Elliptic curve data - 33282.s2

Formats: - HTML - YAML - JSON - 2026-04-07T20:19:46.042786

• 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': '33282y', 'Clabel': '33282y1', 'Cnumber': 1, 'abc_quality': 0.8541295359409509, 'absD': 136331168037938064, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 516, 'ainvs': [1, -1, 1, -283244, -55164193], 'analytic_rank': 1, 'bad_primes': [2, 3, 43], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 33282, 'degree': 433440, 'elladic_images': ['2.2.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0438299195726534805441650388', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 3], 'jinv': [294937, 16], 'lmfdb_iso': '33282.s', 'lmfdb_label': '33282.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -17, -33], 'min_quad_twist_disc': 129, 'modell_images': ['2Cn', '3B.1.2'], 'modm_images': ['2.2.0.a.1', '3.8.0-3.a.1.1', '6.16.0-6.a.1.1', '12.32.0-12.a.2.1', '86.6.0.?', '258.48.0.?', '516.96.2.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.3966785793088360617865248437', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 16641], [3, 2, 3698], [43, 674, 18]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0129429685571096474686859219', 'prec': 103}, 'szpiro_ratio': 4.732245338845808, '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, 1, 0, 1, -3, 0, -1, 1, 0, -3, 0, 0, -1, -1, 0, 1, -3, 0, -7, -3], 'aplist': [1, 0, -3, -1, 0, -1, -3, -7, 3, 9, -7, 11, -6, 0, 0, 9, 12, -1, 5, -3, 11, -1, 15, 9, -10], 'class_deg': 3, 'class_size': 2, 'conductor': 33282, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '33282.s', 'trace_hash': 2022116495914867521}
• 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': '0.016778451928441149830784183838', 'prec': 107}, 'conductor': 33282, 'gens': [[-2309, 23789, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3966785793088360617865248437', 'prec': 100}], 'lmfdb_label': '33282.s2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.20764635241911063661887528258', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.9719387789739516968915961022523564716', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [3, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [3, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': 'a', '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '33282.s2'}
• ec_torsion_growth •

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

  
  
  • id: 1653496
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '33282.s2', 'torsion': [3]}
  • id: 1653497
    {'degree': 3, 'field': [-8, -14, -1, 1], 'lmfdb_label': '33282.s2', 'torsion': [2, 2]}
  • id: 1653498
    {'degree': 3, 'field': [121, 29, -1, 1], 'lmfdb_label': '33282.s2', 'torsion': [3]}
  • id: 1653500
    {'degree': 6, 'field': [64, 112, 188, 30, 15, -1, 1], 'lmfdb_label': '33282.s2', 'torsion': [2, 6]}
  • id: 1653499
    {'degree': 6, 'field': [1083, 57, -56, -3, 4, -3, 1], 'lmfdb_label': '33282.s2', 'torsion': [3, 3]}
  • id: 1653501
    {'degree': 9, 'field': [-64, 0, 0, -124, 0, 0, -12, 0, 0, 1], 'lmfdb_label': '33282.s2', 'torsion': [2, 6]}
  • id: 1653502
    {'degree': 12, 'field': [-428, 1536, -1311, 935, 253, -116, 138, 46, -34, 4, 5, -5, 1], 'lmfdb_label': '33282.s2', 'torsion': [2, 4]}
  • id: 1653503
    {'degree': 18, 'field': [1, -9, 54, -109, 15, 87, 666, -2352, 4407, -5403, 4704, -2667, 1064, -303, 183, -92, 9, 0, 1], 'lmfdb_label': '33282.s2', 'torsion': [9]}
  • id: 1653504
    {'degree': 18, 'field': [3267, -14553, 36657, -67032, 93006, -78474, 39154, -14568, 10269, -7983, 5055, -1824, 382, -210, 198, -108, 39, -9, 1], 'lmfdb_label': '33282.s2', 'torsion': [6, 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: 778958
    {'conductor': 33282, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '33282.s2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 778959
    {'conductor': 33282, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '33282.s2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 778960
    {'conductor': 33282, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '33282.s2', 'prime': 43, '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: 1886282
    {'adelic_gens': [[480, 511, 425, 47], [163, 514, 114, 503], [259, 12, 6, 73], [7, 12, 450, 403], [5, 2, 478, 501], [1, 0, 12, 1], [1, 12, 0, 1], [505, 12, 504, 13]], 'adelic_image': '516.96.2.?', 'conductor': 33282, 'lmfdb_label': '33282.s2', 'prime': 0}
  • id: 148363
    {'conductor': 33282, 'elladic_image': '2.2.0.1', 'lmfdb_label': '33282.s2', 'modell_image': '2Cn', 'prime': 2}
  • id: 148364
    {'conductor': 33282, 'elladic_image': '3.8.0.2', 'lmfdb_label': '33282.s2', 'modell_image': '3B.1.2', 'prime': 3}
• ec_padic •

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

  
  
  • id: 1623659
    {'lmfdb_iso': '33282.s', 'p': 5, 'prec': 20, 'unit': 14335338424014, 'val': 1}
  • id: 1623660
    {'lmfdb_iso': '33282.s', 'p': 7, 'prec': 20, 'unit': 6386428835891012, 'val': 1}
  • id: 1623665
    {'lmfdb_iso': '33282.s', 'p': 13, 'prec': 20, 'unit': 1411357890701825901870, 'val': 1}
  • id: 1623667
    {'lmfdb_iso': '33282.s', 'p': 17, 'prec': 20, 'unit': 54173929941049231641210, 'val': 1}
  • id: 1623656
    {'lmfdb_iso': '33282.s', 'p': 19, 'prec': 20, 'unit': 579478615256403878070445, 'val': 1}
  • id: 1623671
    {'lmfdb_iso': '33282.s', 'p': 23, 'prec': 20, 'unit': 2204962415181297807566696, 'val': 1}
  • id: 1623664
    {'lmfdb_iso': '33282.s', 'p': 29, 'prec': 20, 'unit': 49744639956720492398402440, 'val': 2}
  • id: 1623661
    {'lmfdb_iso': '33282.s', 'p': 31, 'prec': 20, 'unit': 3485055153207731489156206323, 'val': 1}
  • id: 1623675
    {'lmfdb_iso': '33282.s', 'p': 37, 'prec': 20, 'unit': 256588143598318619192477152378, 'val': 1}
  • id: 1623662
    {'lmfdb_iso': '33282.s', 'p': 41, 'prec': 20, 'unit': 1380573936867565584279366905754, 'val': 1}
  • id: 1623669
    {'lmfdb_iso': '33282.s', 'p': 53, 'prec': 20, 'unit': 224073005099820328803987562777335, 'val': 1}
  • id: 1623673
    {'lmfdb_iso': '33282.s', 'p': 59, 'prec': 20, 'unit': 115734657157892945741842506376180, 'val': 1}
  • id: 1623674
    {'lmfdb_iso': '33282.s', 'p': 61, 'prec': 20, 'unit': 1751099612568680057530340663590004, 'val': 1}
  • id: 1623658
    {'lmfdb_iso': '33282.s', 'p': 67, 'prec': 20, 'unit': 5527480706662040383433767915064206, 'val': 1}
  • id: 1623663
    {'lmfdb_iso': '33282.s', 'p': 71, 'prec': 20, 'unit': 115020264625821665514398002684181664, 'val': 1}
  • id: 1623670
    {'lmfdb_iso': '33282.s', 'p': 73, 'prec': 20, 'unit': 104702858855954832856568873397142073, 'val': 1}
  • id: 1623666
    {'lmfdb_iso': '33282.s', 'p': 79, 'prec': 20, 'unit': 519585805136051443755856666470134986, 'val': 1}
  • id: 1623668
    {'lmfdb_iso': '33282.s', 'p': 83, 'prec': 20, 'unit': 819339295180440434865487598571475392, 'val': 1}
  • id: 1623672
    {'lmfdb_iso': '33282.s', 'p': 89, 'prec': 20, 'unit': 2719893280401036584867148147784552269, 'val': 1}
  • id: 1623657
    {'lmfdb_iso': '33282.s', 'p': 97, 'prec': 20, 'unit': 3876155309014160728455753483821209427, 'val': 1}