Elliptic curve data - 225.b3

Formats: - HTML - YAML - JSON - 2023-12-02T06:13:08.969660

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '225c', 'Clabel': '225c8', 'Cnumber': 8, 'absD': 2451645281953125, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, -1, 1, -24755, 2820872], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 225, 'degree': 768, 'elladic_images': ['32.96.0.65'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6448947090282065549716379094', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 16, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-147281603041, 215233605], 'lmfdb_iso': '225.b', 'lmfdb_label': '225.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -110, -880], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.ba.2', '12.12.0-4.c.1.2', '16.48.0.u.2', '20.12.0.h.1', '24.48.0-8.ba.2.3', '32.96.0-16.u.2.1', '40.48.0.bm.2', '48.96.0-16.u.2.3', '60.24.0-20.h.1.2', '80.192.5.?', '96.192.1.?', '120.96.0.?', '160.384.5.?', '240.384.5.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562433', 'prec': 103}, '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, -1, 0, -1, 0, 0, 0, 3, 0, 0, 4, 0, 2, 0, 0, -1, 2, 0, 4, 0], 'aplist': [-1, 0, 0, 0, 4, 2, 2, 4, 0, 2, 0, 10, -10, -4, 8, -10, 4, -2, -12, 8, -10, 0, 12, 6, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 225, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '225.b', 'trace_hash': 285895329455399408}
• 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': '0.037261695210292151696112379702', 'prec': 107}, 'conductor': 225, 'gens': [], 'heights': [], 'lmfdb_label': '225.b3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.41214796952196784945270551922', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.82429593904393569890541103843228277079', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-789, 785, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'o?', '3': 'a', '5': 'a'}, 'iwp0': 3, 'lmfdb_label': '225.b3'}
• ec_torsion_growth •

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

  
  
  • id: 9647
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [4]}
  • id: 9648
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '225.b3', 'torsion': [4]}
  • id: 9646
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [2, 2]}
  • id: 9650
    {'degree': 4, 'field': [1, 0, -8, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [8]}
  • id: 9649
    {'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [2, 4]}
  • id: 9651
    {'degree': 4, 'field': [49, 0, 16, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [8]}
  • id: 9657
    {'degree': 8, 'field': [1, -16, 22, -13, 10, -7, 7, -4, 1], 'lmfdb_label': '225.b3', 'torsion': [6]}
  • id: 9652
    {'degree': 8, 'field': [6, -60, 178, -80, 19, -20, 2, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [2, 4]}
  • id: 9653
    {'degree': 8, 'field': [25, 0, 0, 0, 5, 0, 0, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [8]}
  • id: 9654
    {'degree': 8, 'field': [81, 0, 36, 0, 7, 0, 4, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [2, 8]}
  • id: 9656
    {'degree': 8, 'field': [225, 0, 600, 0, 280, 0, 40, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [16]}
  • id: 9655
    {'degree': 8, 'field': [625, 0, -1000, 0, 360, 0, -40, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [16]}
  • id: 9659
    {'degree': 16, 'field': [1, 2, 2, 24, 13, -74, 114, -58, -12, 44, -24, -2, 13, -12, 8, -4, 1], 'lmfdb_label': '225.b3', 'torsion': [2, 8]}
  • id: 9665
    {'degree': 16, 'field': [9, 0, -642, 0, -215, 0, -159, 0, 120, 0, 19, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [12]}
  • id: 9664
    {'degree': 16, 'field': [9, 0, 80, 0, 238, 0, 267, 0, 65, 0, -23, 0, -15, 0, -1, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [2, 6]}
  • id: 9660
    {'degree': 16, 'field': [16, 0, 0, 0, -32, 0, 0, 0, 249, 0, 0, 0, -8, 0, 0, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [16]}
  • id: 9661
    {'degree': 16, 'field': [25, 0, 0, 0, 25, 0, 0, 0, 30, 0, 0, 0, -5, 0, 0, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [16]}
  • id: 9666
    {'degree': 16, 'field': [39, -123, 45, 282, -393, 0, 355, -215, -84, 126, 30, -150, 150, -87, 33, -8, 1], 'lmfdb_label': '225.b3', 'torsion': [12]}
  • id: 9663
    {'degree': 16, 'field': [625, 0, 10000, 0, -35000, 0, -29600, 0, 45160, 0, 5920, 0, -1400, 0, -80, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [32]}
  • id: 9658
    {'degree': 16, 'field': [1296, 0, 2016, 0, 2560, 0, 1184, 0, 444, 0, -176, 0, 0, 0, -4, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [4, 4]}
  • id: 9662
    {'degree': 16, 'field': [50625, 0, -45000, 0, 26500, 0, -12000, 0, 3375, 0, 400, 0, -60, 0, 0, 0, 1], 'lmfdb_label': '225.b3', 'torsion': [2, 16]}
• 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: 2011
    {'conductor': 225, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '225.b3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2012
    {'conductor': 225, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '225.b3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1666725
    {'adelic_gens': [[319, 448, 304, 447], [449, 32, 448, 33], [1, 0, 32, 1], [23, 18, 318, 395], [5, 28, 68, 381], [421, 32, 436, 33], [60, 31, 239, 324], [1, 32, 0, 1], [266, 477, 115, 212]], 'adelic_image': '480.768.13.?', 'conductor': 225, 'lmfdb_label': '225.b3', 'prime': 0}
  • id: 951
    {'conductor': 225, 'elladic_image': '32.96.0.65', 'lmfdb_label': '225.b3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 225.b does not appear in ec_padic