Elliptic curve data - 20.a1

Formats: - HTML - YAML - JSON - 2024-07-27T09:54:51.196104

• 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': '20a', 'Clabel': '20a4', 'Cnumber': 4, 'abc_quality': 1.073761143790618, 'absD': 2000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, 1, 0, -41, -116], 'analytic_rank': 0, 'bad_primes': [2, 5], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 20, 'degree': 6, 'elladic_images': ['8.12.0.22', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.38064395118146512547640346211', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [488095744, 125], 'lmfdb_iso': '20.a', 'lmfdb_label': '20.a1', 'lmfdb_number': 1, 'manin_constant': 2, 'min_quad_twist_ainvs': [0, 1, 0, -41, -116], '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', '4.6.0.b.1', '6.24.0-6.a.1.2', '8.12.0-4.b.1.2', '10.6.0.a.1', '12.48.0-12.f.1.6', '20.24.0.e.1', '24.96.0-24.bq.2.3', '30.48.0-30.a.1.2', '40.48.0-20.e.1.6', '60.192.3-60.bk.1.6', '120.384.9.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, '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': '-0.61169301136811356194881416926', 'prec': 107}, 'szpiro_ratio': 7.6036871066956255, '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, -1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, -6, 0, -4, 0], 'aplist': [0, -2, -1, 2, 0, 2, -6, -4, 6, 6, -4, 2, 6, -10, -6, -6, 12, 2, 2, -12, 2, 8, 6, -6, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 20, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '20.a', 'trace_hash': 12896406231020588}
• 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': '2.1410318856267100583891480651', 'prec': 100}, 'conductor': 20, 'gens': [], 'heights': [], 'lmfdb_label': '20.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.8829167613060758663225263660', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.47072919032651896658063159150721550180', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [[-4, 0, 1]], 'xcoord_integral_points': [-4]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 1], '5': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '20.a1'}
• ec_torsion_growth •

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

  
  
  • id: 383
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '20.a1', 'torsion': [2, 2]}
  • id: 384
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '20.a1', 'torsion': [6]}
  • id: 385
    {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '20.a1', 'torsion': [6]}
  • id: 387
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '20.a1', 'torsion': [2, 6]}
  • id: 386
    {'degree': 4, 'field': [2, 0, 0, -2, 1], 'lmfdb_label': '20.a1', 'torsion': [4]}
  • id: 389
    {'degree': 6, 'field': [-4, 0, 0, -8, 0, 0, 1], 'lmfdb_label': '20.a1', 'torsion': [2, 6]}
  • id: 388
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '20.a1', 'torsion': [3, 6]}
  • id: 390
    {'degree': 8, 'field': [-4, 16, -16, -8, 14, 4, -4, -2, 1], 'lmfdb_label': '20.a1', 'torsion': [2, 4]}
  • id: 392
    {'degree': 8, 'field': [1, -2, 0, -4, 11, -4, 0, -2, 1], 'lmfdb_label': '20.a1', 'torsion': [12]}
  • id: 391
    {'degree': 8, 'field': [1, -2, 2, 2, -2, 2, 2, -2, 1], 'lmfdb_label': '20.a1', 'torsion': [2, 4]}
  • id: 393
    {'degree': 12, 'field': [1, 3, -9, -20, 45, 33, -70, -33, 45, 20, -9, -3, 1], 'lmfdb_label': '20.a1', 'torsion': [6, 6]}
  • id: 394
    {'degree': 12, 'field': [2, 0, 0, -8, 0, 0, 12, 0, 0, -6, 0, 0, 1], 'lmfdb_label': '20.a1', 'torsion': [12]}
  • id: 396
    {'degree': 16, 'field': [1, -8, 24, -36, 42, -60, 56, -16, 4, 0, -8, -12, 10, -4, 8, 0, 1], 'lmfdb_label': '20.a1', 'torsion': [8]}
  • id: 395
    {'degree': 16, 'field': [1, -6, 18, -36, 47, -30, -18, 72, -95, 72, -18, -30, 47, -36, 18, -6, 1], 'lmfdb_label': '20.a1', 'torsion': [4, 4]}
  • id: 398
    {'degree': 16, 'field': [1, -2, 2, -8, 10, -2, 16, -18, 3, -18, 16, -2, 10, -8, 2, -2, 1], 'lmfdb_label': '20.a1', 'torsion': [2, 12]}
  • id: 397
    {'degree': 16, 'field': [1, 6, 32, 40, 65, -16, 36, -50, 24, -70, 4, -28, 25, 0, 8, -2, 1], 'lmfdb_label': '20.a1', 'torsion': [2, 12]}
  • id: 399
    {'degree': 18, 'field': [1, 0, 0, -1, 0, 0, 20, 0, 0, 35, 0, 0, 20, 0, 0, -1, 0, 0, 1], 'lmfdb_label': '20.a1', '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: 44
    {'conductor': 20, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '20.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 45
    {'conductor': 20, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '20.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1665912
    {'adelic_gens': [[1, 12, 12, 25], [97, 24, 96, 25], [41, 24, 40, 1], [105, 106, 14, 35], [1, 0, 24, 1], [21, 4, 20, 101], [1, 24, 0, 1], [7, 24, 12, 7], [61, 24, 72, 49], [112, 3, 117, 34]], 'adelic_image': '120.384.9.?', 'conductor': 20, 'lmfdb_label': '20.a1', 'prime': 0}
  • id: 30
    {'conductor': 20, 'elladic_image': '8.12.0.22', 'lmfdb_label': '20.a1', 'modell_image': '2B', 'prime': 2}
  • id: 31
    {'conductor': 20, 'elladic_image': '3.8.0.2', 'lmfdb_label': '20.a1', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 20.a does not appear in ec_padic