Elliptic curve data - 32912.g1

Formats: - HTML - YAML - JSON - 2025-11-06T22:13:25.094739

• 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': '32912b', 'Clabel': '32912b1', 'Cnumber': 1, 'abc_quality': 0.5388382050657431, 'absD': 58305615632, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 34, 'ainvs': [0, 0, 0, -1331, 14641], 'analytic_rank': 2, 'bad_primes': [2, 11, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 32912, 'degree': 21120, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.77881726316519520943982247022', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 6, 'isogeny_degrees': [1], 'jinv': [76032, 17], 'lmfdb_iso': '32912.g', 'lmfdb_label': '32912.g1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -11, 11], 'min_quad_twist_disc': 44, 'modell_images': [], 'modm_images': ['34.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '2.2628600464809203431694789473', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 2057], [11, 52, 272], [17, 18, 1936]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0508286455537002564072172889', 'prec': 103}, 'szpiro_ratio': 3.191305574682443, '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, -2, 0, -2, 0, -3, 0, 0, 0, 1, 0, 0, 0, -1, 0, -7, 0], 'aplist': [0, 0, -2, -2, 0, 1, -1, -7, -2, 2, 2, -8, 10, -5, -1, 6, 12, 0, -9, 6, -14, -16, -17, -15, -16], 'class_deg': 1, 'class_size': 1, 'conductor': 32912, 'isogeny_matrix': [[1]], 'lmfdb_iso': '32912.g', 'trace_hash': 348805691413425374}
• 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': '0.21063373091264465694920638628', 'prec': 103}, 'conductor': 32912, 'gens': [[0, 121, 1], [-39, 1307, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '0.43905513445177607492632272645', 'prec': 103}, {'__RealLiteral__': 0, 'data': '5.1686211067334291964675530780', 'prec': 100}], 'lmfdb_label': '32912.g1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '1.0491673966905639652289207739', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.1223569521244272997475388078712521366', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': [-24, 0]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 4, 0], '5': [2, 0], '7': [4, 0], '11': 'a', '13': [2, 0], '17': [2, 0], '19': [2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '32912.g1'}
• ec_torsion_growth •

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

  
  
  • id: 1637944
    {'degree': 3, 'field': [-11, -11, 0, 1], 'lmfdb_label': '32912.g1', 'torsion': [2]}
  • id: 1637945
    {'degree': 6, 'field': [1, -3, -5, 15, -5, -3, 1], 'lmfdb_label': '32912.g1', 'torsion': [2, 2]}
  • id: 1637946
    {'degree': 8, 'field': [-12, 0, 180, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '32912.g1', 'torsion': [3]}
  • id: 1637947
    {'degree': 12, 'field': [153, 0, -418, 0, -723, 0, 110, 0, -14, 0, 0, 0, 1], 'lmfdb_label': '32912.g1', '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: 770525
    {'conductor': 32912, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '32912.g1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 770526
    {'conductor': 32912, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '32912.g1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 770527
    {'conductor': 32912, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '32912.g1', 'prime': 17, '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': [[3, 2, 3, 3], [1, 2, 0, 1], [1, 0, 2, 1], [1, 1, 33, 0], [33, 2, 32, 3]], 'adelic_image': '34.2.0.?', 'conductor': 32912, 'lmfdb_label': '32912.g1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 1604994
    {'lmfdb_iso': '32912.g', 'p': 5, 'prec': 20, 'unit': 14867857840046, 'val': 2}
  • id: 1604995
    {'lmfdb_iso': '32912.g', 'p': 7, 'prec': 20, 'unit': 140112049264587, 'val': 4}
  • id: 1604999
    {'lmfdb_iso': '32912.g', 'p': 13, 'prec': 20, 'unit': 58761641617076681812, 'val': 0}
  • id: 1604991
    {'lmfdb_iso': '32912.g', 'p': 19, 'prec': 20, 'unit': 1443187729136219752802546, 'val': 2}
  • id: 1605005
    {'lmfdb_iso': '32912.g', 'p': 23, 'prec': 20, 'unit': 74310246132834898316161752, 'val': 2}
  • id: 1605009
    {'lmfdb_iso': '32912.g', 'p': 29, 'prec': 20, 'unit': 3160094889567790134892280147, 'val': 2}
  • id: 1604996
    {'lmfdb_iso': '32912.g', 'p': 31, 'prec': 20, 'unit': 255522001189395144089456015, 'val': 2}
  • id: 1605010
    {'lmfdb_iso': '32912.g', 'p': 37, 'prec': 20, 'unit': 507646456212877336233886230882, 'val': 2}
  • id: 1604997
    {'lmfdb_iso': '32912.g', 'p': 41, 'prec': 20, 'unit': 3874666621328319188484643965105, 'val': 2}
  • id: 1604998
    {'lmfdb_iso': '32912.g', 'p': 43, 'prec': 20, 'unit': 450653018352243517117307531434, 'val': 2}
  • id: 1605008
    {'lmfdb_iso': '32912.g', 'p': 47, 'prec': 20, 'unit': 34106075673488639265478618457225, 'val': 2}
  • id: 1605003
    {'lmfdb_iso': '32912.g', 'p': 53, 'prec': 20, 'unit': 83194346026750463365483183576625, 'val': 2}
  • id: 1605001
    {'lmfdb_iso': '32912.g', 'p': 59, 'prec': 20, 'unit': 3298243624615584906670678996441226, 'val': 2}
  • id: 1604993
    {'lmfdb_iso': '32912.g', 'p': 67, 'prec': 20, 'unit': 32820511714653691672588723468785677, 'val': 2}
  • id: 1605007
    {'lmfdb_iso': '32912.g', 'p': 71, 'prec': 20, 'unit': 114363797617673545790293551787395485, 'val': 2}
  • id: 1605004
    {'lmfdb_iso': '32912.g', 'p': 73, 'prec': 20, 'unit': 129935349615161000511279774914997921, 'val': 2}
  • id: 1605000
    {'lmfdb_iso': '32912.g', 'p': 79, 'prec': 20, 'unit': 58910380254848921619996999410698213, 'val': 2}
  • id: 1605002
    {'lmfdb_iso': '32912.g', 'p': 83, 'prec': 20, 'unit': 1326978665885786697274196480302554436, 'val': 2}
  • id: 1605006
    {'lmfdb_iso': '32912.g', 'p': 89, 'prec': 20, 'unit': 8594053484653437565457839547565453317, 'val': 2}
  • id: 1604992
    {'lmfdb_iso': '32912.g', 'p': 97, 'prec': 20, 'unit': 7702109281726383503663241808038474708, 'val': 2}