Elliptic curve data - 11.a1

Formats: - HTML - YAML - JSON - 2023-09-28T15:25:59.112794

• 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': '11a', 'Clabel': '11a2', 'Cnumber': 2, 'absD': 11, 'adelic_genus': 37, 'adelic_index': 1200, 'adelic_level': 550, 'ainvs': [0, -1, 1, -7820, -263580], 'analytic_rank': 0, 'bad_primes': [11], 'class_deg': 25, 'class_size': 3, 'cm': 0, 'conductor': 11, 'degree': 5, 'elladic_images': ['25.120.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540515', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 25, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5, 25], 'jinv': [-52893159101157376, 11], 'lmfdb_iso': '11.a', 'lmfdb_label': '11.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -7820, -263580], 'min_quad_twist_disc': 1, 'modell_images': ['5B.1.2'], 'modm_images': ['5.24.0-5.a.2.2', '22.2.0.a.1', '25.120.0-25.a.2.2', '110.48.1.?', '275.600.12.?', '550.1200.37.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 1, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.49670911509864712261136540515', 'prec': 103}, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, -1, 2, 1, 2, -2, 0, -2, -2, 1, -2, 4, 4, -1, -4, -2, 4, 0, 2], 'aplist': [-2, -1, 1, -2, 1, 4, -2, 0, -1, 0, 7, 3, -8, -6, 8, -6, 5, 12, -7, -3, 4, -10, -6, 15, -7], 'class_deg': 25, 'class_size': 3, 'conductor': 11, 'isogeny_matrix': [[1, 5, 25], [5, 1, 5], [25, 5, 1]], 'lmfdb_iso': '11.a', 'trace_hash': 1428752966040989219}
• 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': '0.37030872469119186354160134237', 'prec': 103}, 'conductor': 11, 'gens': [], 'heights': [], 'lmfdb_label': '11.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.25384186085591068433775892335', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.25384186085591068433775892335043887465', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 1, 0], '3': [0, 0], '5': [0, 2], '11': [1, 0]}, 'iwp0': 7, 'lmfdb_label': '11.a1'}
• ec_torsion_growth •

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

  
  
  • id: 6
    {'degree': 3, 'field': [1, 1, -1, 1], 'lmfdb_label': '11.a1', 'torsion': [2]}
  • id: 7
    {'degree': 4, 'field': [1, -1, 1, -1, 1], 'lmfdb_label': '11.a1', 'torsion': [5]}
  • id: 8
    {'degree': 5, 'field': [-11, 0, 0, 0, 0, 1], 'lmfdb_label': '11.a1', 'torsion': [5]}
  • id: 9
    {'degree': 6, 'field': [1, -1, 2, -3, 2, -1, 1], 'lmfdb_label': '11.a1', 'torsion': [2, 2]}
  • id: 10
    {'degree': 8, 'field': [-1, 1, 2, -7, 7, -7, 7, -4, 1], 'lmfdb_label': '11.a1', 'torsion': [3]}
  • id: 11
    {'degree': 12, 'field': [-1, 6, -10, 4, -3, 12, -8, -4, 5, -2, 6, -4, 1], 'lmfdb_label': '11.a1', 'torsion': [4]}
  • id: 12
    {'degree': 12, 'field': [1, 1, 2, 4, 7, -8, 3, 2, -3, 2, 0, -1, 1], 'lmfdb_label': '11.a1', 'torsion': [10]}
  • id: 13
    {'degree': 15, 'field': [1331, 0, 0, 0, 0, 2541, 0, 0, 0, 0, -11, 0, 0, 0, 0, 1], 'lmfdb_label': '11.a1', 'torsion': [10]}
  • id: 14
    {'degree': 20, 'field': [20736, -8640, -13680, -4380, 11785, -30338, 12890, 13055, 4555, -11860, 9489, -4380, 815, -35, 20, -77, 70, -35, 15, -5, 1], 'lmfdb_label': '11.a1', 'torsion': [5, 5]}
  • id: 16
    {'degree': 20, 'field': [1771561, 0, 0, 0, 0, -54571, 0, 0, 0, 0, 1881, 0, 0, 0, 0, -41, 0, 0, 0, 0, 1], 'lmfdb_label': '11.a1', 'torsion': [25]}
  • id: 15
    {'degree': 20, 'field': [25937424601, 0, 0, 0, 0, -72634001, 0, 0, 0, 0, 227601, 0, 0, 0, 0, -451, 0, 0, 0, 0, 1], 'lmfdb_label': '11.a1', 'torsion': [25]}
• 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

  
  {'conductor': 11, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '11.a1', 'prime': 11, '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: 1665888
    {'adelic_gens': [[336, 145, 515, 216], [38, 41, 191, 539], [1, 50, 0, 1], [1, 0, 50, 1], [440, 9, 127, 213], [501, 50, 500, 51]], 'adelic_image': '550.1200.37.?', 'conductor': 11, 'lmfdb_label': '11.a1', 'prime': 0}
  • id: 0
    {'conductor': 11, 'elladic_image': '25.120.0.3', 'lmfdb_label': '11.a1', 'modell_image': '5B.1.2', 'prime': 5}
• lmfdb_iso 11.a does not appear in ec_padic