Elliptic curve data - 215600.bk2

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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': '215600i', 'Clabel': '215600i1', 'Cnumber': 1, 'abc_quality': 0.8204006326490144, 'absD': 4141244800000000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 1848, 'ainvs': [0, 1, 0, 38792, 981588], 'analytic_rank': 1, 'bad_primes': [2, 5, 7, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 215600, 'degree': 1244160, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6855912422629817040947811596', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 36, 'isogeny_degrees': [1, 3], 'jinv': [34295, 22], 'lmfdb_iso': '215600.bk', 'lmfdb_label': '215600.bk2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 2, 1], 'min_quad_twist_disc': 140, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '84.8.0.?', '88.2.0.?', '264.8.0.?', '1848.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8062755058907804890646185114', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 13475], [5, 14, 8624], [7, 26, 4400], [11, 12, 19600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0534696211140205076089668891', 'prec': 103}, 'szpiro_ratio': 3.526654995224586, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, -5, 0, 0, 0, 0, 0, -7, 0], 'aplist': [0, -2, 0, 0, 1, -5, 0, -7, -3, 3, 5, -4, -12, -5, 0, 6, 12, 10, -14, -3, -8, 4, -15, -3, 13], 'class_deg': 3, 'class_size': 2, 'conductor': 215600, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '215600.bk', 'trace_hash': 2188981677018769709}
• 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': '0.034348996162979699952213651932', 'prec': 107}, 'conductor': 215600, 'gens': [[44, 1666, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.8062755058907804890646185114', 'prec': 100}], 'lmfdb_label': '215600.bk2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.27340004180898883238504885736', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0689433625523226883744462282536538326', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [44]}
• lmfdb_label 215600.bk2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9400357
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '215600.bk2', 'torsion': [3]}
  • id: 9400358
    {'degree': 3, 'field': [-10, -5, 0, 1], 'lmfdb_label': '215600.bk2', 'torsion': [2]}
  • id: 9400359
    {'degree': 6, 'field': [22, 0, 37, 0, 4, 0, 1], 'lmfdb_label': '215600.bk2', 'torsion': [2, 2]}
  • id: 9400361
    {'degree': 6, 'field': [72, -320, 172, -20, -31, 0, 1], 'lmfdb_label': '215600.bk2', 'torsion': [6]}
  • id: 9400360
    {'degree': 6, 'field': [11460, -5400, 2620, -44, 138, -2, 1], 'lmfdb_label': '215600.bk2', 'torsion': [3]}
  • id: 9400362
    {'degree': 12, 'field': [-2588278, 0, -2974839, 0, -689087, 0, -33614, 0, 4116, 0, -91, 0, 1], 'lmfdb_label': '215600.bk2', 'torsion': [4]}
  • id: 9400364
    {'degree': 12, 'field': [672400, 0, -71200, 0, 14040, 0, -4112, 0, 657, 0, -34, 0, 1], 'lmfdb_label': '215600.bk2', 'torsion': [2, 6]}
  • id: 9400363
    {'degree': 12, 'field': [108741609, 73999278, 15187278, 2381538, -673961, -215916, 82508, -14988, 111, -114, 38, -6, 1], 'lmfdb_label': '215600.bk2', 'torsion': [3, 3]}
  • id: 9400365
    {'degree': 18, 'field': [7094669, -23020308, 16538790, 14091124, -17777733, -4702554, 9130530, 776676, -2645358, -38950, 449055, -3744, -45171, 486, 2625, -16, -81, 0, 1], 'lmfdb_label': '215600.bk2', 'torsion': [9]}
  • id: 9400366
    {'degree': 18, 'field': [261522825124, 24916355024, 128565757540, 9577719888, 33569007472, 1574402632, 5259335676, 110396384, 493701900, 3062552, 28011776, 6484, 962205, -1016, 19507, -12, 215, 0, 1], 'lmfdb_label': '215600.bk2', 'torsion': [6]}
• 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: 5342776
    {'conductor': 215600, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '215600.bk2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5342777
    {'conductor': 215600, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '215600.bk2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5342778
    {'conductor': 215600, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '215600.bk2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5342779
    {'conductor': 215600, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '215600.bk2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 3041631
    {'adelic_gens': [[3, 4, 8, 11], [4, 3, 9, 7], [263, 0, 0, 1847], [1, 0, 6, 1], [78, 721, 385, 771], [925, 798, 399, 547], [1385, 1050, 0, 1847], [673, 798, 1491, 547], [1581, 1582, 518, 1049], [1843, 6, 1842, 7], [1, 6, 0, 1]], 'adelic_image': '1848.16.0.?', 'conductor': 215600, 'lmfdb_label': '215600.bk2', 'prime': 0}
  • id: 792884
    {'conductor': 215600, 'elladic_image': '3.4.0.1', 'lmfdb_label': '215600.bk2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 215600.bk does not appear in ec_padic