Elliptic curve data - 43688.a1

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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': '43688a', 'Clabel': '43688a1', 'Cnumber': 1, 'abc_quality': 0.6975840178544935, 'absD': 1398016, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 10922, 'ainvs': [0, 0, 0, -28, 4], 'analytic_rank': 1, 'bad_primes': [2, 43, 127], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 43688, 'degree': 14304, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.13120774103985024369993675124', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [9483264, 5461], 'lmfdb_iso': '43688.a', 'lmfdb_label': '43688.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -28, 4], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['10922.2.0.?'], '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': '0.98452878453774221015785262872', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 5461], [43, 44, 1016], [127, 128, 344]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.59330586141314711664475816555', 'prec': 107}, 'szpiro_ratio': 2.0225140787328177, '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, -3, 0, -1, 0, 5, 0, 6, 0, 4, 0, 2, 0, 3, 0, 3, 0, 4, 0], 'aplist': [0, -3, -1, 5, 4, 2, 3, 4, -6, -3, -8, -6, 9, 1, 9, -6, 0, 10, 2, -6, -6, -8, 6, -13, 8], 'class_deg': 1, 'class_size': 1, 'conductor': 43688, 'isogeny_matrix': [[1]], 'lmfdb_iso': '43688.a', 'trace_hash': 1108844277760622162}
• 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': '1.3000665846010098471580394877', 'prec': 100}, 'conductor': 43688, 'gens': [[0, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.98452878453774221015785262872', 'prec': 103}], 'lmfdb_label': '43688.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.3016369503676127643854395595', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.5320556583851629771498703203184737551', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [0, 49]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [2, 0], '47': [1, 0], '127': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '43688.a1'}
• ec_torsion_growth •

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

  
  
  • id: 2141528
    {'degree': 3, 'field': [-4, -28, 0, 1], 'lmfdb_label': '43688.a1', 'torsion': [2]}
  • id: 2141529
    {'degree': 6, 'field': [-87376, 0, 7056, 0, -168, 0, 1], 'lmfdb_label': '43688.a1', 'torsion': [2, 2]}
  • id: 2141530
    {'degree': 8, 'field': [-21168, 0, 432, 0, -504, 0, 0, 0, 1], 'lmfdb_label': '43688.a1', 'torsion': [3]}
  • id: 2141531
    {'degree': 12, 'field': [87376, 0, 18144, 0, -105840, 0, 1080, 0, -840, 0, 0, 0, 1], 'lmfdb_label': '43688.a1', '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: 1039112
    {'conductor': 43688, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '43688.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1039113
    {'conductor': 43688, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '43688.a1', 'prime': 43, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1039114
    {'conductor': 43688, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '43688.a1', 'prime': 127, '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': [[5335, 2, 5335, 3], [1, 0, 2, 1], [1, 2, 0, 1], [1, 1, 10921, 0], [10921, 2, 10920, 3], [5591, 2, 5591, 3]], 'adelic_image': '10922.2.0.?', 'conductor': 43688, 'lmfdb_label': '43688.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2179179
    {'lmfdb_iso': '43688.a', 'p': 5, 'prec': 20, 'unit': 15212579271924, 'val': 1}
  • id: 2179180
    {'lmfdb_iso': '43688.a', 'p': 7, 'prec': 20, 'unit': 3097586634244358, 'val': 1}
  • id: 2179183
    {'lmfdb_iso': '43688.a', 'p': 11, 'prec': 20, 'unit': 20015470439959027722, 'val': 1}
  • id: 2179185
    {'lmfdb_iso': '43688.a', 'p': 13, 'prec': 20, 'unit': 1132681979594880596469, 'val': 1}
  • id: 2179187
    {'lmfdb_iso': '43688.a', 'p': 17, 'prec': 20, 'unit': 225081267298142873072448, 'val': 1}
  • id: 2179188
    {'lmfdb_iso': '43688.a', 'p': 19, 'prec': 20, 'unit': 1002257318741770833831846, 'val': 1}
  • id: 2179191
    {'lmfdb_iso': '43688.a', 'p': 23, 'prec': 20, 'unit': 72702593556090168966701415, 'val': 1}
  • id: 2179184
    {'lmfdb_iso': '43688.a', 'p': 29, 'prec': 20, 'unit': 3612319831974047305034704935, 'val': 1}
  • id: 2179181
    {'lmfdb_iso': '43688.a', 'p': 31, 'prec': 20, 'unit': 195269428974144530739154851, 'val': 2}
  • id: 2179196
    {'lmfdb_iso': '43688.a', 'p': 37, 'prec': 20, 'unit': 268692268987462434082648716043, 'val': 1}
  • id: 2179182
    {'lmfdb_iso': '43688.a', 'p': 41, 'prec': 20, 'unit': 128619226429417612320486482020, 'val': 1}
  • id: 2179186
    {'lmfdb_iso': '43688.a', 'p': 47, 'prec': 20, 'unit': 43789480208144127996464972903554, 'val': 1}
  • id: 2179189
    {'lmfdb_iso': '43688.a', 'p': 53, 'prec': 20, 'unit': 7020162032622632968620367501359, 'val': 1}
  • id: 2179195
    {'lmfdb_iso': '43688.a', 'p': 61, 'prec': 20, 'unit': 8024368622242658537366119582117932, 'val': 1}
  • id: 2179178
    {'lmfdb_iso': '43688.a', 'p': 67, 'prec': 20, 'unit': 16912871911444568677177948569448503, 'val': 1}
  • id: 2179193
    {'lmfdb_iso': '43688.a', 'p': 71, 'prec': 20, 'unit': 120647541066723525808502128400141917, 'val': 1}
  • id: 2179190
    {'lmfdb_iso': '43688.a', 'p': 73, 'prec': 20, 'unit': 115735325553139397547185913910285316, 'val': 1}
  • id: 2179194
    {'lmfdb_iso': '43688.a', 'p': 79, 'prec': 20, 'unit': 414566816879463419366640896104532444, 'val': 1}
  • id: 2179177
    {'lmfdb_iso': '43688.a', 'p': 83, 'prec': 20, 'unit': 2240594627599738327164247416341283066, 'val': 1}
  • id: 2179192
    {'lmfdb_iso': '43688.a', 'p': 89, 'prec': 20, 'unit': 4919301342146444174279860897357702198, 'val': 1}
  • id: 2179176
    {'lmfdb_iso': '43688.a', 'p': 97, 'prec': 20, 'unit': 421206696179350998773004646005574587, 'val': 2}