Elliptic curve data - 15210.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': '15210n', 'Clabel': '15210n5', 'Cnumber': 5, 'abc_quality': 1.0339287621454463, 'absD': 18700047030896010, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [1, -1, 0, -104220, 11180430], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 15210, 'degree': 147456, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8466406639471200483159860423', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [35578826569, 5314410], 'lmfdb_iso': '15210.k', 'lmfdb_label': '15210.k5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -69, -194], 'min_quad_twist_disc': -39, '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', '39.8.0-3.a.1.2', '40.12.0.v.1', '60.48.0.c.4', '78.24.0.?', '104.12.0.?', '120.192.5.?', '156.48.0.?', '312.192.1.?', '520.24.0.?', '780.96.0.?', '1560.384.5.?'], '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, 7605], [3, 2, 1690], [5, 6, 3042], [13, 86, 90]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703055', 'prec': 107}, 'szpiro_ratio': 4.805585440802277, '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, 4, -1, 0, 1, 0, 0, 0, -4, 0, 1, -6, 0, 4, -1], 'aplist': [-1, 0, -1, 4, 0, 0, -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': 15210, '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': '15210.k', 'trace_hash': 1348567361393527049}
• 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': '0.024890195006655893531996795939', 'prec': 107}, 'conductor': 15210, 'gens': [], 'heights': [], 'lmfdb_label': '15210.k5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.37098238033420191849979723322', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4839295213368076739991889328695723739', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[963, -963, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [0, 0], '13': 'a'}, 'iwp0': 5, 'lmfdb_label': '15210.k5'}
• ec_torsion_growth •

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

  
  
  • id: 781885
    {'degree': 2, 'field': [-195, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [4]}
  • id: 781884
    {'degree': 2, 'field': [-78, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [4]}
  • id: 781883
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [2, 2]}
  • id: 781886
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '15210.k5', 'torsion': [6]}
  • id: 781890
    {'degree': 4, 'field': [30, -30, 31, -2, 1], 'lmfdb_label': '15210.k5', 'torsion': [12]}
  • id: 781889
    {'degree': 4, 'field': [66, -24, 25, -2, 1], 'lmfdb_label': '15210.k5', 'torsion': [12]}
  • id: 781887
    {'degree': 4, 'field': [289, 0, -44, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [2, 4]}
  • id: 781888
    {'degree': 4, 'field': [390, 0, 1, -2, 1], 'lmfdb_label': '15210.k5', 'torsion': [2, 6]}
  • id: 781891
    {'degree': 6, 'field': [9, 39, 36, 19, -16, -1, 1], 'lmfdb_label': '15210.k5', 'torsion': [6]}
  • id: 781893
    {'degree': 8, 'field': [3, 60, 118, -328, 95, 80, -22, -4, 1], 'lmfdb_label': '15210.k5', 'torsion': [8]}
  • id: 781895
    {'degree': 8, 'field': [21414, -3924, 4474, -1132, 647, -100, 38, -4, 1], 'lmfdb_label': '15210.k5', 'torsion': [2, 12]}
  • id: 781894
    {'degree': 8, 'field': [26881, 1592, 8095, -778, 1104, -92, 55, -2, 1], 'lmfdb_label': '15210.k5', 'torsion': [8]}
  • id: 781892
    {'degree': 8, 'field': [228336, 101760, 44272, 3520, 2044, -80, 68, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [2, 4]}
  • id: 781897
    {'degree': 12, 'field': [-711, 5118, -4893, 110, -1320, 1158, 161, -366, -30, 70, -3, -6, 1], 'lmfdb_label': '15210.k5', 'torsion': [2, 6]}
  • id: 781896
    {'degree': 12, 'field': [900, 0, -2100, 0, 2800, 0, -757, 0, 147, 0, -19, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [3, 6]}
  • id: 781899
    {'degree': 12, 'field': [2721, 1122, 2179, 820, -4050, 842, -151, -282, 230, 20, -21, -2, 1], 'lmfdb_label': '15210.k5', 'torsion': [12]}
  • id: 781898
    {'degree': 12, 'field': [4923, 7398, -12855, 10926, -5264, -858, 1253, -702, 24, 90, -7, -6, 1], 'lmfdb_label': '15210.k5', 'torsion': [12]}
  • id: 781904
    {'degree': 16, 'field': [9, 180, 3246, 9048, 33319, -49864, 91442, -51372, 37378, -7244, 7414, -1328, 709, -72, 38, -4, 1], 'lmfdb_label': '15210.k5', 'torsion': [24]}
  • id: 781901
    {'degree': 16, 'field': [729, 13608, 58752, -23832, -223800, 111288, 206392, -128288, -58503, 45416, 4988, -6552, 182, 392, -36, -8, 1], 'lmfdb_label': '15210.k5', 'torsion': [2, 8]}
  • id: 781905
    {'degree': 16, 'field': [11350, -9900, 104450, -83800, 62065, 29440, -18070, 24320, 976, 1240, 2708, -280, 454, -20, 32, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [24]}
  • id: 781900
    {'degree': 16, 'field': [203661441, -181527120, 80899200, -57834000, 16040194, 1059160, 896000, -238560, -86649, 37640, 800, 2240, 134, -40, 0, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [4, 4]}
  • id: 781903
    {'degree': 16, 'field': [203661441, 0, 77052228, 0, 34016518, 0, 6747776, 0, 701175, 0, 45016, 0, 2178, 0, 68, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [2, 12]}
  • id: 781902
    {'degree': 16, 'field': [402243136, 0, 334662208, 0, 114774560, 0, 20237688, 0, 2124329, 0, 136392, 0, 5270, 0, 112, 0, 1], 'lmfdb_label': '15210.k5', 'torsion': [2, 8]}
  • id: 781906
    {'degree': 18, 'field': [169744, 1171632, 1622304, -2069108, 941952, -777360, 995471, -184878, 38310, -39305, 10797, 1602, 641, -1146, 183, 49, 0, -6, 1], 'lmfdb_label': '15210.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: 336251
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15210.k5', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 336252
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '15210.k5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 336253
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15210.k5', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 336254
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '15210.k5', 'prime': 13, 'reduction_type': 0, '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: 1765308
    {'adelic_gens': [[779, 936, 988, 571], [352, 1443, 117, 274], [1002, 559, 1157, 92], [1, 12, 12, 145], [1537, 24, 1536, 25], [479, 0, 0, 1559], [15, 106, 254, 131], [1, 24, 0, 1], [391, 624, 390, 1], [1, 0, 24, 1]], 'adelic_image': '1560.384.5.?', 'conductor': 15210, 'lmfdb_label': '15210.k5', 'prime': 0}
  • id: 71888
    {'conductor': 15210, 'elladic_image': '4.6.0.1', 'lmfdb_label': '15210.k5', 'modell_image': '2B', 'prime': 2}
  • id: 71889
    {'conductor': 15210, 'elladic_image': '3.4.0.1', 'lmfdb_label': '15210.k5', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 15210.k does not appear in ec_padic