Elliptic curve data - 162.a1

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '162a', 'Clabel': '162a1', 'Cnumber': 1, 'absD': 2916, 'adelic_genus': 1, 'adelic_index': 128, 'adelic_level': 12, 'ainvs': [1, -1, 0, -6, 8], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 162, 'degree': 12, 'elladic_images': ['4.8.0.2', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.59780648594258934269379073216', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3], 'jinv': [-35937, 4], 'lmfdb_iso': '162.a', 'lmfdb_label': '162.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -6, 8], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.1'], 'modm_images': ['3.8.0-3.a.1.2', '4.8.0.b.1', '12.128.1-12.b.2.3'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 14, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.30593488386876331370037026683', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1471126302766441883914133506', 'prec': 103}, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, -1, 0, 1, -3, 0, -4, -1, 0, 3, 0, 0, -1, 4, 0, 1, -3, 0, -4, -3], 'aplist': [-1, 0, -3, -4, 0, -1, -3, -4, 0, 9, -4, -1, 6, 8, -12, -6, 0, -1, -4, -12, 11, -16, -12, -3, 2], 'class_deg': 3, 'class_size': 2, 'conductor': 162, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '162.a', 'trace_hash': 497496804025843963}
• 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': '3.3055833792932480348863218361', 'prec': 100}, 'conductor': 162, 'gens': [[4, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.30593488386876331370037026683', 'prec': 103}], 'lmfdb_label': '162.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '4.3954427628508688800304866220', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.89647951413638449139673303664113674186', 'prec': 133}, 'tamagawa_product': 6, 'torsion_generators': [[1, 1, 1]], 'xcoord_integral_points': [-2, -1, 1, 2, 4, 7, 46]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [3, 0]}, 'iwp0': 0, 'lmfdb_label': '162.a1'}
• ec_torsion_growth •

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

  
  
  • id: 6412
    {'degree': 3, 'field': [-4, -3, 0, 1], 'lmfdb_label': '162.a1', 'torsion': [6]}
  • id: 6416
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '162.a1', 'torsion': [3, 3]}
  • id: 6414
    {'degree': 6, 'field': [1, 0, 0, -4, 0, 0, 1], 'lmfdb_label': '162.a1', 'torsion': [12]}
  • id: 6413
    {'degree': 6, 'field': [2, 6, 9, -2, 0, 0, 1], 'lmfdb_label': '162.a1', 'torsion': [2, 6]}
  • id: 6415
    {'degree': 6, 'field': [4, 12, 9, -2, -3, 0, 1], 'lmfdb_label': '162.a1', 'torsion': [12]}
  • id: 6417
    {'degree': 9, 'field': [15, -27, 27, 9, -9, 18, 0, -9, 0, 1], 'lmfdb_label': '162.a1', 'torsion': [9]}
  • id: 6418
    {'degree': 12, 'field': [1, 0, 0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 1], 'lmfdb_label': '162.a1', 'torsion': [4, 12]}
  • id: 6419
    {'degree': 18, 'field': [1, -9, 39, -108, 228, -420, 696, -978, 1143, -1183, 1143, -978, 696, -420, 228, -108, 39, -9, 1], 'lmfdb_label': '162.a1', 'torsion': [3, 12]}
• 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: 1235
    {'conductor': 162, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '162.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1236
    {'conductor': 162, 'conductor_valuation': 4, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '162.a1', 'prime': 3, '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: 1666426
    {'adelic_gens': [[9, 4, 8, 5], [1, 9, 9, 10], [3, 4, 4, 3], [1, 9, 0, 7]], 'adelic_image': '12.128.1.?', 'conductor': 162, 'lmfdb_label': '162.a1', 'prime': 0}
  • id: 630
    {'conductor': 162, 'elladic_image': '4.8.0.2', 'lmfdb_label': '162.a1', 'modell_image': '2G', 'prime': 2}
  • id: 631
    {'conductor': 162, 'elladic_image': '3.8.0.1', 'lmfdb_label': '162.a1', 'modell_image': '3B.1.1', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1029
    {'lmfdb_iso': '162.a', 'p': 5, 'prec': 20, 'unit': 7359691041949, 'val': 1}
  • id: 1030
    {'lmfdb_iso': '162.a', 'p': 7, 'prec': 20, 'unit': 10417354695831170, 'val': 1}
  • id: 1035
    {'lmfdb_iso': '162.a', 'p': 13, 'prec': 20, 'unit': 63204785719709623500, 'val': 2}
  • id: 1037
    {'lmfdb_iso': '162.a', 'p': 17, 'prec': 20, 'unit': 207266402895884631294934, 'val': 1}
  • id: 1038
    {'lmfdb_iso': '162.a', 'p': 19, 'prec': 20, 'unit': 735035669031452910245827, 'val': 1}
  • id: 1034
    {'lmfdb_iso': '162.a', 'p': 29, 'prec': 20, 'unit': 4209565055598012563604430685, 'val': 1}
  • id: 1031
    {'lmfdb_iso': '162.a', 'p': 31, 'prec': 20, 'unit': 13708643636995872197364458285, 'val': 1}
  • id: 1045
    {'lmfdb_iso': '162.a', 'p': 37, 'prec': 20, 'unit': 583083582876908935739707672290, 'val': 1}
  • id: 1032
    {'lmfdb_iso': '162.a', 'p': 41, 'prec': 20, 'unit': 1545371234909654986948627458745, 'val': 1}
  • id: 1033
    {'lmfdb_iso': '162.a', 'p': 43, 'prec': 20, 'unit': 9044098034790986523732468088050, 'val': 1}
  • id: 1036
    {'lmfdb_iso': '162.a', 'p': 47, 'prec': 20, 'unit': 458162993069062608041324286049, 'val': 2}
  • id: 1039
    {'lmfdb_iso': '162.a', 'p': 53, 'prec': 20, 'unit': 166984491435342976541099256210776, 'val': 1}
  • id: 1044
    {'lmfdb_iso': '162.a', 'p': 61, 'prec': 20, 'unit': 4705966135341803988774890149823613, 'val': 1}
  • id: 1028
    {'lmfdb_iso': '162.a', 'p': 67, 'prec': 20, 'unit': 44295070278955385668450300601185647, 'val': 1}
  • id: 1042
    {'lmfdb_iso': '162.a', 'p': 71, 'prec': 20, 'unit': 66467368886995430891863570411358020, 'val': 1}
  • id: 1040
    {'lmfdb_iso': '162.a', 'p': 73, 'prec': 20, 'unit': 170773938302802929283491893300008803, 'val': 1}
  • id: 1043
    {'lmfdb_iso': '162.a', 'p': 79, 'prec': 20, 'unit': 29332805633130999471955413663607505, 'val': 1}
  • id: 1027
    {'lmfdb_iso': '162.a', 'p': 83, 'prec': 20, 'unit': 890224179490503049969033461774865639, 'val': 1}
  • id: 1041
    {'lmfdb_iso': '162.a', 'p': 89, 'prec': 20, 'unit': 8642827118179193299618177527883453234, 'val': 1}
  • id: 1026
    {'lmfdb_iso': '162.a', 'p': 97, 'prec': 20, 'unit': 38912069988480442196698756568818633027, 'val': 1}