Elliptic curve data - 1248.f2

Formats: - HTML - YAML - JSON - 2022-06-26T14:31:29.619835

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  absD	numeric
  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[]
  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': '1248e', 'Clabel': '1248e2', 'Cnumber': 2, 'absD': 3158618112, 'ainvs': [0, 1, 0, -369, -513], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1248, 'degree': 768, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.51271634234938137039558294885', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4], 'jinv': [1360251712, 771147], 'lmfdb_iso': '1248.f', 'lmfdb_label': '1248.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -369, -513], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.39011799503959577487430912727', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.18043083821056393902164917261', '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, 1, 0, -2, 0, 0, 0, 1, 0, -4, 0, 1, 0, -2, 0, -6, 0, 8, 0], 'aplist': [0, 1, -2, 0, -4, 1, -6, 8, -8, 2, -8, -10, 6, 4, 0, -14, 12, -10, 8, 0, -14, 4, -4, -10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 1248, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '1248.f', 'trace_hash': 1865816417566786042}
• 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': '0.35864125324678496749312727713', 'prec': 103}, 'conductor': 1248, 'gens': [[-6, 39, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.39011799503959577487430912727', 'prec': 103}], 'lmfdb_label': '1248.f2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.1752609593546950284024196610', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7509426946705929200919585110309812070', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-19, 0, 1]], 'xcoord_integral_points': [-19, -6, -3, 33, 449]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [4, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1248.f2'}
• ec_torsion_growth •

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

  
  
  • id: 61989
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [2, 2]}
  • id: 61991
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '1248.f2', 'torsion': [4]}
  • id: 61990
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [4]}
  • id: 61993
    {'degree': 4, 'field': [-3, 0, 0, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [2, 4]}
  • id: 61992
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [2, 4]}
  • id: 61997
    {'degree': 8, 'field': [-27, 0, -112, 0, -18, 0, 0, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [6]}
  • id: 61996
    {'degree': 8, 'field': [9, 0, -54, 0, 321, 0, -18, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [8]}
  • id: 61994
    {'degree': 8, 'field': [9, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [4, 4]}
  • id: 61995
    {'degree': 8, 'field': [900, 0, -416, 0, 60, 0, 0, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [8]}
  • id: 61999
    {'degree': 16, 'field': [1, 0, 0, 0, 106, 0, 0, 0, 11235, 0, 0, 0, 106, 0, 0, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [2, 8]}
  • id: 62001
    {'degree': 16, 'field': [1, 0, 8, 0, 10, 0, -128, 0, -289, 0, -128, 0, 10, 0, 8, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [2, 6]}
  • id: 62002
    {'degree': 16, 'field': [36, 144, 288, 528, 192, -552, 128, 208, 340, -792, 712, -400, 188, -84, 32, -8, 1], 'lmfdb_label': '1248.f2', 'torsion': [12]}
  • id: 62000
    {'degree': 16, 'field': [324, 0, -16848, 0, 21384, 0, 432, 0, -6240, 0, -1464, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [2, 8]}
  • id: 62003
    {'degree': 16, 'field': [729, 0, -3024, 0, 12058, 0, -2016, 0, 351, 0, -224, 0, 18, 0, 0, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [12]}
  • id: 61998
    {'degree': 16, 'field': [43046721, 0, 0, 0, -984150, 0, 0, 0, 15939, 0, 0, 0, -150, 0, 0, 0, 1], 'lmfdb_label': '1248.f2', 'torsion': [2, 8]}
• 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: 18506
    {'conductor': 1248, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '1248.f2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 18507
    {'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '1248.f2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 18508
    {'conductor': 1248, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '1248.f2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  {'conductor': 1248, 'elladic_image': '4.12.0.8', 'lmfdb_label': '1248.f2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 31151
    {'lmfdb_iso': '1248.f', 'p': 5, 'prec': 20, 'unit': 14234464279079, 'val': 1}
  • id: 31157
    {'lmfdb_iso': '1248.f', 'p': 11, 'prec': 20, 'unit': 2104226439694368690, 'val': 1}
  • id: 31158
    {'lmfdb_iso': '1248.f', 'p': 17, 'prec': 20, 'unit': 11185940613788423955723, 'val': 1}
  • id: 31159
    {'lmfdb_iso': '1248.f', 'p': 19, 'prec': 20, 'unit': 1445427642717442614219576, 'val': 1}
  • id: 31162
    {'lmfdb_iso': '1248.f', 'p': 23, 'prec': 20, 'unit': 74436734206111129219005889, 'val': 1}
  • id: 31155
    {'lmfdb_iso': '1248.f', 'p': 29, 'prec': 20, 'unit': 5907899587872591746749216877, 'val': 1}
  • id: 31152
    {'lmfdb_iso': '1248.f', 'p': 31, 'prec': 20, 'unit': 6565733869461249873988855102, 'val': 1}
  • id: 31166
    {'lmfdb_iso': '1248.f', 'p': 37, 'prec': 20, 'unit': 512195580310597181528641827558, 'val': 1}
  • id: 31153
    {'lmfdb_iso': '1248.f', 'p': 41, 'prec': 20, 'unit': 4247081455981237241961077943390, 'val': 1}
  • id: 31154
    {'lmfdb_iso': '1248.f', 'p': 43, 'prec': 20, 'unit': 896362679989500543067902009850, 'val': 1}
  • id: 31160
    {'lmfdb_iso': '1248.f', 'p': 53, 'prec': 20, 'unit': 67147201197676227625804247208552, 'val': 1}
  • id: 31164
    {'lmfdb_iso': '1248.f', 'p': 59, 'prec': 20, 'unit': 2032241770109715098472133140328152, 'val': 1}
  • id: 31165
    {'lmfdb_iso': '1248.f', 'p': 61, 'prec': 20, 'unit': 3659763256843686502214245091739876, 'val': 1}
  • id: 31150
    {'lmfdb_iso': '1248.f', 'p': 67, 'prec': 20, 'unit': 37293781696611406505262294256419716, 'val': 1}
  • id: 31161
    {'lmfdb_iso': '1248.f', 'p': 73, 'prec': 20, 'unit': 105037529689303481650796609941762513, 'val': 1}
  • id: 31156
    {'lmfdb_iso': '1248.f', 'p': 79, 'prec': 20, 'unit': 95667003505143215423209078744035043, 'val': 1}
  • id: 31149
    {'lmfdb_iso': '1248.f', 'p': 83, 'prec': 20, 'unit': 13832743541861449429614711154005799, 'val': 1}
  • id: 31163
    {'lmfdb_iso': '1248.f', 'p': 89, 'prec': 20, 'unit': 3738968355694354547147189517907707993, 'val': 1}
  • id: 31148
    {'lmfdb_iso': '1248.f', 'p': 97, 'prec': 20, 'unit': 42381619688725088364501385447974896738, 'val': 1}