Elliptic curve data - 66270.k5

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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': '66270m', 'Clabel': '66270m4', 'Cnumber': 4, 'abc_quality': 1.0339287621454463, 'absD': 57285169736590890, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 5640, 'ainvs': [1, 0, 1, -151363, 19510316], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 47], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 66270, 'degree': 847872, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9399336417373261280020950380', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 4, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [35578826569, 5314410], 'lmfdb_iso': '66270.k', 'lmfdb_label': '66270.k5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -69, -194], 'min_quad_twist_disc': -47, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.96.1.dj.4', '40.12.0.v.1', '60.48.0.c.4', '120.192.5.?', '141.8.0.?', '282.24.0.?', '376.12.0.?', '564.48.0.?', '940.12.0.?', '1128.192.1.?', '1880.24.0.?', '2820.96.0.?', '5640.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 11045], [3, 4, 22090], [5, 6, 13254], [47, 1106, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703113', 'prec': 107}, 'szpiro_ratio': 4.2693270103622085, '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, 1, -1, -4, -1, 1, -1, 0, 1, -2, 4, 1, 1, 6, -1, 4, 1], 'aplist': [-1, 1, 1, -4, 0, -2, 6, 4, 0, 6, -8, 2, 6, 4, 0, -6, 0, -10, 4, 0, -2, 8, 12, 18, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 66270, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '66270.k', 'trace_hash': 887332721452784612}
• 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': '0.020653566069352762718039894502', 'prec': 107}, 'conductor': 66270, 'gens': [], 'heights': [], 'lmfdb_label': '66270.k5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.33793771093611342863156256005', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0276262656166805717893753603013828069', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[1159, -1163, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [5, 0], '5': [1, 0], '47': 'a'}, 'iwp0': 5, 'lmfdb_label': '66270.k5'}
• ec_torsion_growth •

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

  
  
  • id: 3162045
    {'degree': 2, 'field': [-235, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [4]}
  • id: 3162044
    {'degree': 2, 'field': [-94, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [4]}
  • id: 3162043
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [2, 2]}
  • id: 3162046
    {'degree': 2, 'field': [12, -1, 1], 'lmfdb_label': '66270.k5', 'torsion': [6]}
  • id: 3162050
    {'degree': 4, 'field': [54, -34, 35, -2, 1], 'lmfdb_label': '66270.k5', 'torsion': [12]}
  • id: 3162049
    {'degree': 4, 'field': [102, -28, 29, -2, 1], 'lmfdb_label': '66270.k5', 'torsion': [12]}
  • id: 3162047
    {'degree': 4, 'field': [441, 0, -52, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [2, 4]}
  • id: 3162048
    {'degree': 4, 'field': [474, -4, 5, -2, 1], 'lmfdb_label': '66270.k5', 'torsion': [2, 6]}
  • id: 3162051
    {'degree': 6, 'field': [-2553, -2637, 1306, -99, -8, -3, 1], 'lmfdb_label': '66270.k5', 'torsion': [6]}
  • id: 3162055
    {'degree': 8, 'field': [39366, -7020, 7818, -1636, 919, -124, 46, -4, 1], 'lmfdb_label': '66270.k5', 'torsion': [2, 12]}
  • id: 3162053
    {'degree': 8, 'field': [83052, 33552, -45240, -864, 3952, -24, -116, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [8]}
  • id: 3162052
    {'degree': 8, 'field': [442096, 144640, 70064, 4160, 3036, -80, 84, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [2, 4]}
  • id: 3162054
    {'degree': 8, 'field': [11357286, -767040, -11996, -22560, 681, -470, 99, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [8]}
  • id: 3162057
    {'degree': 12, 'field': [-23851791, 39568122, -6566097, -7408170, 2575210, -142038, -24709, -5766, 2520, -150, -7, -6, 1], 'lmfdb_label': '66270.k5', 'torsion': [2, 6]}
  • id: 3162056
    {'degree': 12, 'field': [2387025, 0, 1374675, 0, 292150, 0, 32903, 0, 2082, 0, 71, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [3, 6]}
  • id: 3162059
    {'degree': 12, 'field': [6619185, 23264190, 819165, -5370120, 597460, 30250, 6529, -5962, 1400, 140, -35, -2, 1], 'lmfdb_label': '66270.k5', 'torsion': [12]}
  • id: 3162058
    {'degree': 12, 'field': [152769600, 0, -43989600, 0, 4674400, 0, -263224, 0, 8328, 0, -142, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [12]}
  • id: 3162064
    {'degree': 16, 'field': [180081900, -83373120, 117988176, -78795168, 64810642, -34818176, 19179416, -7246176, 2792143, -712480, 202864, -35008, 7594, -840, 140, -8, 1], 'lmfdb_label': '66270.k5', 'torsion': [24]}
  • id: 3162065
    {'degree': 16, 'field': [377438766, -426917736, 402489214, -233557496, 134357029, -55832754, 24249408, -7631898, 2632606, -618860, 171568, -29238, 6504, -750, 130, -8, 1], 'lmfdb_label': '66270.k5', 'torsion': [24]}
  • id: 3162060
    {'degree': 16, 'field': [763472161, -499568480, 163443200, -129608400, 34758706, 3509160, 1264000, -380320, -104329, 55960, 800, 2720, 246, -40, 0, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [4, 4]}
  • id: 3162063
    {'degree': 16, 'field': [763472161, 0, 320541396, 0, 99843222, 0, 15798048, 0, 1408615, 0, 80472, 0, 3282, 0, 84, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [2, 12]}
  • id: 3162061
    {'degree': 16, 'field': [1456873641, 5630471928, -7498674168, -1391850720, 2715575488, 108654312, -389495760, -3217728, 27829290, -648, -1074392, 1824, 22560, -24, -240, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [2, 8]}
  • id: 3162062
    {'degree': 16, 'field': [136963647396, 0, -38537051640, 0, 5064886696, 0, -400596540, 0, 20513661, 0, -686840, 0, 14586, 0, -180, 0, 1], 'lmfdb_label': '66270.k5', 'torsion': [2, 8]}
  • id: 3162066
    {'degree': 18, 'field': [7076335824, 911580480, 4991297328, -265811532, 1574279820, -190023588, 287331011, -37280985, 33042804, -3879008, 2535867, -253053, 134082, -10773, 4761, -274, 102, -3, 1], 'lmfdb_label': '66270.k5', 'torsion': [18]}
• 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: 1602435
    {'conductor': 66270, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '66270.k5', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1602436
    {'conductor': 66270, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '66270.k5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 1602437
    {'conductor': 66270, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '66270.k5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1602438
    {'conductor': 66270, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '66270.k5', 'prime': 47, 'reduction_type': 0, '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: 2102948
    {'adelic_gens': [[1, 12, 12, 145], [2821, 3384, 3572, 2069], [1552, 3243, 2397, 1834], [4231, 3384, 4230, 1], [4319, 0, 0, 5639], [4842, 799, 4277, 2492], [5617, 24, 5616, 25], [1, 24, 0, 1], [15, 106, 4334, 2051], [1, 0, 24, 1]], 'adelic_image': '5640.384.5.?', 'conductor': 66270, 'lmfdb_label': '66270.k5', 'prime': 0}
  • id: 277520
    {'conductor': 66270, 'elladic_image': '4.6.0.1', 'lmfdb_label': '66270.k5', 'modell_image': '2B', 'prime': 2}
  • id: 277521
    {'conductor': 66270, 'elladic_image': '3.4.0.1', 'lmfdb_label': '66270.k5', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 66270.k does not appear in ec_padic