Elliptic curve data - 206910.eo1

Formats: - HTML - YAML - JSON - 2024-05-07T23:15:43.345149

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '206910q', 'Clabel': '206910q4', 'Cnumber': 4, 'abc_quality': 0.962838731498289, 'absD': 57510682994531250, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 5016, 'ainvs': [1, -1, 1, -676292, -213586491], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 206910, 'degree': 2621440, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1111713299847940525890318668', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 118, 'isogeny_degrees': [1, 2, 4], 'jinv': [26487576322129, 44531250], 'lmfdb_iso': '206910.eo', 'lmfdb_label': '206910.eo1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -621, -6207], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '264.24.0.?', '456.24.0.?', '836.12.0.?', '1672.24.0.?', '5016.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.36291754925155393486043745936', 'prec': 103}, 'szpiro_ratio': 4.239099357668444, '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, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, -2, 0, 0, 1, 2, 0, 1, 1], 'aplist': [1, 0, 1, 0, 0, -2, 2, 1, -4, 6, 4, -6, 10, 4, 12, -6, 12, 2, 4, -8, 6, 4, -12, -10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 206910, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '206910.eo', 'trace_hash': 761869260632119124}
• 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': '0.014664250880825615172478689906', 'prec': 107}, 'conductor': 206910, 'gens': [], 'heights': [], 'lmfdb_label': '206910.eo1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16649833600766783293977403190', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.3279467522453706540727690208067124682', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-1957, 1953, 2]], 'xcoord_integral_points': []}
• lmfdb_label 206910.eo1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9050207
    {'degree': 2, 'field': [-114, 0, 1], 'lmfdb_label': '206910.eo1', 'torsion': [2, 2]}
  • id: 9050208
    {'degree': 2, 'field': [66, 0, 1], 'lmfdb_label': '206910.eo1', 'torsion': [4]}
  • id: 9050209
    {'degree': 2, 'field': [209, 0, 1], 'lmfdb_label': '206910.eo1', 'torsion': [4]}
  • id: 9050210
    {'degree': 4, 'field': [2025, 0, -24, 0, 1], 'lmfdb_label': '206910.eo1', 'torsion': [2, 4]}
  • id: 9050211
    {'degree': 8, 'field': [-3333600, -437760, 143712, 21888, 7476, -912, -180, 0, 1], 'lmfdb_label': '206910.eo1', 'torsion': [2, 4]}
  • id: 9050214
    {'degree': 8, 'field': [-2793017, -913485, -169682, 38849, -4650, -193, -20, -3, 1], 'lmfdb_label': '206910.eo1', 'torsion': [6]}
  • id: 9050212
    {'degree': 8, 'field': [100246, -6600, 7228, -1256, 629, -4, 6, -4, 1], 'lmfdb_label': '206910.eo1', 'torsion': [8]}
  • id: 9050213
    {'degree': 8, 'field': [3170512, 171568, 223360, 592, 5734, -206, 91, -2, 1], 'lmfdb_label': '206910.eo1', 'torsion': [8]}
  • id: 9050217
    {'degree': 16, 'field': [46990450, -73694920, 131419364, -124619688, 85449074, -28286816, 10075864, -129000, -470477, 290616, -15056, -21640, 2090, 672, -76, -8, 1], 'lmfdb_label': '206910.eo1', 'torsion': [2, 8]}
  • id: 9050215
    {'degree': 16, 'field': [43409722500, -11400912000, 1497139200, -157101120, 1101517596, -105563088, -9980928, -13493952, 6309981, 414504, 103968, -35568, 4362, -456, 0, 0, 1], 'lmfdb_label': '206910.eo1', 'torsion': [4, 4]}
  • id: 9050216
    {'degree': 16, 'field': [162026621128, 46029509584, 40011620168, 6972746736, 3573860300, 304710224, 157213336, 14688, 4903366, -222300, 167578, -5852, 3875, -300, 50, -4, 1], 'lmfdb_label': '206910.eo1', 'torsion': [2, 8]}
  • id: 9050219
    {'degree': 16, 'field': [440173863936, 0, 2535478272, 0, -472454912, 0, 958333344, 0, 38461920, 0, 202184, 0, 5748, 0, 132, 0, 1], 'lmfdb_label': '206910.eo1', 'torsion': [12]}
  • id: 9050218
    {'degree': 16, 'field': [6780495830575, -15021043989450, 10118642514725, -1376389809470, -261441038720, 139614001790, 2190056343, -3923123186, -133385232, 88264738, -5348793, -536026, 44128, 1786, -259, -6, 1], 'lmfdb_label': '206910.eo1', 'torsion': [2, 6]}
  • id: 9050220
    {'degree': 16, 'field': [40349885848336, 0, 8252228832928, 0, 672054533788, 0, 26772236881, 0, 581487970, 0, 8085241, 0, 75373, 0, 418, 0, 1], 'lmfdb_label': '206910.eo1', '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: 5125062
    {'conductor': 206910, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '206910.eo1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5125063
    {'conductor': 206910, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '206910.eo1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5125064
    {'conductor': 206910, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '206910.eo1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 5125065
    {'conductor': 206910, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '206910.eo1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5125066
    {'conductor': 206910, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '206910.eo1', 'prime': 19, '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: 2988396
    {'adelic_gens': [[2003, 1540, 3410, 2685], [911, 0, 0, 5015], [1, 0, 8, 1], [5009, 8, 5008, 9], [296, 2277, 2123, 4102], [1, 8, 0, 1], [1, 4, 4, 17], [320, 2739, 1397, 914], [1200, 4169, 3355, 606], [7, 6, 5010, 5011]], 'adelic_image': '5016.48.0.?', 'conductor': 206910, 'lmfdb_label': '206910.eo1', 'prime': 0}
  • id: 764480
    {'conductor': 206910, 'elladic_image': '8.12.0.11', 'lmfdb_label': '206910.eo1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 206910.eo does not appear in ec_padic