Elliptic curve data - 89280.em2

Formats: - HTML - YAML - JSON - 2025-05-28T20:41:17.612647

• 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': '89280by', 'Clabel': '89280by3', 'Cnumber': 3, 'abc_quality': 0.9843684825243706, 'absD': 3970971258716160, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3720, 'ainvs': [0, 0, 0, -80652, 8278256], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 31], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 89280, 'degree': 393216, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7414910511931886505218621176', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 116, 'isogeny_degrees': [1, 2, 4], 'jinv': [607199886722, 41558445], 'lmfdb_iso': '89280.em', 'lmfdb_label': '89280.em2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -2240, -39072], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.1', '40.12.0.v.1', '60.12.0-4.c.1.1', '120.24.0.?', '248.12.0.?', '744.24.0.?', '1240.24.0.?', '3720.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9508730951938552512562069624', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 45], [3, 8, 9920], [5, 6, 17856], [31, 32, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.21022640106587794981649399374', 'prec': 103}, 'szpiro_ratio': 3.992032003922008, '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, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 1, 0, 0, 2, -6, -4, -4, 2, -1, 2, 6, 4, 0, -10, 12, -10, -4, 0, 14, -8, 12, -10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 89280, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '89280.em', 'trace_hash': 407744948831400109}
• 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': '0.030715677026873155848441869819', 'prec': 107}, 'conductor': 89280, 'gens': [[46, 2160, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9508730951938552512562069624', 'prec': 100}], 'lmfdb_label': '89280.em2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.43182534734993390769324978265', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.7394916157418177740503583770270206775', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[196, 0, 1]], 'xcoord_integral_points': [46, 196]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': [1, 5, 0], '11': [1, 1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [3, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '89280.em2'}
• ec_torsion_growth •

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

  
  
  • id: 4176192
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [4]}
  • id: 4176191
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [2, 2]}
  • id: 4176193
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [4]}
  • id: 4176194
    {'degree': 4, 'field': [1, 0, -8, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [2, 4]}
  • id: 4176198
    {'degree': 8, 'field': [-16875, 0, 0, 0, 450, 0, 22, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [6]}
  • id: 4176195
    {'degree': 8, 'field': [186, -696, 772, -168, 125, -52, 22, -4, 1], 'lmfdb_label': '89280.em2', 'torsion': [2, 4]}
  • id: 4176196
    {'degree': 8, 'field': [625, 0, -3500, 0, 2160, 0, -140, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [8]}
  • id: 4176197
    {'degree': 8, 'field': [1900, -3320, 2402, -1056, 302, -24, -7, -2, 1], 'lmfdb_label': '89280.em2', 'torsion': [8]}
  • id: 4176199
    {'degree': 16, 'field': [2116, 14720, 51200, 104000, 118436, 44560, 0, -9920, -459, 1160, 800, -80, -54, -40, 0, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [4, 4]}
  • id: 4176204
    {'degree': 16, 'field': [77841, 0, -103788, 0, 34596, 0, -24516, 0, 9846, 0, 156, 0, 36, 0, -12, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [12]}
  • id: 4176201
    {'degree': 16, 'field': [217156, 0, -187544, 0, 150752, 0, -64740, 0, 23021, 0, -4920, 0, 722, 0, -44, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [2, 8]}
  • id: 4176202
    {'degree': 16, 'field': [222784, 0, -9728, 0, -14720, 0, -64256, 0, 19600, 0, -584, 0, 148, 0, -20, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [2, 6]}
  • id: 4176200
    {'degree': 16, 'field': [570923236, 0, -1584430512, 0, 1003523188, 0, -224750064, 0, 21603165, 0, -1006404, 0, 23278, 0, -252, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [2, 8]}
  • id: 4176203
    {'degree': 16, 'field': [43785562500, 0, -17514225000, 0, -94162500, 0, -19440000, 0, 270000, 0, -96660, 0, 4384, 0, -76, 0, 1], 'lmfdb_label': '89280.em2', 'torsion': [12]}
• 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: 2181973
    {'conductor': 89280, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '89280.em2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2181974
    {'conductor': 89280, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '89280.em2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2181975
    {'conductor': 89280, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '89280.em2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2181976
    {'conductor': 89280, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '89280.em2', '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: 2251966
    {'adelic_gens': [[152, 2007, 3573, 1106], [748, 2481, 2751, 1246], [1801, 1248, 2244, 1273], [2479, 0, 0, 3719], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [163, 156, 2682, 781], [7, 6, 3714, 3715], [3713, 8, 3712, 9]], 'adelic_image': '3720.48.0.?', 'conductor': 89280, 'lmfdb_label': '89280.em2', 'prime': 0}
  • id: 363056
    {'conductor': 89280, 'elladic_image': '4.6.0.1', 'lmfdb_label': '89280.em2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 4619064
    {'lmfdb_iso': '89280.em', 'p': 13, 'prec': 20, 'unit': 68475079430438251068, 'val': 2}
  • id: 4619066
    {'lmfdb_iso': '89280.em', 'p': 17, 'prec': 20, 'unit': 4822694173445596869481, 'val': 1}
  • id: 4619057
    {'lmfdb_iso': '89280.em', 'p': 19, 'prec': 20, 'unit': 444398470656623306829949, 'val': 1}
  • id: 4619070
    {'lmfdb_iso': '89280.em', 'p': 23, 'prec': 20, 'unit': 6047125579033652620397651, 'val': 1}
  • id: 4619063
    {'lmfdb_iso': '89280.em', 'p': 29, 'prec': 20, 'unit': 147254850822158650237244537, 'val': 2}
  • id: 4619060
    {'lmfdb_iso': '89280.em', 'p': 37, 'prec': 20, 'unit': 468946897207611806810101312567, 'val': 1}
  • id: 4619061
    {'lmfdb_iso': '89280.em', 'p': 41, 'prec': 20, 'unit': 67782747269591623087133708451, 'val': 2}
  • id: 4619062
    {'lmfdb_iso': '89280.em', 'p': 43, 'prec': 20, 'unit': 10659278016022784096911637027413, 'val': 1}
  • id: 4619068
    {'lmfdb_iso': '89280.em', 'p': 53, 'prec': 20, 'unit': 326106708762294720302822494083802, 'val': 1}
  • id: 4619072
    {'lmfdb_iso': '89280.em', 'p': 59, 'prec': 20, 'unit': 3909054408469399741893343791054346, 'val': 1}
  • id: 4619073
    {'lmfdb_iso': '89280.em', 'p': 61, 'prec': 20, 'unit': 5804272163611164744435348591042138, 'val': 1}
  • id: 4619059
    {'lmfdb_iso': '89280.em', 'p': 67, 'prec': 20, 'unit': 28625697958859083498820479699186919, 'val': 1}
  • id: 4619069
    {'lmfdb_iso': '89280.em', 'p': 73, 'prec': 20, 'unit': 161563374286654081272830635223026948, 'val': 1}
  • id: 4619065
    {'lmfdb_iso': '89280.em', 'p': 79, 'prec': 20, 'unit': 123092041011979309305166199552077639, 'val': 1}
  • id: 4619067
    {'lmfdb_iso': '89280.em', 'p': 83, 'prec': 20, 'unit': 1547797242054589024700078588146353804, 'val': 1}
  • id: 4619071
    {'lmfdb_iso': '89280.em', 'p': 89, 'prec': 20, 'unit': 3007011537640687975760788823624202850, 'val': 1}
  • id: 4619058
    {'lmfdb_iso': '89280.em', 'p': 97, 'prec': 20, 'unit': 25273754575098675705563190360591209930, 'val': 1}