Elliptic curve data - 3971.b2

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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': '3971b', 'Clabel': '3971b2', 'Cnumber': 2, 'abc_quality': 1.012998630378065, 'absD': 7576786180931, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 10450, 'ainvs': [0, 1, 1, -3730, 157593], 'analytic_rank': 1, 'bad_primes': [11, 19], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 3971, 'degree': 7200, 'elladic_images': ['5.60.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1642096484648171653154994545', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 5, 'iso_nlabel': 1, 'isogeny_degrees': [1, 5], 'jinv': [-122023936, 161051], 'lmfdb_iso': '3971.b', 'lmfdb_label': '3971.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -10, -20], 'min_quad_twist_disc': -19, 'modell_images': ['5Cs.4.1'], 'modm_images': ['5.60.0.a.1', '22.2.0.a.1', '95.120.0.?', '110.120.5.?', '275.300.12.?', '550.600.37.?', '2090.240.5.?', '5225.600.12.?', '10450.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.1225675167272302521928779175', 'prec': 100}, 'semistable': False, 'serre_invariants': [[5, 2, 361], [11, 12, 361], [19, 182, 11]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.30800984111840306468901426144', 'prec': 107}, 'szpiro_ratio': 4.522195524710625, '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, 2, 1, 2, 1, 2, -2, 0, -2, 2, 1, 2, -4, -4, 1, -4, -2, -4, 0, 2], 'aplist': [2, 1, 1, -2, 1, -4, -2, 0, -1, 0, -7, -3, 8, -6, 8, 6, -5, 12, 7, 3, 4, 10, -6, -15, 7], 'class_deg': 25, 'class_size': 3, 'conductor': 3971, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '3971.b', 'trace_hash': 255144284925459725}
• 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': '0.097449664392418911458316142728', 'prec': 107}, 'conductor': 3971, 'gens': [[-147, 3967, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '1.1225675167272302521928779175', 'prec': 100}], 'lmfdb_label': '3971.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.66935096951503013826141370190', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.5139165566745138133921444429123188929', 'prec': 130}, 'tamagawa_product': 10, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 3, 0], '3': [1, 0], '5': [3, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': 'a', '23': [3, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '3971.b2'}
• ec_torsion_growth •

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

  
  
  • id: 206690
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '3971.b2', 'torsion': [5]}
  • id: 206691
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '3971.b2', 'torsion': [2]}
  • id: 206692
    {'degree': 4, 'field': [101, 24, -24, -1, 1], 'lmfdb_label': '3971.b2', 'torsion': [5]}
  • id: 206693
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '3971.b2', 'torsion': [2, 2]}
  • id: 206694
    {'degree': 6, 'field': [77, 11, 72, -13, 16, -1, 1], 'lmfdb_label': '3971.b2', 'torsion': [10]}
  • id: 206695
    {'degree': 8, 'field': [-4399, -3232, -1057, 423, -177, 48, -2, -2, 1], 'lmfdb_label': '3971.b2', 'torsion': [3]}
  • id: 206696
    {'degree': 8, 'field': [625, -125, -100, 45, 11, 9, -4, -1, 1], 'lmfdb_label': '3971.b2', 'torsion': [5, 5]}
  • id: 206697
    {'degree': 12, 'field': [-1761701, 1202504, 185926, -519210, 162055, 5524, 2944, 1192, -561, -80, 6, -2, 1], 'lmfdb_label': '3971.b2', 'torsion': [4]}
  • id: 206699
    {'degree': 12, 'field': [15625, -3125, -8125, 4000, 675, -555, 326, -111, 27, 32, -13, -1, 1], 'lmfdb_label': '3971.b2', 'torsion': [2, 10]}
  • id: 206698
    {'degree': 12, 'field': [1501511, -602877, -947708, 145298, 223609, -16136, -28857, 408, 2005, 28, -70, -1, 1], 'lmfdb_label': '3971.b2', 'torsion': [10]}
  • id: 206700
    {'degree': 16, 'field': [335241, 0, 386460, 0, 268104, 0, 121429, 0, 33920, 0, 5947, 0, 637, 0, 38, 0, 1], 'lmfdb_label': '3971.b2', 'torsion': [15]}
• 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: 74040
    {'conductor': 3971, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '3971.b2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 74041
    {'conductor': 3971, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '3971.b2', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1689778
    {'adelic_gens': [[16, 35, 1765, 3861], [1, 0, 50, 1], [381, 6650, 4085, 571], [2851, 6650, 7904, 5777], [1, 50, 0, 1], [10401, 50, 10400, 51], [549, 0, 0, 10449], [1, 50, 10, 501]], 'adelic_image': '10450.1200.37.?', 'conductor': 3971, 'lmfdb_label': '3971.b2', 'prime': 0}
  • id: 19688
    {'conductor': 3971, 'elladic_image': '5.60.0.1', 'lmfdb_label': '3971.b2', 'modell_image': '5Cs.4.1', 'prime': 5}
• ec_padic •

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

  
  
  • id: 138627
    {'lmfdb_iso': '3971.b', 'p': 5, 'prec': 20, 'unit': 17817202319648, 'val': 1}
  • id: 138628
    {'lmfdb_iso': '3971.b', 'p': 7, 'prec': 20, 'unit': 5931117019385569, 'val': 1}
  • id: 138632
    {'lmfdb_iso': '3971.b', 'p': 13, 'prec': 20, 'unit': 664079150797066686608, 'val': 1}
  • id: 138634
    {'lmfdb_iso': '3971.b', 'p': 17, 'prec': 20, 'unit': 144654683745370307010216, 'val': 1}
  • id: 138639
    {'lmfdb_iso': '3971.b', 'p': 23, 'prec': 20, 'unit': 2930858456759178183431344, 'val': 2}
  • id: 138629
    {'lmfdb_iso': '3971.b', 'p': 31, 'prec': 20, 'unit': 12837893913414593528503719130, 'val': 1}
  • id: 138644
    {'lmfdb_iso': '3971.b', 'p': 37, 'prec': 20, 'unit': 224692611346648088345000247888, 'val': 1}
  • id: 138630
    {'lmfdb_iso': '3971.b', 'p': 41, 'prec': 20, 'unit': 3575362193097045706284212521701, 'val': 1}
  • id: 138631
    {'lmfdb_iso': '3971.b', 'p': 43, 'prec': 20, 'unit': 2799953341057776973349935834406, 'val': 1}
  • id: 138642
    {'lmfdb_iso': '3971.b', 'p': 47, 'prec': 20, 'unit': 47045330135578345954707759027928, 'val': 1}
  • id: 138636
    {'lmfdb_iso': '3971.b', 'p': 53, 'prec': 20, 'unit': 370669518304716212144539281383922, 'val': 1}
  • id: 138637
    {'lmfdb_iso': '3971.b', 'p': 59, 'prec': 20, 'unit': 2142638330934829161418290304889436, 'val': 1}
  • id: 138643
    {'lmfdb_iso': '3971.b', 'p': 61, 'prec': 20, 'unit': 3246500979610975511992240615245599, 'val': 1}
  • id: 138626
    {'lmfdb_iso': '3971.b', 'p': 67, 'prec': 20, 'unit': 26091373524502108123627223421991682, 'val': 1}
  • id: 138641
    {'lmfdb_iso': '3971.b', 'p': 71, 'prec': 20, 'unit': 27126805237946739161686400263472918, 'val': 1}
  • id: 138638
    {'lmfdb_iso': '3971.b', 'p': 73, 'prec': 20, 'unit': 132788348631412249390280297862877838, 'val': 1}
  • id: 138633
    {'lmfdb_iso': '3971.b', 'p': 79, 'prec': 20, 'unit': 1023878355064647986414062436231396141, 'val': 1}
  • id: 138635
    {'lmfdb_iso': '3971.b', 'p': 83, 'prec': 20, 'unit': 1446428270547530783669391414753098270, 'val': 1}
  • id: 138640
    {'lmfdb_iso': '3971.b', 'p': 89, 'prec': 20, 'unit': 5651006227096909409248946037392071185, 'val': 1}
  • id: 138625
    {'lmfdb_iso': '3971.b', 'p': 97, 'prec': 20, 'unit': 1820977099308113242276567372796969034, 'val': 1}