Elliptic curve data - 225.d1

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• 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': '225b', 'Clabel': '225b2', 'Cnumber': 2, 'absD': 7688671875, 'ainvs': [0, 0, 1, 0, -4219], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 3, 'class_size': 2, 'cm': -3, 'conductor': 225, 'degree': 120, 'elladic_images': ['5.30.0.2', '27.648.18.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.57580039636244460329040428732', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 3, 'isogeny_degrees': [1, 3], 'jinv': [0, 1], 'lmfdb_iso': '225.d', 'lmfdb_label': '225.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 1], 'min_quad_twist_disc': -15, 'modell_images': ['5Ns.2.1', '3B.1.2'], 'nonmax_primes': [3, 5], 'nonmax_rad': 15, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, '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, -2, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 4, 0, 0, -1, 0], 'aplist': [0, 0, 0, 5, 0, 5, 0, -1, 0, 0, -7, -10, 0, 5, 0, 0, 0, -13, 5, 0, -10, -4, 0, 0, 5], 'class_deg': 3, 'class_size': 2, 'conductor': 225, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '225.d', 'trace_hash': 49423681071508381}
• 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': '0.31613030502258025158853715196', 'prec': 103}, 'conductor': 225, 'gens': [], 'heights': [], 'lmfdb_label': '225.d1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.60418195389101983687716770297', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2083639077820396737543354059356218783', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': 'a', '5': 'a'}, 'iwp0': 5, 'lmfdb_label': '225.d1'}
• ec_torsion_growth •

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

  
  
  • id: 9524
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '225.d1', 'torsion': [3]}
  • id: 9526
    {'degree': 3, 'field': [-5, 0, 0, 1], 'lmfdb_label': '225.d1', 'torsion': [3]}
  • id: 9525
    {'degree': 3, 'field': [-3, -3, -1, 1], 'lmfdb_label': '225.d1', 'torsion': [2]}
  • id: 9527
    {'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '225.d1', 'torsion': [2, 6]}
  • id: 9528
    {'degree': 6, 'field': [36, -18, -9, 3, 6, -3, 1], 'lmfdb_label': '225.d1', 'torsion': [3, 3]}
  • id: 9529
    {'degree': 8, 'field': [1, 1, -13, 13, -5, 2, 2, -1, 1], 'lmfdb_label': '225.d1', 'torsion': [5]}
  • id: 9530
    {'degree': 9, 'field': [1, 0, 0, 23, 0, 0, -7, 0, 0, 1], 'lmfdb_label': '225.d1', 'torsion': [6]}
  • id: 9531
    {'degree': 12, 'field': [-11, 8, 36, -38, -53, 156, -176, 108, -27, -16, 16, -6, 1], 'lmfdb_label': '225.d1', 'torsion': [4]}
  • id: 9532
    {'degree': 12, 'field': [19, -49, 102, -126, 109, -42, -13, 36, -24, 7, 2, -3, 1], 'lmfdb_label': '225.d1', 'torsion': [21]}
  • id: 9533
    {'degree': 16, 'field': [1, -5, 16, -30, 57, -110, 183, -240, 250, -215, 157, -100, 57, -30, 14, -5, 1], 'lmfdb_label': '225.d1', 'torsion': [5, 15]}
  • id: 9535
    {'degree': 18, 'field': [27, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '225.d1', 'torsion': [6, 6]}
  • id: 9534
    {'degree': 18, 'field': [64, -96, -144, 336, -336, 342, 231, -699, 1314, -1465, 1371, -1089, 723, -399, 207, -102, 39, -9, 1], 'lmfdb_label': '225.d1', 'torsion': [3, 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: 1995
    {'conductor': 225, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '225.d1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1996
    {'conductor': 225, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '225.d1', 'prime': 5, 'reduction_type': 0, '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: 1024
    {'conductor': 225, 'elladic_image': '27.648.18.4', 'lmfdb_label': '225.d1', 'modell_image': '3B.1.2', 'prime': 3}
  • id: 1021
    {'conductor': 225, 'elladic_image': '5.30.0.2', 'lmfdb_label': '225.d1', 'modell_image': '5Ns.2.1', 'prime': 5}
• lmfdb_iso 225.d does not appear in ec_padic