Elliptic curve data - 209814.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': '209814cs', 'Clabel': '209814cs2', 'Cnumber': 2, 'abc_quality': 1.0630472715106667, 'absD': 6523309327535751168, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2244, 'ainvs': [1, 1, 0, -4722351185, 124904674969749], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 209814, 'degree': 83607552, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8383921694474907501068161168', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [362515826352179162139875, 203046912], 'lmfdb_iso': '209814.k', 'lmfdb_label': '209814.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -16340316, 25422339226], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '132.6.0.?', '204.6.0.?', '748.6.0.?', '2244.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.8866338117229180249082935671', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 3179], [3, 4, 69938], [7, 2, 104907], [11, 42, 1734], [17, 162, 726]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8223116792197900739665629134', 'prec': 100}, 'szpiro_ratio': 6.401213489254457, '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, 0, 1, -2, -1, 1, 0, 0, -1, 4, 2, 0, 1, 0, -1, 0, 0], 'aplist': [-1, -1, 0, -2, 0, 4, 0, 0, -8, 2, -8, -6, 2, 8, -6, 2, 6, 2, 0, -8, -2, 2, -4, -2, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 209814, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '209814.k', 'trace_hash': 866720613106458652}
• 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': '0.00046346284457769742230929872179', 'prec': 113}, 'conductor': 209814, 'gens': [[-56830, 14510783, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.8866338117229180249082935671', 'prec': 100}], 'lmfdb_label': '209814.k1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10179230055747044375010074115', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1650351769578101134575447890973154369', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[158699, -158699, 2]], 'xcoord_integral_points': [-56830]}
• lmfdb_label 209814.k1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9172137
    {'degree': 2, 'field': [-187, 0, 1], 'lmfdb_label': '209814.k1', 'torsion': [2, 2]}
  • id: 9172138
    {'degree': 4, 'field': [136, -20, -34, -1, 1], 'lmfdb_label': '209814.k1', 'torsion': [4]}
  • id: 9172141
    {'degree': 8, 'field': [-10930, 2653, -2302, -703, 355, -7, 7, -4, 1], 'lmfdb_label': '209814.k1', 'torsion': [6]}
  • id: 9172140
    {'degree': 8, 'field': [4624, 0, -7548, 0, 1616, 0, -87, 0, 1], 'lmfdb_label': '209814.k1', 'torsion': [2, 4]}
  • id: 9172139
    {'degree': 8, 'field': [2186757, -1045860, 130724, -3158, -1621, 670, 22, -2, 1], 'lmfdb_label': '209814.k1', 'torsion': [2, 4]}
  • id: 9172142
    {'degree': 16, 'field': [4550311936, 0, -6312166912, 0, 112839472, 0, 49531064, 0, 2677096, 0, -505186, 0, 16681, 0, -214, 0, 1], 'lmfdb_label': '209814.k1', 'torsion': [8]}
  • id: 9172143
    {'degree': 16, 'field': [7113235600, 0, -1260859712, 0, 517279936, 0, -48177368, 0, 5016568, 0, -316508, 0, 10537, 0, -170, 0, 1], 'lmfdb_label': '209814.k1', 'torsion': [2, 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: 5199898
    {'conductor': 209814, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '209814.k1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5199899
    {'conductor': 209814, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '209814.k1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5199900
    {'conductor': 209814, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '209814.k1', 'prime': 11, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5199901
    {'conductor': 209814, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '209814.k1', 'prime': 17, '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: 3006641
    {'adelic_gens': [[1636, 1, 1835, 0], [1, 2, 2, 5], [1, 4, 0, 1], [749, 4, 1498, 9], [2114, 1, 1187, 0], [1, 0, 4, 1], [2241, 4, 2240, 5], [3, 4, 8, 11], [1684, 565, 561, 1684]], 'adelic_image': '2244.12.0.?', 'conductor': 209814, 'lmfdb_label': '209814.k1', 'prime': 0}
  • id: 774409
    {'conductor': 209814, 'elladic_image': '2.3.0.1', 'lmfdb_label': '209814.k1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 209814.k does not appear in ec_padic