Elliptic curve data - 331056.cx1

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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': '331056cx', 'Clabel': '331056cx1', 'Cnumber': 1, 'abc_quality': 0.6712578745765572, 'absD': 232655563008, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 228, 'ainvs': [0, 0, 0, -1815, -18634], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 331056, 'degree': 179200, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.88235501800625445416098324804', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 75, 'isogeny_degrees': [1, 2], 'jinv': [54000, 19], 'lmfdb_iso': '331056.cx', 'lmfdb_label': '331056.cx1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -15, -14], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.c.1', '76.6.0.?', '114.6.0.?', '228.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.0958509829316307900531855289', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 6897], [3, 6, 36784], [11, 62, 2736], [19, 20, 17424]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0533438109332551136636212645', 'prec': 103}, 'szpiro_ratio': 2.6848945943338904, '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, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 1, 0], 'aplist': [0, 0, 0, 0, 0, 2, 4, 1, 2, 6, -4, 2, -2, 4, 10, -6, 4, -2, -4, 4, 6, 8, 2, -6, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 331056, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '331056.cx', 'trace_hash': 1735630488509954644}
• 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': '0.17123643168546819421727740453', 'prec': 103}, 'conductor': 331056, 'gens': [[685, 14392, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '6.0958509829316307900531855289', 'prec': 100}], 'lmfdb_label': '331056.cx1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.75261617521962142158965047514', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.1756721029655474207843389354394851837', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-11, 0, 1]], 'xcoord_integral_points': [-11]}
• lmfdb_label 331056.cx1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13875684
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '331056.cx1', 'torsion': [2, 2]}
  • id: 13875685
    {'degree': 4, 'field': [6897, 0, -165, 0, 1], 'lmfdb_label': '331056.cx1', 'torsion': [4]}
  • id: 13875688
    {'degree': 8, 'field': [-12426, -9804, -4218, -1080, -360, -30, 2, -2, 1], 'lmfdb_label': '331056.cx1', 'torsion': [6]}
  • id: 13875686
    {'degree': 8, 'field': [2304, 0, -5364, 0, -60, 0, -45, 0, 1], 'lmfdb_label': '331056.cx1', 'torsion': [2, 4]}
  • id: 13875687
    {'degree': 8, 'field': [2108304, 0, 47916, 0, 2541, 0, -33, 0, 1], 'lmfdb_label': '331056.cx1', 'torsion': [2, 4]}
  • id: 13875689
    {'degree': 16, 'field': [59182249, 0, 11840560, 0, 1267922, 0, 1255600, 0, 354115, 0, 40880, 0, 2522, 0, 80, 0, 1], 'lmfdb_label': '331056.cx1', 'torsion': [8]}
  • id: 13875690
    {'degree': 16, 'field': [861989364, -1517251824, 940908960, 55357344, -162021708, 41540472, -9598224, 4156296, -807456, -20352, 26028, -7152, 1060, 172, -52, -4, 1], 'lmfdb_label': '331056.cx1', 'torsion': [2, 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: 8190600
    {'conductor': 331056, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '331056.cx1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8190601
    {'conductor': 331056, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '331056.cx1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8190602
    {'conductor': 331056, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '331056.cx1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8190603
    {'conductor': 331056, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '331056.cx1', 'prime': 19, '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

  
  
  • id: 3734898
    {'adelic_gens': [[1, 2, 2, 5], [194, 1, 131, 0], [3, 4, 8, 11], [225, 4, 224, 5], [173, 58, 56, 171], [1, 4, 0, 1], [80, 1, 151, 0], [1, 0, 4, 1]], 'adelic_image': '228.12.0.?', 'conductor': 331056, 'lmfdb_label': '331056.cx1', 'prime': 0}
  • id: 1152119
    {'conductor': 331056, 'elladic_image': '2.3.0.1', 'lmfdb_label': '331056.cx1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 331056.cx does not appear in ec_padic