Elliptic curve data - 27200.bc1

Formats: - HTML - YAML - JSON - 2024-06-10T07:31:50.354270

• 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': '27200ci', 'Clabel': '27200ci2', 'Cnumber': 2, 'abc_quality': 1.003516346580922, 'absD': 5030912000000000000000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 2040, 'ainvs': [0, -1, 0, -10625633, 13764923137], 'analytic_rank': 1, 'bad_primes': [2, 5, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 27200, 'degree': 1161216, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9342124135527585007301523005', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 28, 'isogeny_degrees': [1, 3], 'jinv': [-32391289681150609, 1228250000000], 'lmfdb_iso': '27200.bc', 'lmfdb_label': '27200.bc1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -6641, -215575], 'min_quad_twist_disc': -40, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '102.8.0.?', '120.8.0.?', '680.2.0.?', '2040.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3519603556926250614302780049', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0897726864957903493039244517', 'prec': 100}, 'szpiro_ratio': 5.8969320592751115, '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, -1, 0, 0, 0, 2, 0, -2, 0, 0, 0, -1, 0, 0, 0, 1, 0, -1, 0], 'aplist': [0, -1, 0, 2, 0, -1, 1, -1, -6, 3, -5, 8, 6, 10, -3, -3, 3, -11, -2, -9, -11, -8, 12, 15, 7], 'class_deg': 3, 'class_size': 2, 'conductor': 27200, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '27200.bc', 'trace_hash': 386438902242885651}
• 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': '0.0028273233514289371395928990508', 'prec': 110}, 'conductor': 27200, 'gens': [[4752, 265625, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3519603556926250614302780049', 'prec': 100}], 'lmfdb_label': '27200.bc1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.13554696927976990882969465258', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3980990912128411564112061373713621815', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': [4752]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': 'a', '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [2, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '27200.bc1'}
• ec_torsion_growth •

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

  
  
  • id: 1362711
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '27200.bc1', 'torsion': [3]}
  • id: 1362712
    {'degree': 3, 'field': [10, -6, -1, 1], 'lmfdb_label': '27200.bc1', 'torsion': [2]}
  • id: 1362715
    {'degree': 6, 'field': [-20, -40, -34, 12, 9, -2, 1], 'lmfdb_label': '27200.bc1', 'torsion': [6]}
  • id: 1362714
    {'degree': 6, 'field': [250, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '27200.bc1', 'torsion': [3]}
  • id: 1362713
    {'degree': 6, 'field': [270, -360, 171, -20, 2, 0, 1], 'lmfdb_label': '27200.bc1', 'torsion': [2, 2]}
  • id: 1362716
    {'degree': 12, 'field': [-880, 1520, -836, -432, 724, 212, -639, 380, -97, 4, 7, -4, 1], 'lmfdb_label': '27200.bc1', 'torsion': [4]}
  • id: 1362718
    {'degree': 12, 'field': [1225, -3150, 4525, -3690, 4466, -3942, 2757, -1470, 666, -210, 53, -6, 1], 'lmfdb_label': '27200.bc1', 'torsion': [2, 6]}
  • id: 1362717
    {'degree': 12, 'field': [63001, -1506, -3729, 9950, -3660, -1626, 641, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '27200.bc1', 'torsion': [3, 3]}
  • id: 1362719
    {'degree': 18, 'field': [-9242866000880, 2724116318400, -1053916909536, -254752488112, 57316592640, -2415947280, -3019448436, 539415528, 35741640, -6421196, 2838498, -229848, 14259, 4782, -903, -22, -60, 0, 1], 'lmfdb_label': '27200.bc1', 'torsion': [9]}
  • id: 1362720
    {'degree': 18, 'field': [64000, 0, 0, 0, 0, 0, 5284, 0, 0, 0, 0, 0, 116, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '27200.bc1', '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: 627568
    {'conductor': 27200, 'conductor_valuation': 6, 'discriminant_valuation': 25, 'j_denominator_valuation': 7, 'kodaira_symbol': -19, 'lmfdb_label': '27200.bc1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 627569
    {'conductor': 27200, 'conductor_valuation': 2, 'discriminant_valuation': 15, 'j_denominator_valuation': 9, 'kodaira_symbol': -13, 'lmfdb_label': '27200.bc1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 627570
    {'conductor': 27200, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '27200.bc1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1845370
    {'adelic_gens': [[4, 3, 9, 7], [2035, 6, 2034, 7], [1019, 2034, 1017, 2021], [1223, 2034, 1629, 2021], [241, 6, 723, 19], [1, 6, 0, 1], [3, 4, 8, 11], [938, 1107, 775, 1027], [1, 0, 6, 1], [1529, 2034, 507, 2021]], 'adelic_image': '2040.16.0.?', 'conductor': 27200, 'lmfdb_label': '27200.bc1', 'prime': 0}
  • id: 123039
    {'conductor': 27200, 'elladic_image': '3.4.0.1', 'lmfdb_label': '27200.bc1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1302150
    {'lmfdb_iso': '27200.bc', 'p': 7, 'prec': 20, 'unit': 4503505509880033, 'val': 1}
  • id: 1302154
    {'lmfdb_iso': '27200.bc', 'p': 13, 'prec': 20, 'unit': 31548605727219353238, 'val': 1}
  • id: 1302157
    {'lmfdb_iso': '27200.bc', 'p': 19, 'prec': 20, 'unit': 642375280007015810238205, 'val': 1}
  • id: 1302160
    {'lmfdb_iso': '27200.bc', 'p': 23, 'prec': 20, 'unit': 27872468917172539961465556, 'val': 1}
  • id: 1302153
    {'lmfdb_iso': '27200.bc', 'p': 29, 'prec': 20, 'unit': 4424543045984818411915231569, 'val': 1}
  • id: 1302165
    {'lmfdb_iso': '27200.bc', 'p': 31, 'prec': 20, 'unit': 4711194556090948737491500261, 'val': 1}
  • id: 1302149
    {'lmfdb_iso': '27200.bc', 'p': 37, 'prec': 20, 'unit': 525022336432321661929203887431, 'val': 1}
  • id: 1302151
    {'lmfdb_iso': '27200.bc', 'p': 41, 'prec': 20, 'unit': 797654570333201959407291190695, 'val': 1}
  • id: 1302152
    {'lmfdb_iso': '27200.bc', 'p': 43, 'prec': 20, 'unit': 2095416865060617609127731787901, 'val': 1}
  • id: 1302163
    {'lmfdb_iso': '27200.bc', 'p': 47, 'prec': 20, 'unit': 27380447760401071577568253345151, 'val': 1}
  • id: 1302158
    {'lmfdb_iso': '27200.bc', 'p': 53, 'prec': 20, 'unit': 216287937799951784346641859686333, 'val': 1}
  • id: 1302156
    {'lmfdb_iso': '27200.bc', 'p': 59, 'prec': 20, 'unit': 125756758829786740285742871631122, 'val': 1}
  • id: 1302164
    {'lmfdb_iso': '27200.bc', 'p': 61, 'prec': 20, 'unit': 1809880820580711504296212142680703, 'val': 1}
  • id: 1302148
    {'lmfdb_iso': '27200.bc', 'p': 67, 'prec': 20, 'unit': 3470873674740316460044546058583531, 'val': 1}
  • id: 1302162
    {'lmfdb_iso': '27200.bc', 'p': 71, 'prec': 20, 'unit': 95784975934883094220652605876196710, 'val': 1}
  • id: 1302159
    {'lmfdb_iso': '27200.bc', 'p': 73, 'prec': 20, 'unit': 227284622985717975519581092971549140, 'val': 1}
  • id: 1302155
    {'lmfdb_iso': '27200.bc', 'p': 79, 'prec': 20, 'unit': 889128225223411814479140457752436270, 'val': 1}
  • id: 1302147
    {'lmfdb_iso': '27200.bc', 'p': 83, 'prec': 20, 'unit': 229392475659824374067620112412070594, 'val': 1}
  • id: 1302161
    {'lmfdb_iso': '27200.bc', 'p': 89, 'prec': 20, 'unit': 9761375484296952061874469932251678082, 'val': 1}
  • id: 1302146
    {'lmfdb_iso': '27200.bc', 'p': 97, 'prec': 20, 'unit': 40530067977786663815175185661310571747, 'val': 1}