Elliptic curve data - 9800.i1

Formats: - HTML - YAML - JSON - 2024-04-25T17:54:52.964118

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '9800k', 'Clabel': '9800k2', 'Cnumber': 2, 'abc_quality': 0.8901419193332675, 'absD': 6860000000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 56, 'ainvs': [0, 1, 0, -6008, 125488], 'analytic_rank': 0, 'bad_primes': [2, 5, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 9800, 'degree': 18432, 'elladic_images': ['8.6.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1696142031284135664771054065', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2], 'jinv': [2185454, 625], 'lmfdb_iso': '9800.i', 'lmfdb_label': '9800.i1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -240, 1100], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.e.1', '28.6.0.c.1', '56.12.0.bd.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.75696720586574814739874189064', 'prec': 107}, 'szpiro_ratio': 4.103998485052034, '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, -2, 0, 0, 0, 0, 0, 1, 0, 4, 0, -2, 0, 0, 0, 0, 0, 2, 0], 'aplist': [0, -2, 0, 0, 4, -2, 0, 2, 4, 10, 4, 2, -12, 4, -4, -2, 10, 6, -4, -12, 4, -4, -14, 8, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 9800, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '9800.i', 'trace_hash': 1562596356758508727}
• 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': '0.096401992715485031274759077981', 'prec': 107}, 'conductor': 9800, 'gens': [], 'heights': [], 'lmfdb_label': '9800.i1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.69595295000416928180912591773', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3919059000083385636182518354641259152', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[23, 0, 1]], 'xcoord_integral_points': [23]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '5': 'a', '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '9800.i1'}
• ec_torsion_growth •

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

  
  
  • id: 509514
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '9800.i1', 'torsion': [2, 2]}
  • id: 509515
    {'degree': 4, 'field': [350, 0, 35, 0, 1], 'lmfdb_label': '9800.i1', 'torsion': [4]}
  • id: 509518
    {'degree': 8, 'field': [-33075, 0, 8820, 0, -630, 0, 0, 0, 1], 'lmfdb_label': '9800.i1', 'torsion': [6]}
  • id: 509516
    {'degree': 8, 'field': [5041, 0, -2838, 0, 538, 0, -38, 0, 1], 'lmfdb_label': '9800.i1', 'torsion': [2, 4]}
  • id: 509517
    {'degree': 8, 'field': [14884, 0, -2384, 0, 52, 0, -8, 0, 1], 'lmfdb_label': '9800.i1', 'torsion': [2, 4]}
  • id: 509519
    {'degree': 16, 'field': [16, 0, 32, 0, 188, 0, 16, 0, -62, 0, -8, 0, 47, 0, -4, 0, 1], 'lmfdb_label': '9800.i1', 'torsion': [8]}
  • id: 509520
    {'degree': 16, 'field': [2772225, 0, -9772380, 0, 11997036, 0, -5074856, 0, -116530, 0, -64340, 0, -1160, 0, -16, 0, 1], 'lmfdb_label': '9800.i1', '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: 206888
    {'conductor': 9800, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '9800.i1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 206889
    {'conductor': 9800, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '9800.i1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 206890
    {'conductor': 9800, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '9800.i1', 'prime': 7, 'reduction_type': 0, '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: 1728806
    {'adelic_gens': [[1, 2, 2, 5], [36, 25, 49, 8], [2, 1, 27, 0], [3, 4, 8, 11], [53, 4, 52, 5], [12, 1, 39, 0], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '56.12.0.?', 'conductor': 9800, 'lmfdb_label': '9800.i1', 'prime': 0}
  • id: 47470
    {'conductor': 9800, 'elladic_image': '8.6.0.3', 'lmfdb_label': '9800.i1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 9800.i does not appear in ec_padic