Elliptic curve data - 8640.ch2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '8640ch', 'Clabel': '8640ch1', 'Cnumber': 1, 'abc_quality': 0.6989700043360189, 'absD': 100776960, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 120, 'ainvs': [0, 0, 0, 108, 216], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 8640, 'degree': 3456, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.22406166492191210153150304033', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 59, 'isogeny_degrees': [1, 3], 'jinv': [6912, 5], 'lmfdb_iso': '8640.ch', 'lmfdb_label': '8640.ch2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 27, -27], 'min_quad_twist_disc': -8, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '24.8.0-3.a.1.4', '30.8.0.b.1', '120.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 135], [3, 2, 160], [5, 6, 1728]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1775202020457912581959576552', 'prec': 103}, 'szpiro_ratio': 2.8309300329204583, '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, 4, 0, 0, 0, 6, 0, 4, 0, 0, 0, -3, 0, -7, 0], 'aplist': [0, 0, 1, 4, 6, 4, -3, -7, 9, 0, 7, -2, 6, 2, 0, -9, -12, 7, 2, -6, 2, 1, 9, -6, 8], 'class_deg': 3, 'class_size': 2, 'conductor': 8640, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '8640.ch', 'trace_hash': 475005772891032722}
• 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': '0.63882589287576636037939261371', 'prec': 103}, 'conductor': 8640, 'gens': [], 'heights': [], 'lmfdb_label': '8640.ch2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2024728589596404921537776744', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6074185768789214764613330231710703096', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '8640.ch2'}
• ec_torsion_growth •

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

  
  
  • id: 451604
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '8640.ch2', 'torsion': [3]}
  • id: 451605
    {'degree': 3, 'field': [-1, 3, 0, 1], 'lmfdb_label': '8640.ch2', 'torsion': [2]}
  • id: 451607
    {'degree': 6, 'field': [-24, 0, 28, 0, -2, 0, 1], 'lmfdb_label': '8640.ch2', 'torsion': [3]}
  • id: 451606
    {'degree': 6, 'field': [1, -3, 3, -1, 3, -3, 1], 'lmfdb_label': '8640.ch2', 'torsion': [2, 2]}
  • id: 451608
    {'degree': 6, 'field': [3, 6, 21, -2, 12, 0, 1], 'lmfdb_label': '8640.ch2', 'torsion': [6]}
  • id: 451609
    {'degree': 12, 'field': [-15, 0, 36, 0, -30, 0, 30, 0, -15, 0, 0, 0, 1], 'lmfdb_label': '8640.ch2', 'torsion': [4]}
  • id: 451610
    {'degree': 12, 'field': [4, 0, -24, 0, 156, 0, 76, 0, 24, 0, 6, 0, 1], 'lmfdb_label': '8640.ch2', 'torsion': [3, 3]}
  • id: 451611
    {'degree': 12, 'field': [64, 0, 96, 0, 144, 0, -8, 0, 36, 0, 6, 0, 1], 'lmfdb_label': '8640.ch2', 'torsion': [2, 6]}
  • id: 451613
    {'degree': 18, 'field': [-24, 0, 384, 0, -624, 0, 1144, 0, -864, 0, 456, 0, -86, 0, 36, 0, -6, 0, 1], 'lmfdb_label': '8640.ch2', 'torsion': [6]}
  • id: 451612
    {'degree': 18, 'field': [22472, 0, 5184, 0, -15408, 0, -8724, 0, 5832, 0, 7200, 0, 2718, 0, 468, 0, 36, 0, 1], 'lmfdb_label': '8640.ch2', '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: 180447
    {'conductor': 8640, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '8640.ch2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 180448
    {'conductor': 8640, 'conductor_valuation': 3, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '8640.ch2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 180449
    {'conductor': 8640, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8640.ch2', 'prime': 5, '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: 1721115
    {'adelic_gens': [[1, 0, 6, 1], [59, 0, 0, 119], [4, 3, 9, 7], [115, 6, 114, 7], [89, 0, 0, 119], [3, 4, 8, 11], [95, 114, 96, 113], [113, 114, 99, 101], [1, 6, 0, 1], [8, 27, 1, 16]], 'adelic_image': '120.16.0.?', 'conductor': 8640, 'lmfdb_label': '8640.ch2', 'prime': 0}
  • id: 42294
    {'conductor': 8640, 'elladic_image': '3.4.0.1', 'lmfdb_label': '8640.ch2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 8640.ch does not appear in ec_padic