Elliptic curve data - 21168.ce2

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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': '21168cz', 'Clabel': '21168cz1', 'Cnumber': 1, 'absD': 21168, 'ainvs': [0, 0, 0, 0, 7], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 3, 'class_size': 2, 'cm': -3, 'conductor': 21168, 'degree': 1296, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.49109693789847650481775505556', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 56, 'isogeny_degrees': [1, 3], 'jinv': [0, 1], 'lmfdb_iso': '21168.ce', 'lmfdb_label': '21168.ce2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 0, -7], 'min_quad_twist_disc': -4, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1323], [3, 2, 784]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691958', 'prec': 103}, 'szpiro_ratio': 1.7484473811612185, '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, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 8, 0], 'aplist': [0, 0, 0, 0, 0, 7, 0, 8, 0, 0, 11, -1, 0, 13, 0, 0, 0, 1, -11, 0, 10, 13, 0, 0, 19], 'class_deg': 3, 'class_size': 2, 'conductor': 21168, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '21168.ce', 'trace_hash': 537785266532823851}
• 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': '2.6703081448175377315909608137', 'prec': 100}, 'conductor': 21168, 'gens': [], 'heights': [], 'lmfdb_label': '21168.ce2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.0414172284278810424268528156', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0414172284278810424268528156445130913', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0, 0], '7': 'a', '11': [0, 0, 0], '13': [0, 0], '17': [0, 0, 0], '19': [0, 0], '23': [0, 0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '21168.ce2'}
• ec_torsion_growth •

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

  
  
  • id: 1077321
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '21168.ce2', 'torsion': [3]}
  • id: 1077322
    {'degree': 3, 'field': [-7, 0, 0, 1], 'lmfdb_label': '21168.ce2', 'torsion': [2]}
  • id: 1077325
    {'degree': 6, 'field': [-7, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '21168.ce2', 'torsion': [6]}
  • id: 1077324
    {'degree': 6, 'field': [21, 0, 7, 0, 7, 0, 1], 'lmfdb_label': '21168.ce2', 'torsion': [3]}
  • id: 1077323
    {'degree': 6, 'field': [64, -24, -15, 7, 6, -3, 1], 'lmfdb_label': '21168.ce2', 'torsion': [2, 2]}
  • id: 1077326
    {'degree': 12, 'field': [-1091, 5724, -5202, -464, 5364, -4866, 2106, -348, -48, 16, 12, -6, 1], 'lmfdb_label': '21168.ce2', 'torsion': [4]}
  • id: 1077328
    {'degree': 12, 'field': [21, 0, 126, 0, 147, 0, -120, 0, 39, 0, -6, 0, 1], 'lmfdb_label': '21168.ce2', 'torsion': [7]}
  • id: 1077329
    {'degree': 12, 'field': [36, 36, 126, -330, 195, -84, 127, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '21168.ce2', 'torsion': [2, 6]}
  • id: 1077327
    {'degree': 12, 'field': [441, 0, -147, 0, -98, 0, -7, 0, 42, 0, -7, 0, 1], 'lmfdb_label': '21168.ce2', 'torsion': [3, 3]}
  • id: 1077331
    {'degree': 18, 'field': [729, 0, 0, -1080, 0, 0, 2587, 0, 0, -414, 0, 0, 121, 0, 0, -18, 0, 0, 1], 'lmfdb_label': '21168.ce2', 'torsion': [6]}
  • id: 1077330
    {'degree': 18, 'field': [6777, -82134, 241299, -28026, 45225, -17226, 3240, -9810, -11988, -2600, -981, -540, -609, 90, 135, -6, -18, 0, 1], 'lmfdb_label': '21168.ce2', 'torsion': [9]}
• 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: 481630
    {'conductor': 21168, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '21168.ce2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 481631
    {'conductor': 21168, 'conductor_valuation': 3, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '21168.ce2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 481632
    {'conductor': 21168, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '21168.ce2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
• lmfdb_label 21168.ce2 does not appear in ec_galrep
• lmfdb_iso 21168.ce does not appear in ec_padic