Elliptic curve data - 15210.k2

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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': '15210n7', 'Cnumber': 7, 'abc_quality': 1.1359972360691755, 'absD': 20617639224609375000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [1, -1, 0, -689805, 30185325], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 15210, 'degree': 442368, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3959468082811748940136086608', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [10316097499609, 5859375000], 'lmfdb_iso': '15210.k', 'lmfdb_label': '15210.k2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -454, -544], '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', '12.48.0.c.3', '24.96.1.da.1', '39.8.0-3.a.1.1', '40.12.0.bb.1', '52.12.0-4.c.1.1', '78.24.0.?', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '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, 1521], [3, 8, 169], [5, 6, 3042], [13, 86, 90]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232155', 'prec': 103}, 'szpiro_ratio': 5.394358214577864, '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': '0.0082967316688852978439989319796', 'prec': 110}, 'conductor': 15210, 'gens': [], 'heights': [], 'lmfdb_label': '15210.k2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.18549119016710095924989861661', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4839295213368076739991889328695723739', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-3405, 3405, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 1], '3': 'a', '5': [0, 0], '13': 'a'}, 'iwp0': 5, 'lmfdb_label': '15210.k2'}
• ec_torsion_growth •

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

  
  
  • id: 781920
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [2, 2]}
  • id: 781923
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '15210.k2', 'torsion': [6]}
  • id: 781921
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [4]}
  • id: 781922
    {'degree': 2, 'field': [78, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [4]}
  • id: 781925
    {'degree': 4, 'field': [3, 18, -17, -2, 1], 'lmfdb_label': '15210.k2', 'torsion': [2, 6]}
  • id: 781926
    {'degree': 4, 'field': [9, 0, 7, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [12]}
  • id: 781927
    {'degree': 4, 'field': [87, -6, 7, -2, 1], 'lmfdb_label': '15210.k2', 'torsion': [12]}
  • id: 781924
    {'degree': 4, 'field': [361, 0, 14, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [2, 4]}
  • id: 781928
    {'degree': 6, 'field': [192, 0, 0, -27, 0, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [6]}
  • id: 781929
    {'degree': 8, 'field': [-69, 348, -306, -72, 7, 32, -6, -4, 1], 'lmfdb_label': '15210.k2', 'torsion': [2, 12]}
  • id: 781932
    {'degree': 8, 'field': [441, 252, -180, 72, 85, -12, 14, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [2, 12]}
  • id: 781930
    {'degree': 8, 'field': [2584, -3428, 901, -266, 397, -20, -23, -2, 1], 'lmfdb_label': '15210.k2', 'torsion': [8]}
  • id: 781931
    {'degree': 8, 'field': [11236, 0, 1968, 0, 658, 0, 48, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [8]}
  • id: 781933
    {'degree': 12, 'field': [1200, 360, 1152, -2490, 45, 1080, 187, -366, -30, 70, -3, -6, 1], 'lmfdb_label': '15210.k2', 'torsion': [3, 6]}
  • id: 781935
    {'degree': 12, 'field': [1600, 0, 4173, 0, 4587, 0, 869, 0, 105, 0, 15, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [12]}
  • id: 781936
    {'degree': 12, 'field': [34168, -59616, 31596, -13824, 7386, 1296, 953, 0, 60, -54, -12, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [12]}
  • id: 781934
    {'degree': 12, 'field': [243000, 0, 0, 27648, 0, 0, 1299, 0, 0, -18, 0, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [2, 6]}
  • id: 781940
    {'degree': 16, 'field': [4761, 0, -15156, 0, 9786, 0, 1404, 0, 11899, 0, 4276, 0, 618, 0, 40, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [24]}
  • id: 781937
    {'degree': 16, 'field': [4761, 0, 78876, 0, 142782, 0, 30912, 0, 10975, 0, 2296, 0, 306, 0, 28, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [4, 12]}
  • id: 781938
    {'degree': 16, 'field': [12996, 0, -20232, 0, -4152, 0, 42300, 0, 31621, 0, 8440, 0, 978, 0, 52, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [2, 8]}
  • id: 781941
    {'degree': 16, 'field': [13911, -24144, 75532, -88920, 16208, 17560, 17000, -11576, -5499, 3256, 1364, -704, -186, 112, 4, -8, 1], 'lmfdb_label': '15210.k2', 'torsion': [24]}
  • id: 781939
    {'degree': 16, 'field': [20711601, 0, 9923244, 0, 2986150, 0, 332016, 0, 28599, 0, -2344, 0, 690, 0, -36, 0, 1], 'lmfdb_label': '15210.k2', 'torsion': [2, 8]}
  • id: 781942
    {'degree': 18, 'field': [-17859, -1036431, -348795, 726198, 893304, -522666, -302008, 92514, 120003, -34951, -26283, 11202, 2058, -1236, -264, 160, 3, -9, 1], 'lmfdb_label': '15210.k2', '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: 336259
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '15210.k2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 336260
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '15210.k2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 336261
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '15210.k2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 336262
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '15210.k2', 'prime': 13, '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: 1765305
    {'adelic_gens': [[1104, 247, 169, 246], [1, 12, 12, 145], [1537, 24, 1536, 25], [479, 0, 0, 1559], [1054, 1443, 975, 274], [15, 106, 254, 131], [1, 24, 0, 1], [937, 624, 1404, 1249], [846, 169, 1235, 1496], [1, 0, 24, 1]], 'adelic_image': '1560.384.5.?', 'conductor': 15210, 'lmfdb_label': '15210.k2', 'prime': 0}
  • id: 71882
    {'conductor': 15210, 'elladic_image': '4.6.0.1', 'lmfdb_label': '15210.k2', 'modell_image': '2B', 'prime': 2}
  • id: 71883
    {'conductor': 15210, 'elladic_image': '3.4.0.1', 'lmfdb_label': '15210.k2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 15210.k does not appear in ec_padic