Elliptic curve data - 42042.ck1

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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': '42042ck', 'Clabel': '42042ck6', 'Cnumber': 6, 'abc_quality': 1.0439991800655393, 'absD': 34518639405246994998, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1232, 'ainvs': [1, 1, 1, -13300745907, 590415883494219], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42042, 'degree': 37748736, 'elladic_images': ['16.48.0.126'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.0771718391898389000448166242', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 62, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [2211889682389423686563629156897, 293403593785302], 'lmfdb_iso': '42042.ck', 'lmfdb_label': '42042.ck1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -271443794, -1721367884082], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '16.48.0-8.bb.2.8', '28.12.0-4.c.1.1', '56.48.0-8.bb.2.5', '88.48.0.?', '112.96.0.?', '176.96.0.?', '616.96.0.?', '1232.192.1.?'], '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, 'serre_invariants': [[2, 4, 539], [3, 4, 14014], [7, 32, 858], [11, 12, 3822], [13, 14, 3234]], 'sha': 16, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.1042167646621822474921402525', 'prec': 100}, 'szpiro_ratio': 7.659553841628359, '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, -1, 1, 2, -1, 0, 1, 1, 2, 1, -1, -1, 0, -2, 1, 6, 1, 4, 2], 'aplist': [1, -1, 2, 0, 1, -1, 6, 4, 8, -2, 8, 6, -2, -4, 8, -10, 4, 2, 4, 8, -2, 0, 4, 6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 42042, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '42042.ck', 'trace_hash': 57204526350547742}
• 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': '0.00028748390601279762029307195329', 'prec': 113}, 'conductor': 42042, 'gens': [], 'heights': [], 'lmfdb_label': '42042.ck1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.081798054191766916551285831554', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2350754682730826592822932194551431538', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[266339, -266343, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [0, 0], '7': 'a', '11': [1, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '42042.ck1'}
• ec_torsion_growth •

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

  
  
  • id: 2065217
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [4]}
  • id: 2065215
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [2, 2]}
  • id: 2065216
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [4]}
  • id: 2065219
    {'degree': 4, 'field': [1, 0, -9, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [8]}
  • id: 2065220
    {'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [8]}
  • id: 2065218
    {'degree': 4, 'field': [225, 0, -58, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [2, 4]}
  • id: 2065225
    {'degree': 8, 'field': [-11968, -4400, 4004, 791, -392, -7, 7, -4, 1], 'lmfdb_label': '42042.ck1', 'torsion': [6]}
  • id: 2065223
    {'degree': 8, 'field': [169, 0, -278, 0, 143, 0, -26, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [2, 8]}
  • id: 2065221
    {'degree': 8, 'field': [478, -472, 452, 32, 5, -28, 14, -4, 1], 'lmfdb_label': '42042.ck1', 'torsion': [2, 4]}
  • id: 2065222
    {'degree': 8, 'field': [522, 408, -340, -144, 93, -28, 14, -4, 1], 'lmfdb_label': '42042.ck1', 'torsion': [8]}
  • id: 2065224
    {'degree': 8, 'field': [13823524, 0, -3190044, 0, 100386, 0, -858, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [16]}
  • id: 2065231
    {'degree': 16, 'field': [-946663235671, 2160758336820, 4223741156344, 1829232104736, -138322437072, -240459436252, -27524354964, 9048423628, 1629710683, -136607588, -33224340, 729060, 284752, 336, -916, -4, 1], 'lmfdb_label': '42042.ck1', 'torsion': [2, 16]}
  • id: 2065226
    {'degree': 16, 'field': [228484, 0, -209328, 0, 239292, 0, 9552, 0, 11653, 0, -516, 0, -18, 0, -12, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [4, 4]}
  • id: 2065227
    {'degree': 16, 'field': [272484, 0, 521424, 0, 330196, 0, 46512, 0, -4627, 0, 12, 0, 158, 0, -12, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [2, 8]}
  • id: 2065233
    {'degree': 16, 'field': [57274624, 0, -30890816, 0, -9709040, 0, 213984, 0, 33744, 0, -16056, 0, 1576, 0, -56, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [12]}
  • id: 2065232
    {'degree': 16, 'field': [14170727208, 10329574464, -6144144292, -7775285056, 2423620430, 1687664440, -449081423, -93708392, 19071060, 2769906, -422331, -68684, 8869, 1162, -146, -8, 1], 'lmfdb_label': '42042.ck1', 'torsion': [2, 6]}
  • id: 2065234
    {'degree': 16, 'field': [15720102794, -17688126280, 24293731176, -13225120876, 6606399602, 120607872, -224672579, 149729704, -27073236, -6711610, 1147853, 105996, -17575, -70, 30, -8, 1], 'lmfdb_label': '42042.ck1', 'torsion': [12]}
  • id: 2065230
    {'degree': 16, 'field': [743885550144, 0, 0, 0, 0, 0, 0, 0, -1081674, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [16]}
  • id: 2065229
    {'degree': 16, 'field': [191089815778576, 0, 0, 0, 0, 0, 0, 0, -17336527, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '42042.ck1', 'torsion': [16]}
  • id: 2065228
    {'degree': 16, 'field': [2590374059839822, -5293154032, -12825714088, 31351747056, -3562690852, -14250806864, 4275249832, 407155968, -101784011, -4824, 2716, -1288, 518, -168, 44, -8, 1], 'lmfdb_label': '42042.ck1', '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: 997955
    {'conductor': 42042, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42042.ck1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 997956
    {'conductor': 42042, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '42042.ck1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 997957
    {'conductor': 42042, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '42042.ck1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 997958
    {'conductor': 42042, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42042.ck1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 997959
    {'conductor': 42042, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '42042.ck1', 'prime': 13, '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: 1944535
    {'adelic_gens': [[1, 16, 0, 1], [1217, 16, 1216, 17], [1086, 309, 233, 626], [324, 309, 775, 626], [912, 5, 515, 1218], [1, 0, 16, 1], [15, 2, 1134, 1219], [5, 4, 1228, 1229], [879, 1216, 872, 1103]], 'adelic_image': '1232.192.1.?', 'conductor': 42042, 'lmfdb_label': '42042.ck1', 'prime': 0}
  • id: 183772
    {'conductor': 42042, 'elladic_image': '16.48.0.126', 'lmfdb_label': '42042.ck1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 42042.ck does not appear in ec_padic