Elliptic curve data - 10816.r4

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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': '10816bb', 'Clabel': '10816bb1', 'Cnumber': 1, 'absD': 308915776, 'ainvs': [0, 0, 0, 169, 0], 'analytic_rank': 0, 'bad_primes': [2, 13], 'class_deg': 4, 'class_size': 4, 'cm': -4, 'conductor': 10816, 'degree': 1920, 'elladic_images': ['16.192.9.178'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.31851534309923150448308469821', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [1728, 1], 'lmfdb_iso': '10816.r', 'lmfdb_label': '10816.r4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 4, 0], 'min_quad_twist_disc': 104, 'modell_images': ['2B'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 169], [13, 86, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3105329259115095182522750833', 'prec': 103}, 'szpiro_ratio': 2.9070872547016986, '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, 0, 0, 0, -2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, -2, 0, 0, 0, 2, 0, 0, 10, 0, -2, -10, 0, 0, -14, 0, 10, 0, 0, 6, 0, 0, -10, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 10816, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '10816.r', 'trace_hash': 303278959070135011}
• 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': '0.52886044754002867903769967537', 'prec': 103}, 'conductor': 10816, 'gens': [], 'heights': [], 'lmfdb_label': '10816.r4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0284555873152993659491810707', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0284555873152993659491810707484154273', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '10816.r4'}
• ec_torsion_growth •

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

  
  
  • id: 559913
    {'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '10816.r4', 'torsion': [4]}
  • id: 559912
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '10816.r4', 'torsion': [2, 2]}
  • id: 559914
    {'degree': 2, 'field': [26, 0, 1], 'lmfdb_label': '10816.r4', 'torsion': [4]}
  • id: 559915
    {'degree': 4, 'field': [169, 0, 0, 0, 1], 'lmfdb_label': '10816.r4', 'torsion': [2, 4]}
  • id: 559919
    {'degree': 8, 'field': [-85683, 0, 0, 0, -1014, 0, 0, 0, 1], 'lmfdb_label': '10816.r4', 'torsion': [6]}
  • id: 559917
    {'degree': 8, 'field': [-25, 120, -54, -116, 19, 44, -10, -4, 1], 'lmfdb_label': '10816.r4', 'torsion': [8]}
  • id: 559916
    {'degree': 8, 'field': [81, 0, 0, 0, 31, 0, 0, 0, 1], 'lmfdb_label': '10816.r4', 'torsion': [4, 4]}
  • id: 559918
    {'degree': 8, 'field': [3704, 1184, 1632, 128, 220, -8, 20, 0, 1], 'lmfdb_label': '10816.r4', 'torsion': [8]}
  • id: 559920
    {'degree': 8, 'field': [35786, -11480, 2224, -1508, 664, -28, -26, 0, 1], 'lmfdb_label': '10816.r4', 'torsion': [2, 10]}
  • id: 559921
    {'degree': 16, 'field': [2129, -12820, 47284, -101060, 145564, -158904, 139328, -98844, 59557, -29464, 12660, -4388, 1338, -308, 64, -8, 1], 'lmfdb_label': '10816.r4', 'torsion': [4, 8]}
  • id: 559924
    {'degree': 16, 'field': [572809, 1210492, -398572, -1915572, 485942, 1047584, -296792, -284100, 85948, 43596, -13292, -3908, 1142, 192, -52, -4, 1], 'lmfdb_label': '10816.r4', 'torsion': [12]}
  • id: 559925
    {'degree': 16, 'field': [3376753, -2167900, 4609328, -2289412, 2641382, -1070048, 856848, -279620, 169748, -43148, 20688, -3900, 1506, -192, 60, -4, 1], 'lmfdb_label': '10816.r4', 'torsion': [2, 20]}
  • id: 559926
    {'degree': 16, 'field': [8746494, -660936, 7955748, -1421520, 3369888, -792384, 878148, -217176, 151624, -34300, 17284, -3232, 1246, -172, 52, -4, 1], 'lmfdb_label': '10816.r4', 'torsion': [12]}
  • id: 559923
    {'degree': 16, 'field': [35249756, 96251776, 118103424, 86643504, 32042056, 15334208, 2707776, 792344, 22346, -23576, -7180, -3044, -28, -108, 30, -4, 1], 'lmfdb_label': '10816.r4', 'torsion': [10]}
  • id: 559922
    {'degree': 16, 'field': [647841853, 81439420, 142522604, -51834804, 24347828, -17884012, 5637250, -2580084, 763771, -229836, 59062, -12032, 2942, -324, 86, -4, 1], 'lmfdb_label': '10816.r4', 'torsion': [6, 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: 230604
    {'conductor': 10816, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '10816.r4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 230605
    {'conductor': 10816, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '10816.r4', '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

  
  {'conductor': 10816, 'elladic_image': '16.192.9.178', 'lmfdb_label': '10816.r4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 10816.r does not appear in ec_padic