Elliptic curve data - 7098.k3

Formats: - HTML - YAML - JSON - 2023-01-30T21:26:10.053340

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '7098o', 'Clabel': '7098o1', 'Cnumber': 1, 'absD': 72153013733892, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 10920, 'ainvs': [1, 0, 1, -76392, -8122814], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 7098, 'degree': 31200, 'elladic_images': ['2.3.0.1', '5.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5608016555658482329851092450', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [4649101309, 6804], 'lmfdb_iso': '7098.k', 'lmfdb_label': '7098.k3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -76392, -8122814], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '5B'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.36291036253030431905500633617', 'prec': 107}, '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, -2, -1, 1, -1, 1, 2, 0, 1, 0, -1, -2, 1, 2, -1, -4, -2], 'aplist': [-1, 1, -2, 1, 0, 0, 2, -4, 6, 0, 0, -2, 0, -4, 8, 4, -6, 12, 2, 0, -14, 0, 14, 4, 2], 'class_deg': 10, 'class_size': 4, 'conductor': 7098, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '7098.k', 'trace_hash': 1203744516179245407}
• 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': '0.044086427465055326005006836392', 'prec': 107}, 'conductor': 7098, 'gens': [], 'heights': [], 'lmfdb_label': '7098.k3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.28719471032622811487280642008', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4359735516311405743640321003967316995', 'prec': 130}, 'tamagawa_product': 20, 'torsion_generators': [[-155, 77, 1]], 'xcoord_integral_points': [-155]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [3, 0], '5': [6, 0], '7': [3, 0], '13': 'a'}, 'iwp0': 7, 'lmfdb_label': '7098.k3'}
• ec_torsion_growth •

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

  
  
  • id: 373596
    {'degree': 2, 'field': [-68, -1, 1], 'lmfdb_label': '7098.k3', 'torsion': [2, 2]}
  • id: 373598
    {'degree': 4, 'field': [3, 4, 2, -1, 1], 'lmfdb_label': '7098.k3', 'torsion': [10]}
  • id: 373597
    {'degree': 4, 'field': [425, 6, -5, -2, 1], 'lmfdb_label': '7098.k3', 'torsion': [4]}
  • id: 373602
    {'degree': 8, 'field': [1257, 1017, -251, -278, 155, 16, -16, -2, 1], 'lmfdb_label': '7098.k3', 'torsion': [2, 10]}
  • id: 373599
    {'degree': 8, 'field': [1296, 0, -3672, 0, 216, 0, -102, 0, 1], 'lmfdb_label': '7098.k3', 'torsion': [2, 4]}
  • id: 373600
    {'degree': 8, 'field': [1444, 0, -490, 0, -111, 0, 56, 0, 1], 'lmfdb_label': '7098.k3', 'torsion': [2, 4]}
  • id: 373601
    {'degree': 8, 'field': [6152, -6082, 1433, 6, 327, -54, -17, -2, 1], 'lmfdb_label': '7098.k3', 'torsion': [6]}
  • id: 373605
    {'degree': 16, 'field': [432, -2016, 10920, -10416, 7792, -7320, 3048, -912, 1595, -816, 276, -240, 77, -12, 18, 0, 1], 'lmfdb_label': '7098.k3', 'torsion': [20]}
  • id: 373604
    {'degree': 16, 'field': [68973984, -97337538, -62559621, 18622638, -55389, 9139518, 5708403, -1568226, 249435, 332394, -43223, -6150, 3249, 26, -39, -6, 1], 'lmfdb_label': '7098.k3', 'torsion': [2, 6]}
  • id: 373603
    {'degree': 16, 'field': [3726511920, 2610729792, 1297432512, 1166678208, 488713104, -11402544, -14926808, 7567456, 626985, -415784, 63484, -1080, -626, -8, 36, -8, 1], 'lmfdb_label': '7098.k3', 'torsion': [8]}
  • id: 373606
    {'degree': 20, 'field': [14798035476, 16504425000, -6600286476, -14096008164, -2092236496, 3566027220, 1253872844, -206656730, -102011420, -5860148, -14506967, -4236824, 1698609, 614048, -30870, -14406, 3542, 568, -67, -4, 1], 'lmfdb_label': '7098.k3', 'torsion': [10]}
• 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: 145680
    {'conductor': 7098, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '7098.k3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 145681
    {'conductor': 7098, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '7098.k3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 145682
    {'conductor': 7098, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7098.k3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 145683
    {'conductor': 7098, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '7098.k3', 'prime': 13, '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: 1710986
    {'adelic_gens': [[10901, 20, 10900, 21], [6, 13, 7195, 10736], [2518, 10905, 5075, 262], [8191, 20, 0, 1], [5461, 6, 0, 1], [1, 10, 10, 101], [1, 0, 20, 1], [4371, 20, 10900, 10787], [3126, 13, 3035, 10736], [11, 16, 10680, 10571], [1, 20, 0, 1]], 'adelic_image': '10920.288.5.?', 'conductor': 7098, 'lmfdb_label': '7098.k3', 'prime': 0}
  • id: 35099
    {'conductor': 7098, 'elladic_image': '2.3.0.1', 'lmfdb_label': '7098.k3', 'modell_image': '2B', 'prime': 2}
  • id: 35100
    {'conductor': 7098, 'elladic_image': '5.6.0.1', 'lmfdb_label': '7098.k3', 'modell_image': '5B', 'prime': 5}
• lmfdb_iso 7098.k does not appear in ec_padic