Elliptic curve data - 266910.ck2

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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': '266910ck3', 'Cnumber': 3, 'abc_quality': 1.0391198239885415, 'absD': 757051842880264964991840000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 203360, 'ainvs': [1, 0, 0, -2178935510140, 1237982811464867600], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31, 41], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 266910, 'degree': 3321888768, 'elladic_images': ['16.96.0.95'], 'faltings_height': {'__RealLiteral__': 0, 'data': '5.3743425335345865269406351819', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 62, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [1144081181272479239133643526834383042983361, 757051842880264964991840000], 'lmfdb_iso': '266910.ck', 'lmfdb_label': '266910.ck2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -2178935510140, 1237982811464867600], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.48.0-8.bb.1.1', '16.96.0-16.v.1.2', '124.24.0.?', '160.192.1.?', '248.96.0.?', '496.192.1.?', '1312.192.2.?', '3280.192.2.?', '4960.384.5.?', '6560.384.5.?', '40672.384.5.?', '101680.384.5.?', '203360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.256657955703678617848108104', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 31], [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': '5.3743425335345865269406351819', 'prec': 100}, 'szpiro_ratio': 7.7507609681964835, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [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': '0.000021473626138405416260578861367', 'prec': 117}, 'conductor': 266910, 'gens': [[69048190, -68757760, 9]], 'heights': [{'__RealLiteral__': 0, 'data': '11.256657955703678617848108104', 'prec': 100}], 'lmfdb_label': '266910.ck2', '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': 4096, 'torsion_generators': [[852260, -392920, 1]], 'xcoord_integral_points': [852260, 853880, 985100]}
• lmfdb_label 266910.ck2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11420228
    {'degree': 2, 'field': [-6355, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [16]}
  • id: 11420227
    {'degree': 2, 'field': [-51, -1, 1], 'lmfdb_label': '266910.ck2', 'torsion': [16]}
  • id: 11420226
    {'degree': 2, 'field': [-31, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [2, 8]}
  • id: 11420229
    {'degree': 4, 'field': [369, 164, -163, -2, 1], 'lmfdb_label': '266910.ck2', 'torsion': [2, 16]}
  • id: 11420234
    {'degree': 8, 'field': [-577630128, 0, 14841308, 0, -83256, 0, 0, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [24]}
  • id: 11420231
    {'degree': 8, 'field': [1442024676, 0, 455704, 0, -75944, 0, 4, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [2, 16]}
  • id: 11420233
    {'degree': 8, 'field': [677283764436, -53080914096, 4506950808, 31918900, 4635061, 159190, -1268, -2, 1], 'lmfdb_label': '266910.ck2', 'torsion': [32]}
  • id: 11420230
    {'degree': 8, 'field': [6520045619844, 0, 30641272, 0, -5106872, 0, 4, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [4, 8]}
  • id: 11420232
    {'degree': 8, 'field': [24823512582400, 0, -71496292000, 0, 61194140, 0, -14350, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [32]}
  • id: 11420239
    {'degree': 16, 'field': [-1453512781238319, 9054721102100832, -8756147666759736, -589891431319440, 276840593794890, 21632406983144, -7054555519576, -133954974808, 33524503055, -22802320, 3517400, 576328, -102182, 2800, -380, -8, 1], 'lmfdb_label': '266910.ck2', 'torsion': [48]}
  • id: 11420238
    {'degree': 16, 'field': [12008761513956, 0, -976465803528, 0, 91053246996, 0, 1775955869, 0, -48813034, 0, -756679, 0, -4619, 0, -62, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [2, 24]}
  • id: 11420235
    {'degree': 16, 'field': [1546379298712070001, 0, 60221082461952712, 0, 417826974740458, 0, -2387688984556, 0, 15744447995, 0, 23231444, 0, -77842, 0, 412, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [4, 16]}
  • id: 11420236
    {'degree': 16, 'field': [1628994983856100000000, 0, -139628141473380000000, 0, 3294883582329150000, 0, -27140263437210000, 0, 91429443795025, 0, -135093396900, 0, 81635715, 0, -17220, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [2, 32]}
  • id: 11420237
    {'degree': 16, 'field': [200549804630115315063105, 18008578638662203451790, 1880898729996405773790, 95215452068680986270, 4364114048192676536, 101410236759806454, 3403684934606082, 91746835208278, 3919992247998, -16020269982, -277594182, -28396782, 1000488, -22822, -618, -6, 1], 'lmfdb_label': '266910.ck2', 'torsion': [2, 32]}
  • id: 11420240
    {'degree': 16, 'field': [350250173266897696267321344, 0, -47411532362301527107657728, 0, 306677266895101354030080, 0, -4186690917216961536, 0, -440091820277760, 0, 1671557929856, 0, -46227552, 0, 0, 0, 1], 'lmfdb_label': '266910.ck2', 'torsion': [48]}
• 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: 6616624
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '266910.ck2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 6616625
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 32, 'j_denominator_valuation': 32, 'kodaira_symbol': 36, 'lmfdb_label': '266910.ck2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 32}
  • id: 6616626
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '266910.ck2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6616627
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '266910.ck2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6616628
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '266910.ck2', 'prime': 31, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6616629
    {'conductor': 266910, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '266910.ck2', 'prime': 41, '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: 3352888
    {'adelic_gens': [[1, 0, 32, 1], [1, 32, 0, 1], [203329, 32, 203328, 33], [5, 28, 68, 381], [32832, 29, 199627, 2562], [38162, 19, 87215, 202318], [23, 18, 200798, 201355], [177943, 2, 177914, 203343], [162711, 26, 38134, 200491], [39703, 26, 124774, 875]], 'adelic_image': '203360.768.13.?', 'conductor': 266910, 'lmfdb_label': '266910.ck2', 'prime': 0}
  • id: 955706
    {'conductor': 266910, 'elladic_image': '16.96.0.95', 'lmfdb_label': '266910.ck2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 266910.ck does not appear in ec_padic