Elliptic curve data - 266910.ck5

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• 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': '266910ck', 'Clabel': '266910ck2', 'Cnumber': 2, 'abc_quality': 1.0261933759868158, 'absD': 7185070196198556975129600000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 101680, 'ainvs': [1, 0, 0, -136184310140, 19343222133507600], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31, 41], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 266910, 'degree': 1660944384, 'elladic_images': ['8.96.0.40'], 'faltings_height': {'__RealLiteral__': 0, 'data': '5.0277689432546138722320191212', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 62, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [279321867933339260687315798724918183361, 7185070196198556975129600000000], 'lmfdb_iso': '266910.ck', 'lmfdb_label': '266910.ck5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -136184310140, 19343222133507600], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.3', '8.96.0-8.l.2.2', '80.192.1.?', '124.48.0.?', '248.192.1.?', '656.192.2.?', '2480.384.5.?', '3280.384.5.?', '20336.384.5.?', '101680.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 22, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.6283289778518393089240540522', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 1], [3, 4, 88970], [5, 6, 53382], [7, 8, 38130], [31, 32, 8610], [41, 42, 6510]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '5.0277689432546138722320191212', 'prec': 100}, 'szpiro_ratio': 7.085057130107852, 'torsion': 16, 'torsion_primes': [2], 'torsion_structure': [2, 8]}
• 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, -1, 1, 1, 1, -4, 1, -2, -1, 1, 1, 2, 1, 4, 1], 'aplist': [1, 1, 1, -1, -4, -2, 2, 4, 8, -2, -1, -10, 1, -4, 0, 6, -4, -2, -12, -8, -6, 0, 4, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 266910, 'isogeny_matrix': [[1, 16, 2, 4, 8, 16, 8, 4], [16, 1, 8, 4, 2, 4, 8, 16], [2, 8, 1, 2, 4, 8, 4, 2], [4, 4, 2, 1, 2, 4, 2, 4], [8, 2, 4, 2, 1, 2, 4, 8], [16, 4, 8, 4, 2, 1, 8, 16], [8, 8, 4, 2, 4, 8, 1, 8], [4, 16, 2, 4, 8, 16, 8, 1]], 'lmfdb_iso': '266910.ck', 'trace_hash': 931246050644346581}
• 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': '0.000042947252276810832521157722735', 'prec': 117}, 'conductor': 266910, 'gens': [[201630, 8931810, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.6283289778518393089240540522', 'prec': 100}], 'lmfdb_label': '266910.ck5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.021858830300185668783235423915', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '15.747672064061544830669644968835662019', 'prec': 130}, 'tamagawa_product': 32768, 'torsion_generators': [[-426120, 213060, 1], [216760, 2784580, 1]], 'xcoord_integral_points': [-426120, -19400, 181480, 201630, 209380, 213880, 216760, 223402, 246280, 578380, 1943680, 2404120]}
• lmfdb_label 266910.ck5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11420217
    {'degree': 4, 'field': [64, 0, -15, 0, 1], 'lmfdb_label': '266910.ck5', 'torsion': [4, 8]}
  • id: 11420219
    {'degree': 4, 'field': [81, 0, -23, 0, 1], 'lmfdb_label': '266910.ck5', 'torsion': [2, 16]}
  • id: 11420218
    {'degree': 4, 'field': [97974, -646, 647, -2, 1], 'lmfdb_label': '266910.ck5', 'torsion': [2, 16]}
  • id: 11420220
    {'degree': 8, 'field': [-577630128, 0, 14841308, 0, -83256, 0, 0, 0, 1], 'lmfdb_label': '266910.ck5', 'torsion': [2, 24]}
  • id: 11420223
    {'degree': 16, 'field': [5499025, 0, -8896340, 0, 14850466, 0, -8639652, 0, 2385219, 0, -216396, 0, 8554, 0, -152, 0, 1], 'lmfdb_label': '266910.ck5', 'torsion': [4, 16]}
  • id: 11420222
    {'degree': 16, 'field': [1763496036, -2387610864, 1616302368, -773312952, 287036632, -82083904, 17608712, -1934380, -91851, -21560, 5872, 3976, 642, -232, 8, -4, 1], 'lmfdb_label': '266910.ck5', 'torsion': [4, 16]}
  • id: 11420225
    {'degree': 16, 'field': [210601447140551855056, -26300810957433655616, -907173698146931968, -136905758762346544, -62690954757716176, 1411614357049784, 119213283165228, 6904085029764, 1433462793223, 15393612366, -498171027, -7014982, -2479510, -16378, 401, -2, 1], 'lmfdb_label': '266910.ck5', 'torsion': [2, 32]}
  • id: 11420221
    {'degree': 16, 'field': [630738110250000000000, 0, -334695829392000000, 0, -16292222206507100, 0, 3684576879092, 0, 156703753561, 0, -4208936, 0, -651338, 0, -28, 0, 1], 'lmfdb_label': '266910.ck5', 'torsion': [8, 8]}
  • id: 11420224
    {'degree': 16, 'field': [30931479257724777206430, -7117515156057098403240, 847531560715034392080, -60179047507304045370, 3722558940209717271, -174494822258774250, 8263383993730008, -301940685672168, 10013620228129, -349076708428, 9146917696, -248490106, 7554457, -82306, 4456, -4, 1], 'lmfdb_label': '266910.ck5', 'torsion': [2, 32]}
• 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: 6616618
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '266910.ck5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 6616619
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '266910.ck5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 6616620
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '266910.ck5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 6616621
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '266910.ck5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6616622
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '266910.ck5', 'prime': 31, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6616623
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '266910.ck5', 'prime': 41, 'reduction_type': 1, '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: 3352891
    {'adelic_gens': [[1, 16, 0, 1], [15, 16, 74, 38209], [81849, 16, 42228, 121], [32801, 16, 95126, 97], [1, 0, 16, 1], [101665, 16, 101664, 17], [1, 16, 4, 65], [81353, 8, 20292, 101641], [5, 16, 4, 76273]], 'adelic_image': '101680.768.13.?', 'conductor': 266910, 'lmfdb_label': '266910.ck5', 'prime': 0}
  • id: 955709
    {'conductor': 266910, 'elladic_image': '8.96.0.40', 'lmfdb_label': '266910.ck5', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 266910.ck does not appear in ec_padic