Elliptic curve data - 31824.bk1

Formats: - HTML - YAML - JSON - 2024-06-01T13:43:13.674936

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '31824h', 'Clabel': '31824h2', 'Cnumber': 2, 'abc_quality': 0.9332211540954428, 'absD': 4825536768, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [0, 0, 0, -7383, 244150], 'analytic_rank': 0, 'bad_primes': [2, 3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 31824, 'degree': 32768, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.88813538968309699848438187959', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 36, 'isogeny_degrees': [1, 2], 'jinv': [238481570896, 25857], 'lmfdb_iso': '31824.bk', 'lmfdb_label': '31824.bk1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -820, 9316], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '34.6.0.a.1', '52.6.0.c.1', '884.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.12326887502425472015806215318', 'prec': 107}, 'szpiro_ratio': 3.6973859744522115, '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, 4, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, 0, 0], 'aplist': [0, 0, 4, -2, -2, -1, -1, 0, 0, 6, -2, 4, -8, -4, -4, -2, 4, 6, 8, -6, 4, -12, 0, -2, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 31824, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '31824.bk', 'trace_hash': 1264624605172302423}
• 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': '0.16926821021871864045236966053', 'prec': 103}, 'conductor': 31824, 'gens': [], 'heights': [], 'lmfdb_label': '31824.bk1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.3145927428679676786696638487', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6291854857359353573393276973581758627', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[50, 0, 1]], 'xcoord_integral_points': [50]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '13': [0, 0], '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '31824.bk1'}
• ec_torsion_growth •

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

  
  
  • id: 1585326
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '31824.bk1', 'torsion': [2, 2]}
  • id: 1585327
    {'degree': 4, 'field': [3, 9, -8, -1, 1], 'lmfdb_label': '31824.bk1', 'torsion': [4]}
  • id: 1585330
    {'degree': 8, 'field': [-22707, 0, 3288, 0, 522, 0, 0, 0, 1], 'lmfdb_label': '31824.bk1', 'torsion': [6]}
  • id: 1585329
    {'degree': 8, 'field': [36, -252, 603, -573, 160, 55, -28, -1, 1], 'lmfdb_label': '31824.bk1', 'torsion': [2, 4]}
  • id: 1585328
    {'degree': 8, 'field': [2602, -1250, 1589, -540, 260, -84, 26, -2, 1], 'lmfdb_label': '31824.bk1', 'torsion': [2, 4]}
  • id: 1585332
    {'degree': 16, 'field': [-267909392, 1093579808, -1166110096, 150860832, -89623024, 16155208, -3883412, -1375368, 464509, -96336, 34720, -7888, 890, 168, -4, -8, 1], 'lmfdb_label': '31824.bk1', 'torsion': [2, 6]}
  • id: 1585331
    {'degree': 16, 'field': [-65089868, 97258136, 104738620, -137056672, -11601586, 48330052, -5884288, -7848164, 1432929, 694828, -139444, -31112, 6605, 584, -134, -4, 1], 'lmfdb_label': '31824.bk1', 'torsion': [8]}
• 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: 743137
    {'conductor': 31824, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '31824.bk1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 743138
    {'conductor': 31824, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '31824.bk1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 743139
    {'conductor': 31824, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '31824.bk1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 743140
    {'conductor': 31824, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '31824.bk1', 'prime': 17, '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: 1876614
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [881, 4, 880, 5], [210, 1, 779, 0], [613, 4, 342, 9], [665, 222, 220, 663]], 'adelic_image': '884.12.0.?', 'conductor': 31824, 'lmfdb_label': '31824.bk1', 'prime': 0}
  • id: 142295
    {'conductor': 31824, 'elladic_image': '2.3.0.1', 'lmfdb_label': '31824.bk1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 31824.bk does not appear in ec_padic