Elliptic curve data - 11616.v1

Formats: - HTML - YAML - JSON - 2026-03-29T05:15:24.338021

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '11616k', 'Clabel': '11616k1', 'Cnumber': 1, 'abc_quality': 1.1575217128087703, 'absD': 7902125789184, 'adelic_genus': 0, 'adelic_index': 4, 'adelic_level': 24, 'ainvs': [0, 1, 0, -19521, 1051983], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 11616, 'degree': 25344, 'elladic_images': ['4.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2954600930595358860895996826', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1], 'jinv': [-937024, 9], 'lmfdb_iso': '11616.v', 'lmfdb_label': '11616.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -161, 849], 'min_quad_twist_disc': 44, 'modell_images': [], 'modm_images': ['4.2.0.a.1', '24.4.0-4.a.1.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.27511489786986788139664731147', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 121], [3, 4, 3872], [11, 42, 96]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.99628393603265645270226149083', 'prec': 107}, 'szpiro_ratio': 4.40889335950959, '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, 0, 1, 0, -1, 0, -2, 0, 1, 0, 0, 0, 1, 0, -1, 0, 5, 0, -8, 0], 'aplist': [0, 1, -1, -2, 0, 1, 5, -8, 6, 3, 4, -11, -3, 2, 4, 3, 6, -10, -2, 6, -2, 0, -12, 13, -9], 'class_deg': 1, 'class_size': 1, 'conductor': 11616, 'isogeny_matrix': [[1]], 'lmfdb_iso': '11616.v', 'trace_hash': 1367384046354456201}
• 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': '0.074951039437376275309061515798', 'prec': 107}, 'conductor': 11616, 'gens': [[-81, 1452, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.27511489786986788139664731147', 'prec': 103}], 'lmfdb_label': '11616.v1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.74270139365193600500397455265', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9038772334966619761665650930866400156', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': [-81, 63, 161]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '11616.v1'}
• ec_torsion_growth •

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

  
  
  • id: 601068
    {'degree': 3, 'field': [2, 4, -1, 1], 'lmfdb_label': '11616.v1', 'torsion': [2]}
  • id: 601069
    {'degree': 6, 'field': [4, 0, 20, 0, -7, 0, 1], 'lmfdb_label': '11616.v1', 'torsion': [2, 2]}
  • id: 601070
    {'degree': 8, 'field': [-192, 0, 320, 0, 48, 0, 0, 0, 1], 'lmfdb_label': '11616.v1', 'torsion': [3]}
  • id: 601071
    {'degree': 12, 'field': [-4, 0, 52, 0, -44, 0, 12, 0, 11, 0, -1, 0, 1], 'lmfdb_label': '11616.v1', 'torsion': [4]}
• 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: 249747
    {'conductor': 11616, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '11616.v1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 249748
    {'conductor': 11616, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '11616.v1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 249749
    {'conductor': 11616, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '11616.v1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1741057
    {'adelic_gens': [[1, 4, 0, 1], [13, 1, 2, 21], [23, 20, 22, 15], [17, 4, 10, 9], [2, 3, 19, 17], [1, 0, 4, 1], [21, 4, 20, 5], [13, 4, 2, 9], [1, 2, 2, 5]], 'adelic_image': '24.4.0.?', 'conductor': 11616, 'lmfdb_label': '11616.v1', 'prime': 0}
  • id: 55742
    {'conductor': 11616, 'elladic_image': '4.2.0.1', 'lmfdb_label': '11616.v1', 'modell_image': '2G', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 503224
    {'lmfdb_iso': '11616.v', 'p': 5, 'prec': 20, 'unit': 16160410494242, 'val': 1}
  • id: 503225
    {'lmfdb_iso': '11616.v', 'p': 7, 'prec': 20, 'unit': 10138680243006688, 'val': 1}
  • id: 503230
    {'lmfdb_iso': '11616.v', 'p': 13, 'prec': 20, 'unit': 2592282675553428913758, 'val': -1}
  • id: 503232
    {'lmfdb_iso': '11616.v', 'p': 17, 'prec': 20, 'unit': 167601058252535842069479, 'val': 1}
  • id: 503233
    {'lmfdb_iso': '11616.v', 'p': 19, 'prec': 20, 'unit': 405741967497510714323775, 'val': 1}
  • id: 503236
    {'lmfdb_iso': '11616.v', 'p': 23, 'prec': 20, 'unit': 31703578103740069257054619, 'val': 1}
  • id: 503229
    {'lmfdb_iso': '11616.v', 'p': 29, 'prec': 20, 'unit': 5265194253061792342596427031, 'val': 1}
  • id: 503226
    {'lmfdb_iso': '11616.v', 'p': 31, 'prec': 20, 'unit': 14452525040671769389737993546, 'val': 1}
  • id: 503241
    {'lmfdb_iso': '11616.v', 'p': 37, 'prec': 20, 'unit': 374181475821976514274826126743, 'val': 1}
  • id: 503227
    {'lmfdb_iso': '11616.v', 'p': 41, 'prec': 20, 'unit': 2740303266534453620829716267470, 'val': 1}
  • id: 503228
    {'lmfdb_iso': '11616.v', 'p': 43, 'prec': 20, 'unit': 5100988822981788892752959439153, 'val': 1}
  • id: 503231
    {'lmfdb_iso': '11616.v', 'p': 47, 'prec': 20, 'unit': 40823818842816371187194368308145, 'val': 1}
  • id: 503234
    {'lmfdb_iso': '11616.v', 'p': 53, 'prec': 20, 'unit': 35862731007747282048794441194450, 'val': 1}
  • id: 503239
    {'lmfdb_iso': '11616.v', 'p': 59, 'prec': 20, 'unit': 2469265208986699136549271504298956, 'val': 1}
  • id: 503240
    {'lmfdb_iso': '11616.v', 'p': 61, 'prec': 20, 'unit': 4391286534533240911412211358827356, 'val': 1}
  • id: 503223
    {'lmfdb_iso': '11616.v', 'p': 67, 'prec': 20, 'unit': 30436016596323124025292524002257772, 'val': 1}
  • id: 503238
    {'lmfdb_iso': '11616.v', 'p': 71, 'prec': 20, 'unit': 96741028776127980871148592850839136, 'val': 1}
  • id: 503235
    {'lmfdb_iso': '11616.v', 'p': 73, 'prec': 20, 'unit': 180319899507200391200427094333041036, 'val': 1}
  • id: 503222
    {'lmfdb_iso': '11616.v', 'p': 83, 'prec': 20, 'unit': 2295395338925364473066250997685097801, 'val': 1}
  • id: 503237
    {'lmfdb_iso': '11616.v', 'p': 89, 'prec': 20, 'unit': 2714415109035691984471582256401069304, 'val': 1}
  • id: 503221
    {'lmfdb_iso': '11616.v', 'p': 97, 'prec': 20, 'unit': 5276492826941164180680656576028975894, 'val': 1}