Elliptic curve data - 69696.gu1

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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': '69696eu', 'Clabel': '69696eu2', 'Cnumber': 2, 'abc_quality': 0.9412039603715836, 'absD': 1517208151523328, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 132, 'ainvs': [0, 0, 0, -129228, 17782160], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 69696, 'degree': 491520, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7499778335446835457521958315', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 176, 'isogeny_degrees': [1, 2], 'jinv': [19034163, 121], 'lmfdb_iso': '69696.gu', 'lmfdb_label': '69696.gu1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -17, 30], 'min_quad_twist_disc': 88, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '44.6.0.e.1', '132.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.1366567475934473165118095602', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.76334364586144711325343544890', 'prec': 107}, 'szpiro_ratio': 4.207499284883902, '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, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 6, 0], 'aplist': [0, 0, 4, -2, 0, -2, -2, 6, -4, -6, -4, 6, 10, -6, 8, 0, 4, -6, 8, 0, 2, -10, -12, 0, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 69696, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '69696.gu', 'trace_hash': 1957520720511151148}
• 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': '0.030198722189894622445010359316', 'prec': 107}, 'conductor': 69696, 'gens': [[770, 19360, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.1366567475934473165118095602', 'prec': 100}], 'lmfdb_label': '69696.gu1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.47953668895629193478746639926', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.1968424174166504943631507590124200298', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[220, 0, 1]], 'xcoord_integral_points': [220, 770]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 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': '69696.gu1'}
• ec_torsion_growth •

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

  
  
  • id: 3314789
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '69696.gu1', 'torsion': [2, 2]}
  • id: 3314790
    {'degree': 4, 'field': [48, 0, -18, 0, 1], 'lmfdb_label': '69696.gu1', 'torsion': [4]}
  • id: 3314793
    {'degree': 8, 'field': [-5808, 0, 792, 0, 132, 0, 22, 0, 1], 'lmfdb_label': '69696.gu1', 'torsion': [6]}
  • id: 3314791
    {'degree': 8, 'field': [4, 0, 472, 0, 156, 0, 16, 0, 1], 'lmfdb_label': '69696.gu1', 'torsion': [2, 4]}
  • id: 3314792
    {'degree': 8, 'field': [36, 0, -252, 0, 165, 0, -24, 0, 1], 'lmfdb_label': '69696.gu1', 'torsion': [2, 4]}
  • id: 3314794
    {'degree': 16, 'field': [1024, 0, -10874, 0, 19493, 0, -15866, 0, 7252, 0, -1984, 0, 320, 0, -28, 0, 1], 'lmfdb_label': '69696.gu1', 'torsion': [8]}
  • id: 3314795
    {'degree': 16, 'field': [131769, 0, -143748, 0, -157905, 0, -194568, 0, -54087, 0, 6600, 0, 583, 0, 44, 0, 1], 'lmfdb_label': '69696.gu1', 'torsion': [2, 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: 1688573
    {'conductor': 69696, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '69696.gu1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1688574
    {'conductor': 69696, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '69696.gu1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1688575
    {'conductor': 69696, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '69696.gu1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2125367
    {'adelic_gens': [[1, 2, 2, 5], [92, 1, 43, 0], [3, 4, 8, 11], [100, 37, 33, 100], [1, 4, 0, 1], [13, 4, 26, 9], [1, 0, 4, 1], [129, 4, 128, 5]], 'adelic_image': '132.12.0.?', 'conductor': 69696, 'lmfdb_label': '69696.gu1', 'prime': 0}
  • id: 290893
    {'conductor': 69696, 'elladic_image': '2.3.0.1', 'lmfdb_label': '69696.gu1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3570804
    {'lmfdb_iso': '69696.gu', 'p': 5, 'prec': 20, 'unit': 1945344317193, 'val': 1}
  • id: 3570805
    {'lmfdb_iso': '69696.gu', 'p': 7, 'prec': 20, 'unit': 4082304960403318, 'val': 1}
  • id: 3570810
    {'lmfdb_iso': '69696.gu', 'p': 13, 'prec': 20, 'unit': 494527990777238693612, 'val': 1}
  • id: 3570812
    {'lmfdb_iso': '69696.gu', 'p': 17, 'prec': 20, 'unit': 53054936235495367395177, 'val': 1}
  • id: 3570813
    {'lmfdb_iso': '69696.gu', 'p': 19, 'prec': 20, 'unit': 24415491996113951644136, 'val': 1}
  • id: 3570816
    {'lmfdb_iso': '69696.gu', 'p': 23, 'prec': 20, 'unit': 48231120820404933655833053, 'val': 1}
  • id: 3570809
    {'lmfdb_iso': '69696.gu', 'p': 29, 'prec': 20, 'unit': 2432770155198546326278741593, 'val': 1}
  • id: 3570806
    {'lmfdb_iso': '69696.gu', 'p': 31, 'prec': 20, 'unit': 3471382499704096109093417255, 'val': 1}
  • id: 3570819
    {'lmfdb_iso': '69696.gu', 'p': 37, 'prec': 20, 'unit': 300905779746164662346782053661, 'val': 1}
  • id: 3570807
    {'lmfdb_iso': '69696.gu', 'p': 41, 'prec': 20, 'unit': 322651802898756659811321918890, 'val': 1}
  • id: 3570808
    {'lmfdb_iso': '69696.gu', 'p': 43, 'prec': 20, 'unit': 1238124429656102847573595502159, 'val': 1}
  • id: 3570817
    {'lmfdb_iso': '69696.gu', 'p': 47, 'prec': 20, 'unit': 38614653441634361447208631291685, 'val': 1}
  • id: 3570814
    {'lmfdb_iso': '69696.gu', 'p': 59, 'prec': 20, 'unit': 2341154074365548328522809868471959, 'val': 1}
  • id: 3570818
    {'lmfdb_iso': '69696.gu', 'p': 61, 'prec': 20, 'unit': 4158718415967452371161981121423386, 'val': 1}
  • id: 3570803
    {'lmfdb_iso': '69696.gu', 'p': 67, 'prec': 20, 'unit': 28377487454796249073874494628497390, 'val': 1}
  • id: 3570815
    {'lmfdb_iso': '69696.gu', 'p': 73, 'prec': 20, 'unit': 12775206305880733659688589218990484, 'val': 1}
  • id: 3570811
    {'lmfdb_iso': '69696.gu', 'p': 79, 'prec': 20, 'unit': 175926662668703366861729010337453318, 'val': 1}
  • id: 3570802
    {'lmfdb_iso': '69696.gu', 'p': 83, 'prec': 20, 'unit': 1567630182960497658613742925096024431, 'val': 1}
  • id: 3570801
    {'lmfdb_iso': '69696.gu', 'p': 97, 'prec': 20, 'unit': 41122675026426555856603255543113213574, 'val': 1}