Elliptic curve data - 3872.f2

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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': '3872b', 'Clabel': '3872b3', 'Cnumber': 3, 'abc_quality': 1.172456969504371, 'absD': 907039232, 'ainvs': [0, 0, 0, -1331, 18634], 'analytic_rank': 0, 'bad_primes': [2, 11], 'class_deg': 4, 'class_size': 4, 'cm': -16, 'conductor': 3872, 'degree': 1440, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.58156189104762106319592882714', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 2, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4], 'jinv': [287496, 1], 'lmfdb_iso': '3872.f', 'lmfdb_label': '3872.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -11, -14], 'min_quad_twist_disc': -11, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 121], [11, 62, 32]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1372461307715231908979670529', 'prec': 103}, 'szpiro_ratio': 4.017981506837876, '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, -2, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, -2, 0, 0, -6, -2, 0, 0, 10, 0, -2, -10, 0, 0, 14, 0, 10, 0, 0, 6, 0, 0, 10, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 3872, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3872.f', 'trace_hash': 1630781610106707576}
• 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': '0.31250844627365331034045889908', 'prec': 103}, 'conductor': 3872, 'gens': [], 'heights': [], 'lmfdb_label': '3872.f2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.5811601975097989680370686073', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.79058009875489948401853430364932935598', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[22, 0, 1]], 'xcoord_integral_points': [22]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '3872.f2'}
• ec_torsion_growth •

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

  
  
  • id: 201556
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [4]}
  • id: 201557
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [4]}
  • id: 201555
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 2]}
  • id: 201558
    {'degree': 4, 'field': [25, 0, -12, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 4]}
  • id: 201562
    {'degree': 8, 'field': [-1487, -3004, -1166, 284, -164, -16, 10, -4, 1], 'lmfdb_label': '3872.f2', 'torsion': [6]}
  • id: 201560
    {'degree': 8, 'field': [49, 0, -432, 0, 180, 0, -24, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 8]}
  • id: 201561
    {'degree': 8, 'field': [324, 0, -180, 0, 50, 0, -10, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [8]}
  • id: 201559
    {'degree': 8, 'field': [324, 0, 0, 0, -14, 0, 0, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 4]}
  • id: 201563
    {'degree': 8, 'field': [4706, -3404, 656, 200, -4, -20, 2, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [10]}
  • id: 201572
    {'degree': 16, 'field': [-7898, 13860, 4280, -15768, 3556, 7020, -6994, -1224, 4903, -144, -1690, 96, 304, -12, -28, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [12]}
  • id: 201565
    {'degree': 16, 'field': [521, -2044, 2452, 3412, -8540, -784, 11104, -1932, -6779, 2040, 2012, -852, -222, 140, 0, -8, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 8]}
  • id: 201564
    {'degree': 16, 'field': [6561, 0, -14580, 0, 16200, 0, -12600, 0, 6079, 0, -1400, 0, 200, 0, -20, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [4, 4]}
  • id: 201573
    {'degree': 16, 'field': [8633, 11240, 24370, 21692, 19998, 13004, 8642, 3644, 3503, 404, 1050, -36, 188, -8, 20, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [20]}
  • id: 201571
    {'degree': 16, 'field': [35641, 66836, 20596, -44000, -31658, 16816, 13920, -5520, -1820, -484, 1548, -712, 202, -88, 36, -8, 1], 'lmfdb_label': '3872.f2', 'torsion': [20]}
  • id: 201568
    {'degree': 16, 'field': [287422, 304584, 515396, 494400, 350152, 255912, 111716, 64008, 17524, 5388, -1336, -552, -386, -72, -4, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 6]}
  • id: 201567
    {'degree': 16, 'field': [343501, 1451764, 1894326, 400260, -1036782, -1125440, -435766, 20084, -3622, -4644, -3686, 140, 218, -40, 6, -4, 1], 'lmfdb_label': '3872.f2', 'torsion': [10]}
  • id: 201570
    {'degree': 16, 'field': [727609, 0, -1323116, 0, 835276, 0, -293372, 0, 65170, 0, -9356, 0, 844, 0, -44, 0, 1], 'lmfdb_label': '3872.f2', 'torsion': [12]}
  • id: 201569
    {'degree': 16, 'field': [1429921, 1593188, -955844, -1566944, 223582, 704992, -18720, -187632, 940, 31580, -444, -3496, 202, 200, -12, -8, 1], 'lmfdb_label': '3872.f2', 'torsion': [2, 10]}
  • id: 201566
    {'degree': 16, 'field': [7786981, 6245284, 1577594, 905460, 1740158, 39044, -89942, 111696, 14347, -17508, 3562, 568, -628, 60, 8, -4, 1], 'lmfdb_label': '3872.f2', 'torsion': [3, 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: 71943
    {'conductor': 3872, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '3872.f2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 71944
    {'conductor': 3872, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '3872.f2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• lmfdb_label 3872.f2 does not appear in ec_galrep
• lmfdb_iso 3872.f does not appear in ec_padic