Elliptic curve data - 27200.z1

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

  
  {'Ciso': '27200f', 'Clabel': '27200f1', 'Cnumber': 1, 'abc_quality': 0.7662665989164665, 'absD': 111411200, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 68, 'ainvs': [0, -1, 0, -193, 1217], 'analytic_rank': 1, 'bad_primes': [2, 5, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 27200, 'degree': 6144, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.27552853259012763251761700735', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1], 'jinv': [-121945, 17], 'lmfdb_iso': '27200.z', 'lmfdb_label': '27200.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3, 2], 'min_quad_twist_disc': 8, 'modell_images': [], 'modm_images': ['68.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.58405893151828595967658027006', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0324318903221403940416910637', 'prec': 103}, 'szpiro_ratio': 2.705196241817737, '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, -1, 0, -2, 0, 4, 0, -1, 0, 0, 0, -1, 0, 6, 0], 'aplist': [0, -1, 0, -1, 4, -1, -1, 6, 0, 0, -7, -4, -2, 4, 6, 11, -8, -10, 8, 7, -4, -11, -8, -6, 16], 'class_deg': 1, 'class_size': 1, 'conductor': 27200, 'isogeny_matrix': [[1]], 'lmfdb_iso': '27200.z', 'trace_hash': 1484981071174840800}
• 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': '0.57634025904968100792897238375', 'prec': 103}, 'conductor': 27200, 'gens': [[1, 32, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.58405893151828595967658027006', 'prec': 103}], 'lmfdb_label': '27200.z1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.8145333434376891771961693036', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2391776230900790448488830889288150768', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [1, 8]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [7, 0], '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '27200.z1'}
• ec_torsion_growth •

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

  
  
  • id: 1361966
    {'degree': 3, 'field': [-8, 12, -1, 1], 'lmfdb_label': '27200.z1', 'torsion': [2]}
  • id: 1361967
    {'degree': 6, 'field': [17, 0, 47, 0, -1, 0, 1], 'lmfdb_label': '27200.z1', 'torsion': [2, 2]}
  • id: 1361968
    {'degree': 8, 'field': [-10800, 0, -2120, 0, -360, 0, 0, 0, 1], 'lmfdb_label': '27200.z1', 'torsion': [3]}
  • id: 1361969
    {'degree': 12, 'field': [-4714, -1976, -4439, -1490, -95, -496, 401, 34, 35, 60, -9, -6, 1], 'lmfdb_label': '27200.z1', 'torsion': [4]}
• 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: 627292
    {'conductor': 27200, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '27200.z1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 627293
    {'conductor': 27200, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '27200.z1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 627294
    {'conductor': 27200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27200.z1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  {'adelic_gens': [[1, 2, 0, 1], [1, 0, 2, 1], [35, 2, 35, 3], [1, 1, 67, 0], [67, 2, 66, 3], [37, 2, 37, 3]], 'adelic_image': '68.2.0.?', 'conductor': 27200, 'lmfdb_label': '27200.z1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 1301633
    {'lmfdb_iso': '27200.z', 'p': 7, 'prec': 20, 'unit': 5066963735849381, 'val': 1}
  • id: 1301638
    {'lmfdb_iso': '27200.z', 'p': 11, 'prec': 20, 'unit': 18881239800591161852, 'val': 1}
  • id: 1301636
    {'lmfdb_iso': '27200.z', 'p': 13, 'prec': 20, 'unit': 1050397990900655359088, 'val': 1}
  • id: 1301640
    {'lmfdb_iso': '27200.z', 'p': 19, 'prec': 20, 'unit': 768749813387925949002984, 'val': 1}
  • id: 1301647
    {'lmfdb_iso': '27200.z', 'p': 31, 'prec': 20, 'unit': 14405066909943224017261023472, 'val': 1}
  • id: 1301632
    {'lmfdb_iso': '27200.z', 'p': 37, 'prec': 20, 'unit': 372349169244599107681688776050, 'val': 1}
  • id: 1301634
    {'lmfdb_iso': '27200.z', 'p': 41, 'prec': 20, 'unit': 912678660805805109047788305658, 'val': 1}
  • id: 1301635
    {'lmfdb_iso': '27200.z', 'p': 43, 'prec': 20, 'unit': 3283971019564448218854491134867, 'val': 1}
  • id: 1301645
    {'lmfdb_iso': '27200.z', 'p': 47, 'prec': 20, 'unit': 18996306567698860173714407594216, 'val': 1}
  • id: 1301641
    {'lmfdb_iso': '27200.z', 'p': 53, 'prec': 20, 'unit': 232201763661613953488923076570656, 'val': 1}
  • id: 1301639
    {'lmfdb_iso': '27200.z', 'p': 59, 'prec': 20, 'unit': 2604125285624339814122423334173302, 'val': 1}
  • id: 1301646
    {'lmfdb_iso': '27200.z', 'p': 61, 'prec': 20, 'unit': 5598754321256852232283335396855449, 'val': 1}
  • id: 1301631
    {'lmfdb_iso': '27200.z', 'p': 67, 'prec': 20, 'unit': 42726294941051414735644213898554650, 'val': 1}
  • id: 1301644
    {'lmfdb_iso': '27200.z', 'p': 71, 'prec': 20, 'unit': 122678248828992361962530557110111643, 'val': 1}
  • id: 1301642
    {'lmfdb_iso': '27200.z', 'p': 73, 'prec': 20, 'unit': 190629232009464170990226765626714482, 'val': 1}
  • id: 1301637
    {'lmfdb_iso': '27200.z', 'p': 79, 'prec': 20, 'unit': 739936902421520789297387789729003841, 'val': 1}
  • id: 1301630
    {'lmfdb_iso': '27200.z', 'p': 83, 'prec': 20, 'unit': 1476386899588631284617074998735551684, 'val': 1}
  • id: 1301643
    {'lmfdb_iso': '27200.z', 'p': 89, 'prec': 20, 'unit': 3983636309689615145033311312043651456, 'val': 1}
  • id: 1301629
    {'lmfdb_iso': '27200.z', 'p': 97, 'prec': 20, 'unit': 24456153228528552677305581521930757472, 'val': 1}