Elliptic curve data - 66.c3

Formats: - HTML - YAML - JSON - 2025-03-17T13:52:08.379250

• 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': '66c', 'Clabel': '66c1', 'Cnumber': 1, 'abc_quality': 1.073399617726021, 'absD': 2737152, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 1320, 'ainvs': [1, 0, 0, -45, 81], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 66, 'degree': 20, 'elladic_images': ['8.6.0.4', '5.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.056865689820502529185104012521', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [10091699281, 2737152], 'lmfdb_iso': '66.c', 'lmfdb_label': '66.c3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -45, 81], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '5B.1.1'], 'modm_images': ['2.3.0.a.1', '5.24.0-5.a.1.2', '8.6.0.d.1', '10.72.0-10.a.2.1', '40.144.1-40.t.2.4', '66.6.0.a.1', '264.12.0.?', '330.144.1.?', '1320.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 33], [3, 4, 22], [5, 2, 11], [11, 12, 6]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.056865689820502529185104012521', 'prec': 110}, 'szpiro_ratio': 5.498061412664101, 'torsion': 10, 'torsion_primes': [2, 5], 'torsion_structure': [10]}
• 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, -4, 1, -2, 1, 1, -4, 1, 1, 4, -2, -4, 1, -2, 1, 0, -4], 'aplist': [1, 1, -4, -2, 1, 4, -2, 0, -6, 10, -8, -2, 2, 4, -2, 4, 0, -8, -12, 2, -6, 10, 4, 10, -2], 'class_deg': 10, 'class_size': 4, 'conductor': 66, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '66.c', 'trace_hash': 603621058800683965}
• 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': '1.1204511084773999625496993614', 'prec': 100}, 'conductor': 66, 'gens': [], 'heights': [], 'lmfdb_label': '66.c3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.3832296312249704263120506255', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1916148156124852131560253127523339057', 'prec': 130}, 'tamagawa_product': 50, 'torsion_generators': [[0, 9, 1]], 'xcoord_integral_points': [-6, 0, 2, 6, 18]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [1, 0], '5': [2, 0], '11': [1, 0]}, 'iwp0': 7, 'lmfdb_label': '66.c3'}
• ec_torsion_growth •

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

  
  
  • id: 2391
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '66.c3', 'torsion': [2, 10]}
  • id: 2392
    {'degree': 4, 'field': [2, 0, 1, -2, 1], 'lmfdb_label': '66.c3', 'torsion': [20]}
  • id: 2394
    {'degree': 8, 'field': [-24, -96, -18, 84, 31, -14, -6, -2, 1], 'lmfdb_label': '66.c3', 'torsion': [2, 20]}
  • id: 2395
    {'degree': 8, 'field': [-18, -36, 18, 35, -14, -7, 7, -4, 1], 'lmfdb_label': '66.c3', 'torsion': [30]}
  • id: 2393
    {'degree': 8, 'field': [256, 128, 16, 32, 42, -8, 1, -2, 1], 'lmfdb_label': '66.c3', 'torsion': [2, 20]}
  • id: 2397
    {'degree': 16, 'field': [4, 0, -17, 0, -449, 0, -3821, 0, 4951, 0, 1693, 0, -59, 0, 1, 0, 1], 'lmfdb_label': '66.c3', 'torsion': [2, 30]}
  • id: 2396
    {'degree': 16, 'field': [1188, -3168, 5280, -4224, 1500, 1632, -2648, 2416, -1299, 88, 340, -312, 214, -104, 36, -8, 1], 'lmfdb_label': '66.c3', 'torsion': [40]}
  • id: 2398
    {'degree': 20, 'field': [1, 4, 14, 54, 214, -88, -424, -114, 346, -894, -466, 1348, 1538, -782, 58, 88, -32, 18, -2, -2, 1], 'lmfdb_label': '66.c3', 'torsion': [5, 10]}
• 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: 361
    {'conductor': 66, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '66.c3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 362
    {'conductor': 66, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '66.c3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 363
    {'conductor': 66, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '66.c3', 'prime': 11, '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: 1666056
    {'adelic_gens': [[1301, 20, 1300, 21], [1, 20, 0, 1], [661, 6, 0, 1], [1, 10, 10, 101], [531, 20, 1300, 1187], [11, 16, 1080, 971], [1, 0, 20, 1], [6, 13, 355, 1136], [991, 20, 0, 1], [606, 13, 875, 1136]], 'adelic_image': '1320.288.5.?', 'conductor': 66, 'lmfdb_label': '66.c3', 'prime': 0}
  • id: 212
    {'conductor': 66, 'elladic_image': '8.6.0.4', 'lmfdb_label': '66.c3', 'modell_image': '2B', 'prime': 2}
  • id: 213
    {'conductor': 66, 'elladic_image': '5.24.0.1', 'lmfdb_label': '66.c3', 'modell_image': '5B.1.1', 'prime': 5}
• lmfdb_iso 66.c does not appear in ec_padic