Elliptic curve data - 492765.d3

Formats: - HTML - YAML - JSON - 2025-11-02T21:19:28.574953

• 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': '492765d', 'Clabel': '492765d4', 'Cnumber': 4, 'abc_quality': 0.9573510240464985, 'absD': 308555361411787035, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 69160, 'ainvs': [1, 1, 1, -35566, 26835014], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 13, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 492765, 'degree': 6193152, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0356997748748541830972748810', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4], 'jinv': [-105756712489, 6558605235], 'lmfdb_iso': '492765.d', 'lmfdb_label': '492765.d3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -99, -3923], 'min_quad_twist_disc': -19, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '70.6.0.a.1', '140.12.0.?', '380.12.0.?', '520.12.0.?', '532.12.0.?', '728.12.0.?', '1976.12.0.?', '2660.24.0.?', '3640.24.0.?', '9880.24.0.?', '13832.24.0.?', '69160.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.0279034439097482531967198493', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 12635], [3, 4, 164255], [5, 6, 98553], [7, 8, 70395], [13, 14, 37905], [19, 182, 1365]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56348028529163395309276116506', 'prec': 103}, 'szpiro_ratio': 3.641704237109148, '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, -1, -1, -1, 1, -1, 3, 1, 1, 4, 1, 1, 1, 1, -1, 6, -1, 0, 1], 'aplist': [-1, -1, -1, -1, 4, 1, 6, 0, -4, 2, 4, -10, 2, 8, 8, -6, -8, -10, 12, 8, 6, -8, -4, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 492765, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '492765.d', 'trace_hash': 1198153335468142832}
• 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': '0.017053504569951408823352381096', 'prec': 107}, 'conductor': 492765, 'gens': [[-157, 5424, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.0279034439097482531967198493', 'prec': 100}], 'lmfdb_label': '492765.d3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25316547820731903496994232044', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0789044062012746412947552504440261395', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-1357, 1353, 2]], 'xcoord_integral_points': [-157]}
• lmfdb_label 492765.d3 does not appear in ec_iwasawa
• lmfdb_label 492765.d3 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: 12145350
    {'conductor': 492765, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '492765.d3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 12145351
    {'conductor': 492765, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '492765.d3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12145352
    {'conductor': 492765, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '492765.d3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12145353
    {'conductor': 492765, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '492765.d3', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 12145354
    {'conductor': 492765, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '492765.d3', 'prime': 19, '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: 4682338
    {'adelic_gens': [[43679, 0, 0, 69159], [15296, 61883, 10925, 43682], [1, 0, 8, 1], [1, 8, 0, 1], [69153, 8, 69152, 9], [1, 4, 4, 17], [7, 6, 69154, 69155], [47881, 3648, 20444, 14593], [18659, 18658, 23218, 21395], [42124, 43681, 26543, 10926], [20483, 35036, 38722, 36861]], 'adelic_image': '69160.48.0.?', 'conductor': 492765, 'lmfdb_label': '492765.d3', 'prime': 0}
  • id: 1629091
    {'conductor': 492765, 'elladic_image': '4.6.0.1', 'lmfdb_label': '492765.d3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 492765.d does not appear in ec_padic