Elliptic curve data - 15210.k1

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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': '15210n8', 'Cnumber': 8, 'abc_quality': 1.0818126452233845, 'absD': 285018244641000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [1, -1, 0, -8112285, 8895327741], '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': 6, 'faltings_ratio': 12, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [16778985534208729, 81000], 'lmfdb_iso': '15210.k', 'lmfdb_label': '15210.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5334, -150368], '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.3', '39.8.0-3.a.1.1', '40.12.0.v.1', '60.48.0.c.3', '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, 8, 169], [5, 6, 3042], [13, 86, 90]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232155', 'prec': 103}, 'szpiro_ratio': 6.162208775182755, '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.k1', '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': [[6579, -6579, 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.k1'}
• ec_torsion_growth •

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

  
  
  • id: 781945
    {'degree': 2, 'field': [-195, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [4]}
  • id: 781944
    {'degree': 2, 'field': [-78, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [4]}
  • id: 781943
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [2, 2]}
  • id: 781946
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '15210.k1', 'torsion': [6]}
  • id: 781949
    {'degree': 4, 'field': [3, 18, -17, -2, 1], 'lmfdb_label': '15210.k1', 'torsion': [12]}
  • id: 781948
    {'degree': 4, 'field': [39, 26, -25, -2, 1], 'lmfdb_label': '15210.k1', 'torsion': [2, 6]}
  • id: 781950
    {'degree': 4, 'field': [129, 36, -35, -2, 1], 'lmfdb_label': '15210.k1', 'torsion': [12]}
  • id: 781947
    {'degree': 4, 'field': [289, 0, -44, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [2, 4]}
  • id: 781951
    {'degree': 6, 'field': [192, 0, 0, -27, 0, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [6]}
  • id: 781953
    {'degree': 8, 'field': [3, 60, 118, -328, 95, 80, -22, -4, 1], 'lmfdb_label': '15210.k1', 'torsion': [24]}
  • id: 781955
    {'degree': 8, 'field': [129, 276, -116, -292, 77, 80, -22, -4, 1], 'lmfdb_label': '15210.k1', 'torsion': [2, 12]}
  • id: 781954
    {'degree': 8, 'field': [26881, 1592, 8095, -778, 1104, -92, 55, -2, 1], 'lmfdb_label': '15210.k1', 'torsion': [8]}
  • id: 781952
    {'degree': 8, 'field': [228336, 101760, 44272, 3520, 2044, -80, 68, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [2, 4]}
  • id: 781956
    {'degree': 12, 'field': [1200, 360, 1152, -2490, 45, 1080, 187, -366, -30, 70, -3, -6, 1], 'lmfdb_label': '15210.k1', 'torsion': [3, 6]}
  • id: 781958
    {'degree': 12, 'field': [39688, 64800, 31980, -6912, -6906, 1296, 1273, 0, 60, -54, 12, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [12]}
  • id: 781959
    {'degree': 12, 'field': [95614, 256770, 217425, 43632, -8490, 8100, 3613, 0, 375, -54, 30, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [12]}
  • id: 781957
    {'degree': 12, 'field': [691864, 1308960, 194700, -442368, 185730, 32400, -18887, 0, 1500, -54, -60, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [2, 6]}
  • id: 781961
    {'degree': 16, 'field': [729, 13608, 58752, -23832, -223800, 111288, 206392, -128288, -58503, 45416, 4988, -6552, 182, 392, -36, -8, 1], 'lmfdb_label': '15210.k1', 'torsion': [2, 24]}
  • id: 781964
    {'degree': 16, 'field': [76176, 0, 107304, 0, 40225, 0, -15684, 0, -636, 0, 1526, 0, 300, 0, 24, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [24]}
  • id: 781963
    {'degree': 16, 'field': [7889631, -8239344, 11160076, -6173496, 3906728, -955304, 269864, 41992, -8307, -5384, 4676, -1568, -42, 112, 4, -8, 1], 'lmfdb_label': '15210.k1', 'torsion': [2, 12]}
  • id: 781960
    {'degree': 16, 'field': [203661441, -181527120, 80899200, -57834000, 16040194, 1059160, 896000, -238560, -86649, 37640, 800, 2240, 134, -40, 0, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [4, 4]}
  • id: 781962
    {'degree': 16, 'field': [402243136, 0, 334662208, 0, 114774560, 0, 20237688, 0, 2124329, 0, 136392, 0, 5270, 0, 112, 0, 1], 'lmfdb_label': '15210.k1', 'torsion': [2, 8]}
  • id: 781965
    {'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.k1', '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: 336263
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '15210.k1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 336264
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '15210.k1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 336265
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '15210.k1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 336266
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '15210.k1', '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: 1765304
    {'adelic_gens': [[352, 1443, 117, 274], [1002, 559, 1157, 92], [1, 12, 12, 145], [1537, 24, 1536, 25], [479, 0, 0, 1559], [1299, 676, 832, 987], [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.k1', 'prime': 0}
  • id: 71880
    {'conductor': 15210, 'elladic_image': '4.6.0.1', 'lmfdb_label': '15210.k1', 'modell_image': '2B', 'prime': 2}
  • id: 71881
    {'conductor': 15210, 'elladic_image': '3.4.0.1', 'lmfdb_label': '15210.k1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 15210.k does not appear in ec_padic