Elliptic curve data - 27225.bb1

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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': '27225bf', 'Clabel': '27225bf2', 'Cnumber': 2, 'abc_quality': 1.0696334828816438, 'absD': 1030084437188232421875, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 30, 'ainvs': [0, 0, 1, -163114050, 801836784031], 'analytic_rank': 1, 'bad_primes': [3, 5, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 27225, 'degree': 2737152, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2794978489339097292315038343', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 27, 'isogeny_degrees': [1, 3], 'jinv': [-196566176333824, 421875], 'lmfdb_iso': '27225.bb', 'lmfdb_label': '27225.bb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -5991, 176501], 'min_quad_twist_disc': 165, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0.b.1', '15.8.0-3.a.1.2', '30.16.0-6.b.1.2'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3133136830354244883644656628', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 6, 3025], [5, 18, 1089], [11, 52, 225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.32687589985055766685887249725', 'prec': 103}, 'szpiro_ratio': 6.692539874621497, '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, -2, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 4, 6, 0, -7, 0], 'aplist': [0, 0, 0, 1, 0, -2, 6, -7, -6, 0, -1, 7, 6, -8, 0, -6, 12, -1, 7, -6, 13, 11, 0, 18, 1], 'class_deg': 3, 'class_size': 2, 'conductor': 27225, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '27225.bb', 'trace_hash': 1032781245800729501}
• 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': '0.0014173084016710133244706334123', 'prec': 110}, 'conductor': 27225, 'gens': [[7381, 1633, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3133136830354244883644656628', 'prec': 100}], 'lmfdb_label': '27225.bb1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.13419851093383832733024729253', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2298737756573335179620240699873893321', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': [-4961, 7381]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': 'a', '5': 'a', '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '27225.bb1'}
• ec_torsion_growth •

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

  
  
  • id: 1364278
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '27225.bb1', 'torsion': [3]}
  • id: 1364279
    {'degree': 3, 'field': [13, -7, -1, 1], 'lmfdb_label': '27225.bb1', 'torsion': [2]}
  • id: 1364282
    {'degree': 6, 'field': [55, 55, 66, -9, -18, -1, 1], 'lmfdb_label': '27225.bb1', 'torsion': [6]}
  • id: 1364280
    {'degree': 6, 'field': [75, 0, -29, 0, 1, 0, 1], 'lmfdb_label': '27225.bb1', 'torsion': [2, 2]}
  • id: 1364281
    {'degree': 6, 'field': [306, -279, 27, -3, 15, -3, 1], 'lmfdb_label': '27225.bb1', 'torsion': [3]}
  • id: 1364283
    {'degree': 12, 'field': [-24300, 0, -3160, 0, 8844, 0, -2888, 0, 440, 0, -36, 0, 1], 'lmfdb_label': '27225.bb1', 'torsion': [4]}
  • id: 1364285
    {'degree': 12, 'field': [8464, -9936, 3152, 864, -1152, 108, -185, 213, 12, -15, 8, -3, 1], 'lmfdb_label': '27225.bb1', 'torsion': [2, 6]}
  • id: 1364284
    {'degree': 12, 'field': [26896, -16728, 4992, 2210, -645, -1053, 311, 96, -84, 34, 9, -3, 1], 'lmfdb_label': '27225.bb1', 'torsion': [3, 3]}
  • id: 1364286
    {'degree': 18, 'field': [-16605, 108540, -90315, -408960, 610470, -365310, -1356464, -795030, -235179, 44150, -20880, -5220, 690, -630, -225, -10, 6, 0, 1], 'lmfdb_label': '27225.bb1', 'torsion': [9]}
  • id: 1364287
    {'degree': 18, 'field': [13824, 0, 0, -53568, 0, 0, 63880, 0, 0, -6777, 0, 0, 557, 0, 0, -27, 0, 0, 1], 'lmfdb_label': '27225.bb1', '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: 628302
    {'conductor': 27225, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '27225.bb1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 628303
    {'conductor': 27225, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '27225.bb1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 628304
    {'conductor': 27225, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '27225.bb1', 'prime': 11, 'reduction_type': 0, '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: 1845659
    {'adelic_gens': [[9, 10, 20, 29], [1, 0, 6, 1], [4, 3, 9, 7], [25, 6, 24, 7], [3, 4, 8, 11], [23, 0, 0, 29], [4, 15, 5, 14], [1, 6, 0, 1]], 'adelic_image': '30.16.0.?', 'conductor': 27225, 'lmfdb_label': '27225.bb1', 'prime': 0}
  • id: 123218
    {'conductor': 27225, 'elladic_image': '3.4.0.1', 'lmfdb_label': '27225.bb1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1304022
    {'lmfdb_iso': '27225.bb', 'p': 7, 'prec': 20, 'unit': 48097539557624349, 'val': -1}
  • id: 1304025
    {'lmfdb_iso': '27225.bb', 'p': 13, 'prec': 20, 'unit': 286598104509281492495, 'val': 1}
  • id: 1304027
    {'lmfdb_iso': '27225.bb', 'p': 17, 'prec': 20, 'unit': 34354664268611186546745, 'val': 1}
  • id: 1304028
    {'lmfdb_iso': '27225.bb', 'p': 19, 'prec': 20, 'unit': 1782489781292410253820643, 'val': 1}
  • id: 1304031
    {'lmfdb_iso': '27225.bb', 'p': 23, 'prec': 20, 'unit': 1904940257383382380900320, 'val': 1}
  • id: 1304036
    {'lmfdb_iso': '27225.bb', 'p': 31, 'prec': 20, 'unit': 16073290816255020509750489228, 'val': 1}
  • id: 1304021
    {'lmfdb_iso': '27225.bb', 'p': 37, 'prec': 20, 'unit': 557320379431834862671703604975, 'val': 1}
  • id: 1304023
    {'lmfdb_iso': '27225.bb', 'p': 41, 'prec': 20, 'unit': 985984335956560228136320365251, 'val': 1}
  • id: 1304024
    {'lmfdb_iso': '27225.bb', 'p': 43, 'prec': 20, 'unit': 4668053745132965469582456617067, 'val': 1}
  • id: 1304029
    {'lmfdb_iso': '27225.bb', 'p': 53, 'prec': 20, 'unit': 360617018744863181151721676753003, 'val': 1}
  • id: 1304034
    {'lmfdb_iso': '27225.bb', 'p': 59, 'prec': 20, 'unit': 2255898666536375924691371117768993, 'val': 1}
  • id: 1304035
    {'lmfdb_iso': '27225.bb', 'p': 61, 'prec': 20, 'unit': 8331317619717104776484168875953496, 'val': 1}
  • id: 1304020
    {'lmfdb_iso': '27225.bb', 'p': 67, 'prec': 20, 'unit': 8017707433527544057808712952446344, 'val': 1}
  • id: 1304033
    {'lmfdb_iso': '27225.bb', 'p': 71, 'prec': 20, 'unit': 82254878384517779323926118701731299, 'val': 1}
  • id: 1304030
    {'lmfdb_iso': '27225.bb', 'p': 73, 'prec': 20, 'unit': 67900240814980070466330782182196757, 'val': 1}
  • id: 1304026
    {'lmfdb_iso': '27225.bb', 'p': 79, 'prec': 20, 'unit': 384844754676250311773636837263167851, 'val': 1}
  • id: 1304032
    {'lmfdb_iso': '27225.bb', 'p': 89, 'prec': 20, 'unit': 4804345290753841326378081401597116439, 'val': 1}
  • id: 1304019
    {'lmfdb_iso': '27225.bb', 'p': 97, 'prec': 20, 'unit': 587766698815671825537844113380085275911, 'val': -1}