Elliptic curve data - 49725.v2

Formats: - HTML - YAML - JSON - 2024-06-09T05:54:23.233591

• 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': '49725p', 'Clabel': '49725p1', 'Cnumber': 1, 'abc_quality': 0.9198433540434031, 'absD': 23856718640625, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [1, -1, 0, -59067, 5535216], 'analytic_rank': 0, 'bad_primes': [3, 5, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 49725, 'degree': 184320, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4841956767960682508999598992', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2], 'jinv': [2000852317801, 2094417], 'lmfdb_iso': '49725.v', 'lmfdb_label': '49725.v2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -262, -1745], 'min_quad_twist_disc': -15, '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': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.13017057624496321790195761413', 'prec': 103}, 'szpiro_ratio': 4.121676636097447, '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, -2, -3, 0, 0, -6, 0, 1, -2, 0, -1, 1, 0, 4, 0], 'aplist': [1, 0, 0, -2, -6, 1, 1, 4, 0, 6, 10, 4, 0, -12, 8, 2, 8, -10, -12, -2, -4, -4, -12, 6, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 49725, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '49725.v', 'trace_hash': 715022909681034535}
• 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': '0.051385905633302221126182094449', 'prec': 107}, 'conductor': 49725, 'gens': [], 'heights': [], 'lmfdb_label': '49725.v2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.67114093784091479660718491102', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3422818756818295932143698220363197349', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[144, -72, 1]], 'xcoord_integral_points': [144]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': 'a', '5': 'a', '13': [1, 0], '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '49725.v2'}
• ec_torsion_growth •

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

  
  
  • id: 2417812
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '49725.v2', 'torsion': [2, 2]}
  • id: 2417813
    {'degree': 4, 'field': [204, 42, -35, -1, 1], 'lmfdb_label': '49725.v2', 'torsion': [4]}
  • id: 2417816
    {'degree': 8, 'field': [-12951, -282, 201, -471, -240, 42, 15, -4, 1], 'lmfdb_label': '49725.v2', 'torsion': [6]}
  • id: 2417814
    {'degree': 8, 'field': [-1989, -5967, 13779, -8232, 1348, 256, -79, -1, 1], 'lmfdb_label': '49725.v2', 'torsion': [2, 4]}
  • id: 2417815
    {'degree': 8, 'field': [470916, 102132, 103005, 972, 5014, -142, 110, -2, 1], 'lmfdb_label': '49725.v2', 'torsion': [2, 4]}
  • id: 2417817
    {'degree': 16, 'field': [-617154876, -1706251716, -606450078, 782846532, 78173667, -9254466, -8371350, -2373930, 1178076, -88812, -9596, -4906, -202, 422, -58, -4, 1], 'lmfdb_label': '49725.v2', 'torsion': [8]}
  • id: 2417818
    {'degree': 16, 'field': [11094859, 9676092, -20165031, -26557681, -19077407, -2917368, 617793, 423815, -167613, -54427, -15945, 10236, 820, -292, -33, 0, 1], 'lmfdb_label': '49725.v2', 'torsion': [2, 6]}
• 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: 1189540
    {'conductor': 49725, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '49725.v2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1189541
    {'conductor': 49725, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '49725.v2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1189542
    {'conductor': 49725, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '49725.v2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1189543
    {'conductor': 49725, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '49725.v2', '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: 1995010
    {'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': 49725, 'lmfdb_label': '49725.v2', 'prime': 0}
  • id: 213982
    {'conductor': 49725, 'elladic_image': '2.3.0.1', 'lmfdb_label': '49725.v2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 49725.v does not appear in ec_padic