Elliptic curve data - 69678.bs1

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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': '69678bs', 'Clabel': '69678bs3', 'Cnumber': 3, 'abc_quality': 1.0014551545932482, 'absD': 1776162847850496, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 19908, 'ainvs': [1, -1, 1, -2300486, -1342427691], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 79], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 69678, 'degree': 1360800, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2021192882434968127235193026', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 44, 'isogeny_degrees': [1, 3, 9], 'jinv': [15698803397448457, 20709376], 'lmfdb_iso': '69678.bs', 'lmfdb_label': '69678.bs1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5217, -145452], 'min_quad_twist_disc': 21, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '21.8.0-3.a.1.1', '63.24.0-9.a.1.1', '316.2.0.?', '711.36.0.?', '948.8.0.?', '2844.72.3.?', '4977.72.0.?', '6636.16.0.?', '19908.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.6343051536324402166349861135', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 34839], [3, 6, 3871], [7, 26, 1422], [79, 80, 882]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.67985806938178531447322031242', 'prec': 103}, 'szpiro_ratio': 4.982181631578665, '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, 1, 0, 1, 3, 0, 0, 1, 0, 3, 0, 0, -5, 0, 0, 1, 0, 0, -2, 3], 'aplist': [1, 0, 3, 0, 0, -5, 0, -2, 6, 0, 4, 2, -12, 8, -9, -6, -9, -8, -4, 9, -2, 1, 18, 9, -17], 'class_deg': 9, 'class_size': 3, 'conductor': 69678, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '69678.bs', 'trace_hash': 738456993371668309}
• 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': '0.012225411587644138531055545496', 'prec': 107}, 'conductor': 69678, 'gens': [[-21879, 59191, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '5.6343051536324402166349861135', 'prec': 100}], 'lmfdb_label': '69678.bs1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12258708135031076749215768036', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.432474435974672802929222040537194160', 'prec': 130}, 'tamagawa_product': 18, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [5, 1, 0], '19': [3, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0], '79': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '69678.bs1'}
• ec_torsion_growth •

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

  
  
  • id: 3311331
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '69678.bs1', 'torsion': [3]}
  • id: 3311332
    {'degree': 3, 'field': [2, -4, -1, 1], 'lmfdb_label': '69678.bs1', 'torsion': [2]}
  • id: 3311333
    {'degree': 6, 'field': [8, -8, -34, 54, -17, -2, 1], 'lmfdb_label': '69678.bs1', 'torsion': [2, 2]}
  • id: 3311336
    {'degree': 6, 'field': [64, 2, 28, 1, -3, -1, 1], 'lmfdb_label': '69678.bs1', 'torsion': [6]}
  • id: 3311334
    {'degree': 6, 'field': [7380, -2682, 297, -129, -12, -3, 1], 'lmfdb_label': '69678.bs1', 'torsion': [3]}
  • id: 3311335
    {'degree': 6, 'field': [137152, 96684, 56424, 303, -465, -3, 1], 'lmfdb_label': '69678.bs1', 'torsion': [9]}
  • id: 3311339
    {'degree': 12, 'field': [5404, 8652, 11013, 2357, 1380, -837, 1055, -408, 51, 7, 0, -3, 1], 'lmfdb_label': '69678.bs1', 'torsion': [9]}
  • id: 3311340
    {'degree': 12, 'field': [116048, 480, -2924, 4816, -2064, -892, 1157, -862, 379, -120, 35, -6, 1], 'lmfdb_label': '69678.bs1', 'torsion': [2, 6]}
  • id: 3311337
    {'degree': 12, 'field': [26920324, 10628033, -2920295, -1005758, 110846, -37139, -8751, 3973, -287, -2, 34, -3, 1], 'lmfdb_label': '69678.bs1', 'torsion': [4]}
  • id: 3311338
    {'degree': 12, 'field': [34269316, 4091946, -1004169, 2180313, 131868, -73749, 40751, 690, -687, 315, 0, -3, 1], 'lmfdb_label': '69678.bs1', 'torsion': [3, 3]}
  • id: 3311341
    {'degree': 18, 'field': [56783674432, -392976688560, 200021376372, -39667052252, 23042997060, -5073514596, 1066477701, -350498703, 41023221, -9371916, 1522377, -334119, 43892, 5619, 3045, -286, -69, -3, 1], 'lmfdb_label': '69678.bs1', 'torsion': [6]}
  • id: 3311342
    {'degree': 18, 'field': [4021085863936, 8595850543104, 9183109401600, 5797665555712, 2034413940288, 224932172208, -102727801808, -40253540568, -2094160692, 1419179555, 237244221, -16784976, -6149376, -37218, 73770, 1984, -420, -9, 1], 'lmfdb_label': '69678.bs1', 'torsion': [18]}
• 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: 1687122
    {'conductor': 69678, 'conductor_valuation': 1, 'discriminant_valuation': 18, 'j_denominator_valuation': 18, 'kodaira_symbol': 22, 'lmfdb_label': '69678.bs1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 18}
  • id: 1687123
    {'conductor': 69678, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '69678.bs1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1687124
    {'conductor': 69678, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '69678.bs1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1687125
    {'conductor': 69678, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '69678.bs1', 'prime': 79, '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: 2124880
    {'adelic_gens': [[9953, 5670, 0, 1105], [1, 18, 0, 1], [17063, 0, 0, 19907], [1, 0, 18, 1], [10, 9, 81, 73], [9955, 14238, 7119, 8695], [16927, 14238, 18081, 16717], [19891, 18, 19890, 19], [1, 18, 10, 181]], 'adelic_image': '19908.144.3.?', 'conductor': 69678, 'lmfdb_label': '69678.bs1', 'prime': 0}
  • id: 290443
    {'conductor': 69678, 'elladic_image': '9.12.0.1', 'lmfdb_label': '69678.bs1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 3567643
    {'lmfdb_iso': '69678.bs', 'p': 5, 'prec': 20, 'unit': 8600254910324, 'val': 1}
  • id: 3567634
    {'lmfdb_iso': '69678.bs', 'p': 13, 'prec': 20, 'unit': 1018016019543085472696, 'val': 1}
  • id: 3567626
    {'lmfdb_iso': '69678.bs', 'p': 19, 'prec': 20, 'unit': 88270422510231399021201, 'val': 2}
  • id: 3567639
    {'lmfdb_iso': '69678.bs', 'p': 23, 'prec': 20, 'unit': 11721387294914638370299991, 'val': 1}
  • id: 3567631
    {'lmfdb_iso': '69678.bs', 'p': 31, 'prec': 20, 'unit': 20709694546922961308854323057, 'val': 1}
  • id: 3567629
    {'lmfdb_iso': '69678.bs', 'p': 37, 'prec': 20, 'unit': 472750476121826149249770862101, 'val': 1}
  • id: 3567632
    {'lmfdb_iso': '69678.bs', 'p': 41, 'prec': 20, 'unit': 1114331261960000341002956016579, 'val': 1}
  • id: 3567633
    {'lmfdb_iso': '69678.bs', 'p': 43, 'prec': 20, 'unit': 2445086237634454351208067745547, 'val': 1}
  • id: 3567635
    {'lmfdb_iso': '69678.bs', 'p': 47, 'prec': 20, 'unit': 29958662900004880150113750951528, 'val': 1}
  • id: 3567637
    {'lmfdb_iso': '69678.bs', 'p': 53, 'prec': 20, 'unit': 378403779530753653606351825794893, 'val': 1}
  • id: 3567641
    {'lmfdb_iso': '69678.bs', 'p': 59, 'prec': 20, 'unit': 2803351471489827876284398049325673, 'val': 1}
  • id: 3567642
    {'lmfdb_iso': '69678.bs', 'p': 61, 'prec': 20, 'unit': 218602851041018128216035771898206, 'val': 1}
  • id: 3567628
    {'lmfdb_iso': '69678.bs', 'p': 67, 'prec': 20, 'unit': 19282058593960319777424785700750597, 'val': 1}
  • id: 3567630
    {'lmfdb_iso': '69678.bs', 'p': 71, 'prec': 20, 'unit': 46132435851607925631411481471411127, 'val': 1}
  • id: 3567638
    {'lmfdb_iso': '69678.bs', 'p': 73, 'prec': 20, 'unit': 80524591801832786706888719918081308, 'val': 1}
  • id: 3567636
    {'lmfdb_iso': '69678.bs', 'p': 83, 'prec': 20, 'unit': 2696886731103639339204721736135352536, 'val': 1}
  • id: 3567640
    {'lmfdb_iso': '69678.bs', 'p': 89, 'prec': 20, 'unit': 169445592367927407941004276790828320, 'val': 1}
  • id: 3567627
    {'lmfdb_iso': '69678.bs', 'p': 97, 'prec': 20, 'unit': 33971176187183709875751660415320642865, 'val': 1}