Elliptic curve data - 72128.ca2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '72128r', 'Clabel': '72128r1', 'Cnumber': 1, 'abc_quality': 0.918589473035692, 'absD': 60826121732096, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1288, 'ainvs': [0, -1, 0, -515937, -142468255], 'analytic_rank': 1, 'bad_primes': [2, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 72128, 'degree': 368640, 'elladic_images': ['8.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8563179583469687708284777424', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 52, 'isogeny_degrees': [1, 2], 'jinv': [1969910093092, 7889], 'lmfdb_iso': '72128.ca', 'lmfdb_label': '72128.ca2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -2632, 52860], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.c.1', '322.6.0.?', '1288.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '16.141322734750871362150243245', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1127], [7, 32, 1472], [23, 24, 3136]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.040833356927281627613841457933', 'prec': 110}, 'szpiro_ratio': 4.565879009215557, '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, 2, 0, 2, 0, 0, 0, 1, 0, -2, 0, 4, 0, 4, 0, 2, 0, 0, 0], 'aplist': [0, 2, 2, 0, -2, 4, 2, 0, 1, 2, 0, 4, -6, -2, -4, 0, 2, -10, -2, -8, 6, 0, 0, -10, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 72128, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '72128.ca', 'trace_hash': 140286894980575999}
• 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': '0.024413087520379510393011618705', 'prec': 107}, 'conductor': 72128, 'gens': [[397046809, 7906180254560, 141]], 'heights': [{'__RealLiteral__': 0, 'data': '16.141322734750871362150243245', 'prec': 100}], 'lmfdb_label': '72128.ca2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.17813547672501958536571397645', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.501368881308973311658604478783231955', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-415, 0, 1]], 'xcoord_integral_points': [-415]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [4, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '72128.ca2'}
• ec_torsion_growth •

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

  
  
  • id: 3419320
    {'degree': 2, 'field': [-40, -1, 1], 'lmfdb_label': '72128.ca2', 'torsion': [2, 2]}
  • id: 3419321
    {'degree': 4, 'field': [14, -4, 7, -2, 1], 'lmfdb_label': '72128.ca2', 'torsion': [4]}
  • id: 3419324
    {'degree': 8, 'field': [-28812, 0, -2744, 0, 0, 0, 42, 0, 1], 'lmfdb_label': '72128.ca2', 'torsion': [6]}
  • id: 3419323
    {'degree': 8, 'field': [1024, 0, -712, 0, 145, 0, 18, 0, 1], 'lmfdb_label': '72128.ca2', 'torsion': [2, 4]}
  • id: 3419322
    {'degree': 8, 'field': [102400, 0, -41912, 0, -3047, 0, -26, 0, 1], 'lmfdb_label': '72128.ca2', 'torsion': [2, 4]}
  • id: 3419326
    {'degree': 16, 'field': [144, 0, -4871136, 0, -997400, 0, -56592, 0, -81507, 0, -16858, 0, -990, 0, 0, 0, 1], 'lmfdb_label': '72128.ca2', 'torsion': [2, 6]}
  • id: 3419325
    {'degree': 16, 'field': [120467088, -323616384, 296507232, -87099264, -20534920, 18823840, -3282776, -1602048, 668689, 76496, -22644, 2688, 1484, -16, -28, 0, 1], 'lmfdb_label': '72128.ca2', 'torsion': [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: 1748311
    {'conductor': 72128, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '72128.ca2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1748312
    {'conductor': 72128, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '72128.ca2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1748313
    {'conductor': 72128, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '72128.ca2', 'prime': 23, '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

  
  
  • id: 2140736
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [370, 1, 1103, 0], [1285, 4, 1284, 5], [1129, 162, 160, 1127], [645, 4, 2, 9], [562, 1, 1007, 0]], 'adelic_image': '1288.12.0.?', 'conductor': 72128, 'lmfdb_label': '72128.ca2', 'prime': 0}
  • id: 299495
    {'conductor': 72128, 'elladic_image': '8.6.0.1', 'lmfdb_label': '72128.ca2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3700713
    {'lmfdb_iso': '72128.ca', 'p': 5, 'prec': 20, 'unit': 5120698146177, 'val': 1}
  • id: 3700699
    {'lmfdb_iso': '72128.ca', 'p': 11, 'prec': 20, 'unit': 21998478166814989181, 'val': 1}
  • id: 3700705
    {'lmfdb_iso': '72128.ca', 'p': 13, 'prec': 20, 'unit': 346324253892075207209, 'val': 1}
  • id: 3700707
    {'lmfdb_iso': '72128.ca', 'p': 17, 'prec': 20, 'unit': 121416506690432131277973, 'val': 1}
  • id: 3700704
    {'lmfdb_iso': '72128.ca', 'p': 29, 'prec': 20, 'unit': 4726140598109531615930314400, 'val': 1}
  • id: 3700700
    {'lmfdb_iso': '72128.ca', 'p': 37, 'prec': 20, 'unit': 198122589069395451251892547400, 'val': 1}
  • id: 3700702
    {'lmfdb_iso': '72128.ca', 'p': 41, 'prec': 20, 'unit': 2855466757978488026911494067285, 'val': 1}
  • id: 3700703
    {'lmfdb_iso': '72128.ca', 'p': 43, 'prec': 20, 'unit': 2113371979248532060846391090476, 'val': 1}
  • id: 3700706
    {'lmfdb_iso': '72128.ca', 'p': 47, 'prec': 20, 'unit': 38611511768720627612031595777884, 'val': 1}
  • id: 3700711
    {'lmfdb_iso': '72128.ca', 'p': 59, 'prec': 20, 'unit': 3050200052776162603025876350395390, 'val': 1}
  • id: 3700712
    {'lmfdb_iso': '72128.ca', 'p': 61, 'prec': 20, 'unit': 7519816206855843549297075620585824, 'val': 1}
  • id: 3700708
    {'lmfdb_iso': '72128.ca', 'p': 67, 'prec': 20, 'unit': 17162533624219523163018571287536713, 'val': 1}
  • id: 3700701
    {'lmfdb_iso': '72128.ca', 'p': 71, 'prec': 20, 'unit': 148857818141552328082341955781483344, 'val': 1}
  • id: 3700709
    {'lmfdb_iso': '72128.ca', 'p': 73, 'prec': 20, 'unit': 187699362409028956614158807852926301, 'val': 1}
  • id: 3700710
    {'lmfdb_iso': '72128.ca', 'p': 89, 'prec': 20, 'unit': 1262133524897728503723429247520041603, 'val': 1}
  • id: 3700698
    {'lmfdb_iso': '72128.ca', 'p': 97, 'prec': 20, 'unit': 52871676235575221981313113551026499125, 'val': 1}