'adelic_gens': [[1, 18, 0, 1], [1, 18, 10, 181], [10, 9, 81, 73], [487, 18, 486, 19], [262, 9, 369, 496], [494, 495, 261, 8], [496, 117, 387, 38], [1, 0, 18, 1], [212, 495, 153, 20]], 'adelic_image': '504.144.3.?', 'conductor': 84672, 'lmfdb_label': '84672.fx3', 'prime': 0}
  • id: 345770
    {'conductor': 84672, 'elladic_image': '9.12.0.1', 'lmfdb_label': '84672.fx3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 84672.fx does not appear in ec_padic