Elliptic curve data - 89280.s1

Formats: - HTML - YAML - JSON - 2025-07-17T09:40:06.371224

• 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': '89280l', 'Clabel': '89280l2', 'Cnumber': 2, 'abc_quality': 0.9991442130115876, 'absD': 8303040000000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 120, 'ainvs': [0, 0, 0, -110508, 13442832], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 31], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 89280, 'degree': 696320, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8097821500643915478005269637', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2], 'jinv': [168690711527064, 9384765625], 'lmfdb_iso': '89280.s', 'lmfdb_label': '89280.s1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -248643, -45369558], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.a.1', '40.6.0.e.1', '60.6.0.c.1', '120.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3], [3, 6, 9920], [5, 6, 17856], [31, 32, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.66869510219743248818017550265', 'prec': 103}, 'szpiro_ratio': 4.074915483419478, '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, 0, 0, -1, 0, -2, 0, 0, 0, 6, 0, 4, 0, 0, 0, 6, 0, -4, 0], 'aplist': [0, 0, -1, -2, 6, 4, 6, -4, 8, 2, 1, 8, -8, 0, 0, 6, -6, -10, 8, 0, 10, 0, 4, 0, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 89280, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '89280.s', 'trace_hash': 46895501512215094}
• 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': '0.026794348243842470402311980271', 'prec': 107}, 'conductor': 89280, 'gens': [], 'heights': [], 'lmfdb_label': '89280.s1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.40789507598324890671249321310', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2631606078659912536999457048162190123', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[156, 0, 1]], 'xcoord_integral_points': [156]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '31': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '89280.s1'}
• ec_torsion_growth •

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

  
  
  • id: 4175576
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '89280.s1', 'torsion': [2, 2]}
  • id: 4175577
    {'degree': 4, 'field': [4, 2, 0, -1, 1], 'lmfdb_label': '89280.s1', 'torsion': [4]}
  • id: 4175580
    {'degree': 8, 'field': [-12675, 0, -2712, 0, 282, 0, -24, 0, 1], 'lmfdb_label': '89280.s1', 'torsion': [6]}
  • id: 4175578
    {'degree': 8, 'field': [16, 0, -14, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '89280.s1', 'torsion': [2, 4]}
  • id: 4175579
    {'degree': 8, 'field': [14776336, 0, -953312, 0, 0, 0, -248, 0, 1], 'lmfdb_label': '89280.s1', 'torsion': [2, 4]}
  • id: 4175581
    {'degree': 16, 'field': [3913846, -10560632, 9924668, -3079248, 489573, 9848, 167194, 102016, -36077, 21768, 5556, -3440, 1833, -384, 82, -8, 1], 'lmfdb_label': '89280.s1', 'torsion': [8]}
  • id: 4175582
    {'degree': 16, 'field': [58293225, 0, -50693616, 0, 7235100, 0, -1718928, 0, 143742, 0, -16080, 0, 780, 0, -48, 0, 1], 'lmfdb_label': '89280.s1', 'torsion': [2, 6]}
• 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: 2181677
    {'conductor': 89280, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '89280.s1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2181678
    {'conductor': 89280, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '89280.s1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2181679
    {'conductor': 89280, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '89280.s1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2181680
    {'conductor': 89280, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '89280.s1', 'prime': 31, 'reduction_type': 1, '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: 2252092
    {'adelic_gens': [[76, 49, 105, 16], [1, 4, 0, 1], [1, 0, 4, 1], [117, 4, 116, 5], [97, 4, 74, 9], [3, 4, 8, 11], [44, 1, 79, 0], [2, 1, 59, 0], [1, 2, 2, 5]], 'adelic_image': '120.12.0.?', 'conductor': 89280, 'lmfdb_label': '89280.s1', 'prime': 0}
  • id: 363177
    {'conductor': 89280, 'elladic_image': '2.3.0.1', 'lmfdb_label': '89280.s1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 89280.s does not appear in ec_padic