Elliptic curve data - 726.c3

Formats: - HTML - YAML - JSON - 2025-09-08T07:09:23.321071

• 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': '726c', 'Clabel': '726c4', 'Cnumber': 4, 'abc_quality': 1.0250656507343525, 'absD': 4201862785362, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [1, 1, 0, -1454, 100302], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 726, 'degree': 1920, 'elladic_images': ['8.12.0.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1039937355485144005447149799', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [-192100033, 2371842], 'lmfdb_iso': '726.c', 'lmfdb_label': '726.c3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -12, -81], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.d.1', '24.24.0-8.d.1.3', '44.12.0-4.c.1.1', '88.24.0.?', '264.48.0.?'], '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, 4, 121], [3, 4, 242], [11, 72, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.094953900850670871486256809082', 'prec': 110}, 'szpiro_ratio': 5.5509368427869425, '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, 2, 1, 4, -1, 1, -2, 0, -1, 6, -4, -2, 1, -2, -1, -4, 2], 'aplist': [-1, -1, 2, 4, 0, 6, -2, -4, 4, -6, 0, 6, 6, -4, -12, 2, 12, 14, 4, -12, 6, 4, -4, 10, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 726, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '726.c', 'trace_hash': 328687328404034670}
• 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': '0.10992164654919684688552429311', 'prec': 103}, 'conductor': 726, 'gens': [], 'heights': [], 'lmfdb_label': '726.c3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.66153389354131456201320487725', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3230677870826291240264097545082708366', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-229, 229, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 1], '3': [0, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '726.c3'}
• ec_torsion_growth •

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

  
  
  • id: 34024
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [4]}
  • id: 34023
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [2, 2]}
  • id: 34025
    {'degree': 2, 'field': [22, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [4]}
  • id: 34026
    {'degree': 4, 'field': [25, 0, 12, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [2, 4]}
  • id: 34028
    {'degree': 8, 'field': [1, 0, -3, 0, -4, 0, -3, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [8]}
  • id: 34029
    {'degree': 8, 'field': [4, 0, 32, 0, 258, 0, -16, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [8]}
  • id: 34030
    {'degree': 8, 'field': [284, -587, 422, -215, 83, 13, -5, -4, 1], 'lmfdb_label': '726.c3', 'torsion': [6]}
  • id: 34027
    {'degree': 8, 'field': [324, 0, 0, 0, 14, 0, 0, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [2, 4]}
  • id: 34032
    {'degree': 16, 'field': [1, 0, -12, 0, 172, 0, 360, 0, 639, 0, 360, 0, 172, 0, -12, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [2, 8]}
  • id: 34033
    {'degree': 16, 'field': [1, 0, 12, 0, -47, 0, 108, 0, 336, 0, 108, 0, -47, 0, 12, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [2, 8]}
  • id: 34035
    {'degree': 16, 'field': [1024, 0, -22267, 0, 17614, 0, -7521, 0, 3519, 0, -1185, 0, 211, 0, -22, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [12]}
  • id: 34031
    {'degree': 16, 'field': [6561, 0, -14580, 0, 16200, 0, -12600, 0, 6079, 0, -1400, 0, 200, 0, -20, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [4, 4]}
  • id: 34034
    {'degree': 16, 'field': [121104, 0, -53520, 0, 44548, 0, 6552, 0, 912, 0, 636, 0, 84, 0, 12, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [2, 6]}
  • id: 34036
    {'degree': 16, 'field': [262144, 0, 2850176, 0, 1127296, 0, 240672, 0, 56304, 0, 9480, 0, 844, 0, 44, 0, 1], 'lmfdb_label': '726.c3', 'torsion': [12]}
• 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: 9144
    {'conductor': 726, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '726.c3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9145
    {'conductor': 726, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '726.c3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9146
    {'conductor': 726, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '726.c3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1669272
    {'adelic_gens': [[89, 8, 92, 33], [1, 0, 8, 1], [232, 107, 169, 198], [168, 41, 193, 240], [1, 8, 0, 1], [7, 6, 258, 259], [1, 4, 4, 17], [257, 8, 256, 9], [119, 256, 212, 231]], 'adelic_image': '264.48.0.?', 'conductor': 726, 'lmfdb_label': '726.c3', 'prime': 0}
  • id: 3321
    {'conductor': 726, 'elladic_image': '8.12.0.16', 'lmfdb_label': '726.c3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 726.c does not appear in ec_padic