Elliptic curve data - 9032.a1

Formats: - HTML - YAML - JSON - 2025-10-21T04:30:47.472035

• 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': '9032a', 'Clabel': '9032a1', 'Cnumber': 1, 'abc_quality': 0.6709564157416406, 'absD': 18064, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 2258, 'ainvs': [0, 0, 0, -7, 3], 'analytic_rank': 2, 'bad_primes': [2, 1129], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 9032, 'degree': 496, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.48923448296098109553234112425', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [2370816, 1129], 'lmfdb_iso': '9032.a', 'lmfdb_label': '9032.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -7, 3], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['2258.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 8, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.77529483525476900439145516569', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 1129], [1129, 1130, 8]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.72028354314762953200475183140', 'prec': 107}, 'szpiro_ratio': 1.9159332178804462, '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, 0, 0, 1, 0, -5, 0, -3, 0, -2, 0, -4, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, 1, -5, -2, -4, -2, -4, -5, 0, -10, 0, -6, -3, -5, 11, 6, 0, -4, 5, -4, -3, 6, 2, -10], 'class_deg': 1, 'class_size': 1, 'conductor': 9032, 'isogeny_matrix': [[1]], 'lmfdb_iso': '9032.a', 'trace_hash': 2301187233270540886}
• 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': '2.6603799898602470048160364692', 'prec': 100}, 'conductor': 9032, 'gens': [[-1, 3, 1], [3, 3, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.84401592634613412104900880314', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.99737702088169122586002010495', 'prec': 103}], 'lmfdb_label': '9032.a1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '3.4594323241812683036207727008', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.3641600277022780970753527369137301605', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [-2, -1, 3, 39]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 2, 0], '5': [2, 0], '7': [2, 0], '11': [2, 0], '13': [2, 0], '17': [2, 0], '19': [2, 0], '23': [2, 0], '29': [2, 2, 0], '31': [4, 0], '37': [2, 2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0], '1129': 'o?'}, 'iwp0': 0, 'lmfdb_label': '9032.a1'}
• ec_torsion_growth •

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

  
  
  • id: 470829
    {'degree': 3, 'field': [-3, -7, 0, 1], 'lmfdb_label': '9032.a1', 'torsion': [2]}
  • id: 470830
    {'degree': 6, 'field': [27, 129, 128, -31, -36, -2, 1], 'lmfdb_label': '9032.a1', 'torsion': [2, 2]}
  • id: 470831
    {'degree': 8, 'field': [-1323, 0, 324, 0, -126, 0, 0, 0, 1], 'lmfdb_label': '9032.a1', 'torsion': [3]}
  • id: 470832
    {'degree': 12, 'field': [1129, 0, 3402, 0, -6615, 0, 810, 0, -210, 0, 0, 0, 1], 'lmfdb_label': '9032.a1', '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: 189264
    {'conductor': 9032, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '9032.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 189265
    {'conductor': 9032, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '9032.a1', 'prime': 1129, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  {'adelic_gens': [[11, 2, 11, 3], [1, 1, 2257, 0], [2257, 2, 2256, 3], [1, 0, 2, 1], [1, 2, 0, 1]], 'adelic_image': '2258.2.0.?', 'conductor': 9032, 'lmfdb_label': '9032.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 376570
    {'lmfdb_iso': '9032.a', 'p': 5, 'prec': 20, 'unit': 277230066713, 'val': 0}
  • id: 376571
    {'lmfdb_iso': '9032.a', 'p': 7, 'prec': 20, 'unit': 6983129688991420, 'val': 2}
  • id: 376576
    {'lmfdb_iso': '9032.a', 'p': 11, 'prec': 20, 'unit': 17547240423151914103, 'val': 2}
  • id: 376574
    {'lmfdb_iso': '9032.a', 'p': 13, 'prec': 20, 'unit': 16940636686184270793, 'val': 2}
  • id: 376577
    {'lmfdb_iso': '9032.a', 'p': 17, 'prec': 20, 'unit': 170398629291886637989450, 'val': 2}
  • id: 376578
    {'lmfdb_iso': '9032.a', 'p': 19, 'prec': 20, 'unit': 1851645730710100721043908, 'val': 2}
  • id: 376582
    {'lmfdb_iso': '9032.a', 'p': 23, 'prec': 20, 'unit': 13108384197610474843410052, 'val': 2}
  • id: 376586
    {'lmfdb_iso': '9032.a', 'p': 31, 'prec': 20, 'unit': 309637215329146568288339443, 'val': 3}
  • id: 376572
    {'lmfdb_iso': '9032.a', 'p': 41, 'prec': 20, 'unit': 860271517355268161810720886603, 'val': 2}
  • id: 376573
    {'lmfdb_iso': '9032.a', 'p': 43, 'prec': 20, 'unit': 8332799774085089295372677211122, 'val': 2}
  • id: 376585
    {'lmfdb_iso': '9032.a', 'p': 47, 'prec': 20, 'unit': 34856506523681326236862904432144, 'val': 2}
  • id: 376579
    {'lmfdb_iso': '9032.a', 'p': 53, 'prec': 20, 'unit': 64647441479412997690606326573273, 'val': 2}
  • id: 376580
    {'lmfdb_iso': '9032.a', 'p': 59, 'prec': 20, 'unit': 317000245848489911433544458957020, 'val': 2}
  • id: 376569
    {'lmfdb_iso': '9032.a', 'p': 67, 'prec': 20, 'unit': 13138167204459526524789498179906483, 'val': 2}
  • id: 376584
    {'lmfdb_iso': '9032.a', 'p': 71, 'prec': 20, 'unit': 48758217162824964064624981513353940, 'val': 2}
  • id: 376581
    {'lmfdb_iso': '9032.a', 'p': 73, 'prec': 20, 'unit': 17620316923892896464534694403374120, 'val': 2}
  • id: 376575
    {'lmfdb_iso': '9032.a', 'p': 79, 'prec': 20, 'unit': 580343745369028259670842792918902914, 'val': 2}
  • id: 376568
    {'lmfdb_iso': '9032.a', 'p': 83, 'prec': 20, 'unit': 2554067910604223405616386126820751183, 'val': 2}
  • id: 376583
    {'lmfdb_iso': '9032.a', 'p': 89, 'prec': 20, 'unit': 152487673277787826351668466495551107, 'val': 2}
  • id: 376567
    {'lmfdb_iso': '9032.a', 'p': 97, 'prec': 20, 'unit': 37149381958210999129322702854799985952, 'val': 2}