Elliptic curve data - 990.e4

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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': '990b', 'Clabel': '990b4', 'Cnumber': 4, 'abc_quality': 1.0709081254433794, 'absD': 11158283252160000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 264, 'ainvs': [1, -1, 0, 55011, 1066373], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 990, 'degree': 10368, 'elladic_images': ['2.3.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7684759954202212188269555937', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [935355271080573, 566899520000], 'lmfdb_iso': '990.e', 'lmfdb_label': '990.e4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 55011, 1066373], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '6.24.0-6.a.1.2', '24.48.0-24.cb.1.11', '88.6.0.?', '132.48.0.?', '264.96.1.?'], '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, 3], [3, 2, 5], [5, 6, 198], [11, 12, 90]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.94451677891913895028052166601', 'prec': 103}, 'szpiro_ratio': 6.431046051675557, '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, -1, 0, -4, 4, 0, 1, 6, 0, 2, 1], 'aplist': [-1, 0, 1, -4, -1, -4, 6, 2, 6, 6, 8, 2, 6, -10, 6, -6, 0, 8, -4, 6, 14, -16, -12, 0, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 990, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '990.e', 'trace_hash': 1133630191504274849}
• 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': '0.029101894878050451859812977610', 'prec': 107}, 'conductor': 990, 'gens': [], 'heights': [], 'lmfdb_label': '990.e4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.24818409264698797929412461458', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.99273637058795191717649845832585185082', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-77, 77, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 1], '3': 'a', '5': [1, 0], '11': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '990.e4'}
• ec_torsion_growth •

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

  
  
  • id: 47989
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '990.e4', 'torsion': [6]}
  • id: 47988
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [2, 2]}
  • id: 47990
    {'degree': 3, 'field': [-5, 0, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [6]}
  • id: 47991
    {'degree': 4, 'field': [-24, 0, 6, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [4]}
  • id: 47992
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [2, 6]}
  • id: 47993
    {'degree': 6, 'field': [36, -18, -9, 3, 6, -3, 1], 'lmfdb_label': '990.e4', 'torsion': [3, 6]}
  • id: 47994
    {'degree': 6, 'field': [384, 0, 48, 0, -18, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [2, 6]}
  • id: 47996
    {'degree': 8, 'field': [1, 0, 10, 0, -6, 0, 10, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [2, 4]}
  • id: 47997
    {'degree': 8, 'field': [36, 0, 18, 0, 15, 0, -3, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [12]}
  • id: 47995
    {'degree': 8, 'field': [100, 0, 16, 0, 12, 0, -8, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [2, 4]}
  • id: 47999
    {'degree': 12, 'field': [-384, 0, 432, 0, 156, 0, -162, 0, -69, 0, -3, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [12]}
  • id: 47998
    {'degree': 12, 'field': [289, 1020, 3396, 380, -354, 840, 206, 0, 24, -20, 6, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [6, 6]}
  • id: 48002
    {'degree': 16, 'field': [1, 0, -10, 0, 106, 0, 80, 0, -65, 0, 80, 0, 106, 0, -10, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [2, 12]}
  • id: 48001
    {'degree': 16, 'field': [784, 0, 2368, 0, 2872, 0, 1984, 0, 928, 0, 304, 0, 94, 0, 16, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [2, 12]}
  • id: 48000
    {'degree': 16, 'field': [4596736, 0, -905216, 0, -1500016, 0, 669136, 0, -61196, 0, -2656, 0, -496, 0, -4, 0, 1], 'lmfdb_label': '990.e4', 'torsion': [8]}
  • id: 48003
    {'degree': 18, 'field': [67699728, -40865904, 22149612, -8460864, 9957735, -4595157, 2034441, -666432, 407700, -123456, 41634, -14850, 8214, -2160, 432, -96, 39, -9, 1], 'lmfdb_label': '990.e4', '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: 13709
    {'conductor': 990, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '990.e4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 13710
    {'conductor': 990, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '990.e4', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 13711
    {'conductor': 990, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '990.e4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 13712
    {'conductor': 990, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '990.e4', 'prime': 11, 'reduction_type': -1, '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: 1670827
    {'adelic_gens': [[208, 253, 123, 32], [10, 3, 105, 256], [145, 12, 78, 73], [253, 12, 252, 13], [1, 0, 12, 1], [11, 2, 214, 255], [1, 6, 6, 37], [219, 256, 182, 245], [1, 12, 0, 1]], 'adelic_image': '264.96.1.?', 'conductor': 990, 'lmfdb_label': '990.e4', 'prime': 0}
  • id: 4651
    {'conductor': 990, 'elladic_image': '2.3.0.1', 'lmfdb_label': '990.e4', 'modell_image': '2B', 'prime': 2}
  • id: 4652
    {'conductor': 990, 'elladic_image': '3.8.0.2', 'lmfdb_label': '990.e4', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 990.e does not appear in ec_padic