Elliptic curve data - 206910.cy3

Formats: - HTML - YAML - JSON - 2025-11-07T15:51:23.372160

• 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': '206910be', 'Clabel': '206910be2', 'Cnumber': 2, 'abc_quality': 0.9387086030721215, 'absD': 419597943128100, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 25080, 'ainvs': [1, -1, 1, -206933, 36270281], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 206910, 'degree': 1966080, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7661954982602742441206449961', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 76, 'isogeny_degrees': [1, 2], 'jinv': [758800078561, 324900], 'lmfdb_iso': '206910.cy', 'lmfdb_label': '206910.cy3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -190, 992], 'min_quad_twist_disc': 33, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '24.12.0.b.1', '88.12.0.?', '132.12.0.?', '264.24.0.?', '380.12.0.?', '2280.24.0.?', '8360.24.0.?', '12540.24.0.?', '25080.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2150442357610232620029677919', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1089], [3, 8, 22990], [5, 6, 41382], [11, 62, 1710], [19, 20, 10890]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.017941717527034126392050588657', 'prec': 107}, 'szpiro_ratio': 3.948847612082369, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 1, -1, 0, -4, 1, 0, -1, 0, 0, 2, -4, 0, 1, -2, 0, 1, -1], 'aplist': [1, 0, -1, -4, 0, 2, -2, 1, 8, 6, 4, -10, -2, -12, 0, -6, 0, 10, -4, 8, -2, 12, -8, -6, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 206910, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '206910.cy', 'trace_hash': 1998870241739024676}
• 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': '0.029234931614560649268618833886', 'prec': 107}, 'conductor': 206910, 'gens': [[235, 642, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2150442357610232620029677919', 'prec': 100}], 'lmfdb_label': '206910.cy3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.52240657361002461996676430673', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.2572293567884138192475329233009879615', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-525, 262, 1], [267, -134, 1]], 'xcoord_integral_points': [-525, 235, 267, 531]}
• lmfdb_label 206910.cy3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9050358
    {'degree': 4, 'field': [16, 0, -14, 0, 1], 'lmfdb_label': '206910.cy3', 'torsion': [2, 4]}
  • id: 9050359
    {'degree': 4, 'field': [114, -114, 115, -2, 1], 'lmfdb_label': '206910.cy3', 'torsion': [2, 4]}
  • id: 9050357
    {'degree': 4, 'field': [21904, 0, -274, 0, 1], 'lmfdb_label': '206910.cy3', 'torsion': [2, 4]}
  • id: 9050360
    {'degree': 8, 'field': [-1905120, -374544, 53784, -27756, 8028, -252, -111, -1, 1], 'lmfdb_label': '206910.cy3', 'torsion': [2, 6]}
  • id: 9050363
    {'degree': 16, 'field': [-2159124, -1806288, 7908648, 1855392, -9076592, 2553064, 1747556, -742416, -76763, 71480, -5216, -4072, 538, 240, -28, -8, 1], 'lmfdb_label': '206910.cy3', 'torsion': [2, 8]}
  • id: 9050364
    {'degree': 16, 'field': [4044315456, 69451200, -182452512, 224494944, -107567708, -8172996, 7009806, -3720718, 991265, -43558, 11708, -1858, 522, -126, 38, -8, 1], 'lmfdb_label': '206910.cy3', 'torsion': [2, 8]}
  • id: 9050361
    {'degree': 16, 'field': [125019158944, 15694288960, -34226904480, -2923797632, 4687473562, 219057076, -395085530, -7431928, 21348081, 78680, -735910, 1288, 15640, -28, -188, 0, 1], 'lmfdb_label': '206910.cy3', 'torsion': [4, 4]}
  • id: 9050362
    {'degree': 16, 'field': [23513781991396, -3486871807936, 3657816764496, -343973477504, 177146185236, -6052640592, 1785836128, 199613008, -50931603, 331976, 289732, -197496, 35646, -1288, 204, -8, 1], 'lmfdb_label': '206910.cy3', 'torsion': [2, 8]}
• 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: 5125167
    {'conductor': 206910, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '206910.cy3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5125168
    {'conductor': 206910, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '206910.cy3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5125169
    {'conductor': 206910, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '206910.cy3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5125170
    {'conductor': 206910, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '206910.cy3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5125171
    {'conductor': 206910, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '206910.cy3', 'prime': 19, '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: 2988317
    {'adelic_gens': [[1, 0, 4, 1], [25077, 4, 25076, 5], [1, 4, 0, 1], [24003, 6842, 23518, 18239], [12541, 13684, 6842, 2289], [573, 13684, 2288, 9131], [8359, 11396, 9878, 22791], [21891, 6842, 8206, 18239], [15959, 0, 0, 25079]], 'adelic_image': '25080.48.0.?', 'conductor': 206910, 'lmfdb_label': '206910.cy3', 'prime': 0}
  • id: 764408
    {'conductor': 206910, 'elladic_image': '2.6.0.1', 'lmfdb_label': '206910.cy3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 206910.cy does not appear in ec_padic