Elliptic curve data - 495495.bt1

Formats: - HTML - YAML - JSON - 2025-10-12T15:33:53.347276

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

  
  {'Ciso': '495495bt', 'Clabel': '495495bt2', 'Cnumber': 2, 'abc_quality': 1.0865926535263044, 'absD': 2000742427776539806734375, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 5460, 'ainvs': [1, -1, 1, -143217317, -656136869066], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 11, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 495495, 'degree': 80870400, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5012949632003393678111193168', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 45, 'isogeny_degrees': [1, 2], 'jinv': [9316717055063573427, 57377784953125], 'lmfdb_iso': '495495.bt', 'lmfdb_label': '495495.bt1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -131513, -18226094], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '156.6.0.?', '420.6.0.?', '1820.6.0.?', '5460.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 6, 'optimality': 2, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.1276528184460848101695562198', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 4719], [3, 2, 11011], [5, 6, 14157], [7, 8, 70785], [11, 62, 4095], [13, 14, 38115]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4783881103000718272337136001', 'prec': 100}, 'szpiro_ratio': 5.182002946317839, '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, 1, 0, 1, 3, 0, -1, 0, 0, 1, -1, 0, -1, -4, 0, 4, -1], 'aplist': [-1, 0, 1, 1, 0, 1, -4, 4, 0, -4, 0, 8, -6, -2, -2, -6, 8, -2, 0, 10, -14, -12, 6, 6, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 495495, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '495495.bt', 'trace_hash': 877008325209759768}
• 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': '0.00090952331406293852537493091382', 'prec': 113}, 'conductor': 495495, 'gens': [[-7198, 45616, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.1276528184460848101695562198', 'prec': 100}], 'lmfdb_label': '495495.bt1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.043657793183139859653945832914', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5733176027946274519219027655594626978', 'prec': 130}, 'tamagawa_product': 240, 'torsion_generators': [[55243, -55247, 2]], 'xcoord_integral_points': [-7198, -6608, 35567]}
• lmfdb_label 495495.bt1 does not appear in ec_iwasawa
• lmfdb_label 495495.bt1 does not appear in ec_torsion_growth
• 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: 12212812
    {'conductor': 495495, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '495495.bt1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 12212813
    {'conductor': 495495, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '495495.bt1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 12212814
    {'conductor': 495495, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '495495.bt1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 12212815
    {'conductor': 495495, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '495495.bt1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 12212816
    {'conductor': 495495, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '495495.bt1', 'prime': 13, '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: 4698242
    {'adelic_gens': [[3644, 1, 1819, 0], [1, 2, 2, 5], [2341, 4, 4682, 9], [2942, 1, 1259, 0], [1, 4, 0, 1], [1, 0, 4, 1], [3, 4, 8, 11], [5457, 4, 5456, 5], [3277, 4, 1094, 9], [4096, 1369, 1365, 4096]], 'adelic_image': '5460.12.0.?', 'conductor': 495495, 'lmfdb_label': '495495.bt1', 'prime': 0}
  • id: 1637008
    {'conductor': 495495, 'elladic_image': '2.3.0.1', 'lmfdb_label': '495495.bt1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 495495.bt does not appear in ec_padic