Elliptic curve data - 216320.s2

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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': '216320i', 'Clabel': '216320i1', 'Cnumber': 1, 'abc_quality': 1.127266229143732, 'absD': 27688960, 'adelic_genus': 9, 'adelic_index': 336, 'adelic_level': 1040, 'ainvs': [0, 0, 0, -1352, -19136], 'analytic_rank': 1, 'bad_primes': [2, 5, 13], 'class_deg': 13, 'class_size': 2, 'cm': 0, 'conductor': 216320, 'degree': 61440, 'elladic_images': ['13.42.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.46163316342365723455255600059', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 13], 'jinv': [-49353408, 5], 'lmfdb_iso': '216320.s', 'lmfdb_label': '216320.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -338, -2392], 'min_quad_twist_disc': 8, 'modell_images': ['13B.5.4'], 'modm_images': ['13.42.0.b.1', '40.2.0.a.1', '104.84.2.?', '208.168.2.?', '260.84.2.?', '520.168.9.?', '1040.336.9.?'], 'nonmax_primes': [13], 'nonmax_rad': 13, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '10.377630856385365440083501893', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 845], [5, 6, 43264], [13, 38, 1280]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.83229237185319719156123205816', 'prec': 107}, 'szpiro_ratio': 2.705992166781623, '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, 0, 0, 1, 0, -1, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 5, 0], 'aplist': [0, 0, 1, -1, 3, 0, 0, 5, 0, 0, 6, -3, 2, 4, 9, -13, -12, 0, 2, 8, -4, -2, 6, 3, -18], 'class_deg': 13, 'class_size': 2, 'conductor': 216320, 'isogeny_matrix': [[1, 13], [13, 1]], 'lmfdb_iso': '216320.s', 'trace_hash': 1750464777256692172}
• 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': '0.39721947120685839690487029811', 'prec': 103}, 'conductor': 216320, 'gens': [[28545, 4697269, 13]], 'heights': [{'__RealLiteral__': 0, 'data': '10.377630856385365440083501893', 'prec': 100}], 'lmfdb_label': '216320.s2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.39366132179878646830927711869', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.1705437601290706908009255650863157725', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 216320.s2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9430063
    {'degree': 3, 'field': [-26, 13, 0, 1], 'lmfdb_label': '216320.s2', 'torsion': [2]}
  • id: 9430064
    {'degree': 6, 'field': [90, 0, 61, 0, 12, 0, 1], 'lmfdb_label': '216320.s2', 'torsion': [2, 2]}
  • id: 9430065
    {'degree': 8, 'field': [-245388, 0, 38688, 0, -1716, 0, 0, 0, 1], 'lmfdb_label': '216320.s2', 'torsion': [3]}
  • id: 9430066
    {'degree': 12, 'field': [-3893760, 0, 3201536, 0, -789568, 0, 48672, 0, -858, 0, 52, 0, 1], 'lmfdb_label': '216320.s2', 'torsion': [4]}
  • id: 9430067
    {'degree': 12, 'field': [1352, 0, 5408, 0, 6760, 0, 3224, 0, 650, 0, 52, 0, 1], 'lmfdb_label': '216320.s2', 'torsion': [13]}
• 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: 5361044
    {'conductor': 216320, 'conductor_valuation': 8, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '216320.s2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5361045
    {'conductor': 216320, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '216320.s2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5361046
    {'conductor': 216320, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '216320.s2', 'prime': 13, 'reduction_type': 0, '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: 3046093
    {'adelic_gens': [[14, 23, 871, 391], [927, 806, 260, 423], [1, 26, 0, 1], [502, 1027, 429, 122], [638, 13, 819, 1028], [1015, 26, 1014, 27], [766, 1027, 403, 12], [1, 0, 26, 1]], 'adelic_image': '1040.336.9.?', 'conductor': 216320, 'lmfdb_label': '216320.s2', 'prime': 0}
  • id: 795293
    {'conductor': 216320, 'elladic_image': '13.42.0.3', 'lmfdb_label': '216320.s2', 'modell_image': '13B.5.4', 'prime': 13}
• lmfdb_iso 216320.s does not appear in ec_padic