Elliptic curve data - 347633.r2

Formats: - HTML - YAML - JSON - 2025-10-20T15:05:02.298961

• 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': '347633r', 'Clabel': '347633r2', 'Cnumber': 2, 'abc_quality': 0.8608596561528015, 'absD': 470357594339987281213, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [1, 0, 1, 541472, 1032164967], 'analytic_rank': 0, 'bad_primes': [11, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 347633, 'degree': 18063360, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6467897063315930038369861975', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2], 'jinv': [2053225511, 55006237], 'lmfdb_iso': '347633.r', 'lmfdb_label': '347633.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 26, -351], 'min_quad_twist_disc': -143, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '52.6.0.a.1', '68.6.0.c.1', '884.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 20449], [11, 72, 2873], [13, 98, 2057], [17, 18, 20449]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.16536739120163936377927068773', 'prec': 103}, 'szpiro_ratio': 4.313294684862872, '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, -2, -1, -4, -2, 0, -3, 1, -4, 0, 2, 0, 0, 8, -1, -1, 1, 4, 4], 'aplist': [1, -2, -4, 0, 0, 0, -1, 4, -6, 2, 4, -8, 0, 8, -8, 10, -4, -10, 4, -16, 0, 6, -4, 18, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 347633, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '347633.r', 'trace_hash': 1730002410194197670}
• 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': '0.0050237459786790154497428235433', 'prec': 110}, 'conductor': 347633, 'gens': [], 'heights': [], 'lmfdb_label': '347633.r2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.12496672214177435237204911616', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.49986688856709740948819646462555282807', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-3337, 3333, 2]], 'xcoord_integral_points': []}
• lmfdb_label 347633.r2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 14517755
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '347633.r2', 'torsion': [2, 2]}
  • id: 14517756
    {'degree': 4, 'field': [-274, -197, 67, -1, 1], 'lmfdb_label': '347633.r2', 'torsion': [4]}
  • id: 14517759
    {'degree': 8, 'field': [-131193, 18009, -19242, 2465, -1229, -7, 7, -4, 1], 'lmfdb_label': '347633.r2', 'torsion': [6]}
  • id: 14517758
    {'degree': 8, 'field': [160352, 61072, 35068, 1900, 69, -198, 34, -2, 1], 'lmfdb_label': '347633.r2', 'torsion': [2, 4]}
  • id: 14517757
    {'degree': 8, 'field': [628849, 0, 37856, 0, 4147, 0, 104, 0, 1], 'lmfdb_label': '347633.r2', 'torsion': [2, 4]}
  • id: 14517760
    {'degree': 16, 'field': [154455184, 0, 23019152, 0, -7717021, 0, -360841, 0, -65601, 0, -27522, 0, 2509, 0, -89, 0, 1], 'lmfdb_label': '347633.r2', 'torsion': [8]}
  • id: 14517761
    {'degree': 16, 'field': [2530190601, 0, 6399276057, 0, 979620672, 0, 61982293, 0, 3095117, 0, -47777, 0, -1049, 0, 26, 0, 1], 'lmfdb_label': '347633.r2', '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: 8604800
    {'conductor': 347633, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '347633.r2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8604801
    {'conductor': 347633, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '347633.r2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8604802
    {'conductor': 347633, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '347633.r2', 'prime': 17, '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: 3834836
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [664, 225, 221, 664], [881, 4, 880, 5], [105, 4, 210, 9], [342, 1, 271, 0]], 'adelic_image': '884.12.0.?', 'conductor': 347633, 'lmfdb_label': '347633.r2', 'prime': 0}
  • id: 1203904
    {'conductor': 347633, 'elladic_image': '2.3.0.1', 'lmfdb_label': '347633.r2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 347633.r does not appear in ec_padic