Elliptic curve data - 490110.v1

Formats: - HTML - YAML - JSON - 2026-04-28T16:25:01.697995

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '490110v', 'Clabel': '490110v1', 'Cnumber': 1, 'abc_quality': 0.9625177756957166, 'absD': 2773958946871536783720, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 680, 'ainvs': [1, 1, 0, -198203867, 1073950127589], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 17, 31], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 490110, 'degree': 124992000, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3384873820438779057037784788', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1], 'jinv': [-1009639969667617081, 3252418920], 'lmfdb_iso': '490110.v', 'lmfdb_label': '490110.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -206248, -36069442], 'min_quad_twist_disc': -31, 'modell_images': [], 'modm_images': ['680.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '16.134506851934666197576862142', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 81685], [3, 4, 81685], [5, 6, 98022], [7, 2, 163370], [17, 18, 28830], [31, 362, 510]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0491625790537804084176689291', 'prec': 100}, 'szpiro_ratio': 5.260723751389233, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 4, -1, 1, -1, -6, -1, -1, -4, -1, 1, -1, -1, -1, 1], 'aplist': [-1, -1, 1, 4, -6, -1, -1, -1, -2, -3, 0, 8, -10, -2, -3, -5, -12, 2, -10, -13, -7, -11, 6, 18, 7], 'class_deg': 1, 'class_size': 1, 'conductor': 490110, 'isogeny_matrix': [[1]], 'lmfdb_iso': '490110.v', 'trace_hash': 580562261218544117}
• 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': '0.0012595827494548239164688792466', 'prec': 110}, 'conductor': 490110, 'gens': [[9049, 142028, 1], [6697259, 528147577, 29]], 'heights': [{'__RealLiteral__': 0, 'data': '3.3676280589896204034205650507', 'prec': 100}, {'__RealLiteral__': 0, 'data': '5.4966237314655038399839686630', 'prec': 100}], 'lmfdb_label': '490110.v1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.12521756549135932410226284400', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.121942010417488931029978860330716781', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [9049]}
• lmfdb_label 490110.v1 does not appear in ec_iwasawa
• lmfdb_label 490110.v1 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: 12083897
    {'conductor': 490110, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '490110.v1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12083898
    {'conductor': 490110, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '490110.v1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 12083899
    {'conductor': 490110, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '490110.v1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 12083900
    {'conductor': 490110, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '490110.v1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12083901
    {'conductor': 490110, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '490110.v1', 'prime': 31, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  {'adelic_gens': [[1, 1, 679, 0], [241, 2, 241, 3], [341, 2, 341, 3], [511, 2, 511, 3], [1, 0, 2, 1], [1, 2, 0, 1], [137, 2, 137, 3], [679, 2, 678, 3]], 'adelic_image': '680.2.0.?', 'conductor': 490110, 'lmfdb_label': '490110.v1', 'prime': 0}
• lmfdb_iso 490110.v does not appear in ec_padic