Elliptic curve data - 233450.r2

Formats: - HTML - YAML - JSON - 2024-06-10T01:06:18.768327

• 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': '233450r', 'Clabel': '233450r2', 'Cnumber': 2, 'abc_quality': 0.9779324876146849, 'absD': 681236281250000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 93380, 'ainvs': [1, -1, 0, -1492, -1255584], 'analytic_rank': 0, 'bad_primes': [2, 5, 7, 23, 29], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 233450, 'degree': 1198080, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5252163582738392261432530062', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2], 'jinv': [-188132517, 348792976], 'lmfdb_iso': '233450.r', 'lmfdb_label': '233450.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -60, -10033], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.a.1', '18676.6.0.?', '93380.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, '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': '0.31813792394826394519268350628', 'prec': 103}, 'szpiro_ratio': 3.366304842546624, '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, -1, -1, -3, 0, 4, 0, 6, 1, 0, 1, -2, 3, -6, 0], 'aplist': [-1, 0, 0, -1, 4, 6, -2, -6, 1, 1, -8, 8, 10, 4, 0, -2, 10, -10, -4, 8, 4, -8, -4, 14, -6], 'class_deg': 2, 'class_size': 2, 'conductor': 233450, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '233450.r', 'trace_hash': 1681066797588185904}
• 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': '0.047338435834065160164060139104', 'prec': 107}, 'conductor': 233450, 'gens': [], 'heights': [], 'lmfdb_label': '233450.r2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.23074618240500828296218965966', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8459694592400662636975172773115479330', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[451, -451, 2]], 'xcoord_integral_points': []}
• lmfdb_label 233450.r2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10102815
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '233450.r2', 'torsion': [2, 2]}
  • id: 10102816
    {'degree': 4, 'field': [-1280, 0, 135, 0, 1], 'lmfdb_label': '233450.r2', 'torsion': [4]}
  • id: 10102819
    {'degree': 8, 'field': [-19200, 0, 10800, 0, 480, 0, 0, 0, 1], 'lmfdb_label': '233450.r2', 'torsion': [6]}
  • id: 10102818
    {'degree': 8, 'field': [95481, 0, -8768, 0, 739, 0, -32, 0, 1], 'lmfdb_label': '233450.r2', 'torsion': [2, 4]}
  • id: 10102817
    {'degree': 8, 'field': [3724900, 0, -92800, 0, 17165, 0, 290, 0, 1], 'lmfdb_label': '233450.r2', 'torsion': [2, 4]}
  • id: 10102821
    {'degree': 16, 'field': [3669330625, 0, 1465165000, 0, 145445500, 0, 9607000, 0, -1576250, 0, 19000, 0, 1660, 0, 40, 0, 1], 'lmfdb_label': '233450.r2', 'torsion': [2, 6]}
  • id: 10102820
    {'degree': 16, 'field': [21956946558976, 0, -6432879542272, 0, 569100615680, 0, -3725140992, 0, -1427452016, 0, 11247072, 0, 58860, 0, 412, 0, 1], 'lmfdb_label': '233450.r2', '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: 5785241
    {'conductor': 233450, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '233450.r2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5785242
    {'conductor': 233450, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '233450.r2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5785243
    {'conductor': 233450, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '233450.r2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5785244
    {'conductor': 233450, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '233450.r2', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5785245
    {'conductor': 233450, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '233450.r2', 'prime': 29, 'reduction_type': 1, '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: 3150147
    {'adelic_gens': [[74708, 1, 74703, 0], [32481, 4, 64962, 9], [1, 2, 2, 5], [3221, 4, 6442, 9], [1, 4, 0, 1], [1, 0, 4, 1], [70036, 23349, 23345, 70036], [80041, 4, 66702, 9], [93377, 4, 93376, 5], [3, 4, 8, 11]], 'adelic_image': '93380.12.0.?', 'conductor': 233450, 'lmfdb_label': '233450.r2', 'prime': 0}
  • id: 849119
    {'conductor': 233450, 'elladic_image': '2.3.0.1', 'lmfdb_label': '233450.r2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 233450.r does not appear in ec_padic