Elliptic curve data - 129600.ge1

Formats: - HTML - YAML - JSON - 2025-09-27T18:04:36.817402

• 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': '129600eb', 'Clabel': '129600eb1', 'Cnumber': 1, 'abc_quality': 0.9613939151787425, 'absD': 5971968000000000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 120, 'ainvs': [0, 0, 0, -38700, 4734000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 129600, 'degree': 663552, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7236738976444537730785805811', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 160, 'isogeny_degrees': [1, 3], 'jinv': [-2146689, 2000], 'lmfdb_iso': '129600.ge', 'lmfdb_label': '129600.ge1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -24, 80], 'min_quad_twist_disc': 40, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '20.2.0.a.1', '24.8.0-3.a.1.8', '60.8.0.a.1', '120.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 2025], [3, 6, 160], [5, 18, 5184]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.67007197374656922404526988616', 'prec': 107}, 'szpiro_ratio': 3.760017444409237, '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, 0, 0, 1, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 4, 0], 'aplist': [0, 0, 0, 1, 6, 2, 0, 4, 9, 3, -4, 8, 3, 8, -3, -6, 6, 13, -13, 6, 4, -10, 9, -9, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 129600, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '129600.ge', 'trace_hash': 1041070505549621004}
• 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': '0.031829944055616592711284183845', 'prec': 107}, 'conductor': 129600, 'gens': [], 'heights': [], 'lmfdb_label': '129600.ge1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.38838042434619499116409040642', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6605650921543398939690848769937249223', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '7': [2, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '129600.ge1'}
• ec_torsion_growth •

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

  
  
  • id: 5892528
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '129600.ge1', 'torsion': [3]}
  • id: 5892529
    {'degree': 3, 'field': [-8, -3, 0, 1], 'lmfdb_label': '129600.ge1', 'torsion': [2]}
  • id: 5892532
    {'degree': 6, 'field': [-10, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '129600.ge1', 'torsion': [6]}
  • id: 5892530
    {'degree': 6, 'field': [80, 0, 36, 0, 12, 0, 1], 'lmfdb_label': '129600.ge1', 'torsion': [2, 2]}
  • id: 5892531
    {'degree': 6, 'field': [750, 0, 300, 0, 30, 0, 1], 'lmfdb_label': '129600.ge1', 'torsion': [3]}
  • id: 5892533
    {'degree': 12, 'field': [64, -288, 330, -388, 462, -492, 308, -348, 198, -80, 33, -6, 1], 'lmfdb_label': '129600.ge1', 'torsion': [4]}
  • id: 5892535
    {'degree': 12, 'field': [3600, 0, -720, 0, 1161, 0, 80, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '129600.ge1', 'torsion': [2, 6]}
  • id: 5892534
    {'degree': 12, 'field': [62001, 1494, 3771, -10050, 3840, 1374, -359, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '129600.ge1', 'torsion': [3, 3]}
  • id: 5892536
    {'degree': 18, 'field': [-39204000, 0, 12150000, 0, 34749000, 0, 3993300, 0, -4617000, 0, -696600, 0, -48870, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '129600.ge1', 'torsion': [9]}
  • id: 5892537
    {'degree': 18, 'field': [27000, 0, 24300, 0, 26730, 0, -9099, 0, -486, 0, 351, 0, -234, 0, 135, 0, -18, 0, 1], 'lmfdb_label': '129600.ge1', 'torsion': [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: 3196080
    {'conductor': 129600, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '129600.ge1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3196081
    {'conductor': 129600, 'conductor_valuation': 4, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '129600.ge1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 3196082
    {'conductor': 129600, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '129600.ge1', 'prime': 5, 'reduction_type': 0, '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: 2508475
    {'adelic_gens': [[4, 3, 9, 7], [6, 1, 25, 51], [31, 6, 33, 19], [1, 6, 0, 1], [37, 6, 51, 19], [1, 0, 6, 1], [115, 6, 114, 7], [59, 0, 0, 119], [3, 4, 8, 11], [65, 114, 66, 113]], 'adelic_image': '120.16.0.?', 'conductor': 129600, 'lmfdb_label': '129600.ge1', 'prime': 0}
  • id: 504954
    {'conductor': 129600, 'elladic_image': '3.4.0.1', 'lmfdb_label': '129600.ge1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 129600.ge does not appear in ec_padic