Elliptic curve data - 10890.ba4

Formats: - HTML - YAML - JSON - 2025-10-19T12:08:16.948974

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

  
  {'Ciso': '10890ba', 'Clabel': '10890ba5', 'Cnumber': 5, 'abc_quality': 1.0501740895315954, 'absD': 43587043953750, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1320, 'ainvs': [1, -1, 0, -314199, 67866255], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 10890, 'degree': 92160, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7631136216155369523202141105', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [2656166199049, 33750], 'lmfdb_iso': '10890.ba', 'lmfdb_label': '10890.ba4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -289, 1862], 'min_quad_twist_disc': 33, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.4', '24.96.1.da.3', '33.8.0-3.a.1.1', '40.12.0.bb.1', '44.12.0-4.c.1.1', '66.24.0-6.a.1.1', '120.192.5.?', '132.96.0.?', '264.192.1.?', '440.24.0.?', '1320.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1089], [3, 2, 1210], [5, 6, 2178], [11, 62, 90]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.014859840882296834591619703056', 'prec': 107}, 'szpiro_ratio': 5.334453842406557, '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, 0, 1, 1, 0, 4, -1, 0, -1, 0, 0, -2, -4, 0, 1, 6, 0, 4, 1], 'aplist': [-1, 0, 1, 4, 0, -2, 6, 4, 0, -6, 8, 2, -6, 4, 0, 6, 0, 10, -4, 0, -2, -8, 12, -18, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 10890, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '10890.ba', 'trace_hash': 2153690495676324668}
• 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': '0.029415685007866055992359849746', 'prec': 107}, 'conductor': 10890, 'gens': [], 'heights': [], 'lmfdb_label': '10890.ba4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.58349929585354148565000639307', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3339971834141659426000255722641491878', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[1299, -1299, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 0], '11': 'a'}, 'iwp0': 5, 'lmfdb_label': '10890.ba4'}
• ec_torsion_growth •

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

  
  
  • id: 564554
    {'degree': 2, 'field': [-66, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [4]}
  • id: 564555
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [4]}
  • id: 564556
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '10890.ba4', 'torsion': [6]}
  • id: 564553
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [2, 2]}
  • id: 564560
    {'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [12]}
  • id: 564558
    {'degree': 4, 'field': [16, 0, -14, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [2, 6]}
  • id: 564557
    {'degree': 4, 'field': [25, 0, -34, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [2, 4]}
  • id: 564559
    {'degree': 4, 'field': [34, 20, -19, -2, 1], 'lmfdb_label': '10890.ba4', 'torsion': [12]}
  • id: 564561
    {'degree': 6, 'field': [135, -105, 30, 7, 2, -1, 1], 'lmfdb_label': '10890.ba4', 'torsion': [6]}
  • id: 564565
    {'degree': 8, 'field': [-18, 108, -162, 0, 103, -12, -22, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [2, 12]}
  • id: 564562
    {'degree': 8, 'field': [75, -300, 342, -96, 79, -40, 18, -4, 1], 'lmfdb_label': '10890.ba4', 'torsion': [2, 4]}
  • id: 564563
    {'degree': 8, 'field': [100, 0, -3120, 0, 706, 0, -48, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [8]}
  • id: 564564
    {'degree': 8, 'field': [5140, -80, 1081, 598, 73, 16, 13, -2, 1], 'lmfdb_label': '10890.ba4', 'torsion': [8]}
  • id: 564566
    {'degree': 12, 'field': [36, 0, 2292, 0, 1036, 0, 503, 0, 111, 0, 17, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [3, 6]}
  • id: 564569
    {'degree': 12, 'field': [2953, -1282, 745, -628, -230, -522, 329, -186, 148, -20, 19, -2, 1], 'lmfdb_label': '10890.ba4', 'torsion': [12]}
  • id: 564568
    {'degree': 12, 'field': [4335, -2550, -1475, 7766, -2940, -1806, 1793, -1158, 468, -130, 37, -6, 1], 'lmfdb_label': '10890.ba4', 'torsion': [12]}
  • id: 564567
    {'degree': 12, 'field': [17235, 6210, -6915, 1638, -1232, 42, 785, -774, 312, -90, 29, -6, 1], 'lmfdb_label': '10890.ba4', 'torsion': [2, 6]}
  • id: 564570
    {'degree': 16, 'field': [5625, 0, 38700, 0, 71214, 0, -23520, 0, 8623, 0, -1160, 0, 162, 0, -20, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [4, 4]}
  • id: 564573
    {'degree': 16, 'field': [11619, 20448, 18828, -78552, 43440, -18120, 32568, -32904, 22933, -13112, 6292, -2480, 838, -224, 52, -8, 1], 'lmfdb_label': '10890.ba4', 'torsion': [2, 12]}
  • id: 564575
    {'degree': 16, 'field': [21400, 51600, 18840, -79680, 43114, 28068, -18558, -4296, 6141, 552, -834, -24, 100, -12, -12, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [24]}
  • id: 564571
    {'degree': 16, 'field': [140625, 0, -682500, 0, 1091350, 0, -733680, 0, 221511, 0, -33064, 0, 2466, 0, -84, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [2, 8]}
  • id: 564572
    {'degree': 16, 'field': [799236, 0, -353736, 0, 35304, 0, -24804, 0, 8965, 0, -344, 0, 114, 0, 4, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [2, 8]}
  • id: 564574
    {'degree': 16, 'field': [5180176, 0, -26271552, 0, 18734072, 0, -5644800, 0, 884256, 0, -77040, 0, 3758, 0, -96, 0, 1], 'lmfdb_label': '10890.ba4', 'torsion': [24]}
  • id: 564576
    {'degree': 18, 'field': [199984, 1085232, -89064, -1012004, 1111728, -944382, 266849, -13374, -12720, -3179, 12255, -6012, 209, 906, -465, 103, 0, -6, 1], 'lmfdb_label': '10890.ba4', '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: 232743
    {'conductor': 10890, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '10890.ba4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 232744
    {'conductor': 10890, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '10890.ba4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 232745
    {'conductor': 10890, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '10890.ba4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 232746
    {'conductor': 10890, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '10890.ba4', 'prime': 11, '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: 1736146
    {'adelic_gens': [[694, 363, 495, 34], [1057, 264, 924, 529], [1, 12, 12, 145], [606, 649, 275, 56], [1297, 24, 1296, 25], [119, 0, 0, 1319], [15, 106, 14, 11], [824, 759, 385, 934], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '1320.384.5.?', 'conductor': 10890, 'lmfdb_label': '10890.ba4', 'prime': 0}
  • id: 52386
    {'conductor': 10890, 'elladic_image': '4.6.0.1', 'lmfdb_label': '10890.ba4', 'modell_image': '2B', 'prime': 2}
  • id: 52387
    {'conductor': 10890, 'elladic_image': '3.4.0.1', 'lmfdb_label': '10890.ba4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 10890.ba does not appear in ec_padic