Elliptic curve data - 3234.v2

Formats: - HTML - YAML - JSON - 2026-02-24T19:08:30.294273

• 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': '3234u', 'Clabel': '3234u1', 'Cnumber': 1, 'abc_quality': 0.975945888236263, 'absD': 719996158328832, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 616, 'ainvs': [1, 0, 0, -19846, -1682332], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 3234, 'degree': 32256, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5487123418864951816633894496', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2], 'jinv': [-7347774183121, 6119866368], 'lmfdb_iso': '3234.v', 'lmfdb_label': '3234.v2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -405, 4731], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '14.6.0.b.1', '88.6.0.?', '616.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 49], [3, 4, 1078], [7, 32, 33], [11, 12, 294]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.57575726735883852911071307788', 'prec': 103}, 'szpiro_ratio': 5.220898562181026, '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, 1, 1, 1, 4, 1, 0, 1, 1, 4, -1, 1, 6, 0, 4, 1, 4, 1, 2, 4], 'aplist': [1, 1, 4, 0, -1, 6, 4, 2, -8, -6, -6, -6, -12, 4, -6, 2, 0, -10, 4, -12, 0, -16, 14, 14, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 3234, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '3234.v', 'trace_hash': 1615710769416343254}
• 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': '0.045165367852688509899194605712', 'prec': 107}, 'conductor': 3234, 'gens': [], 'heights': [], 'lmfdb_label': '3234.v2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.19426372758259079297102446745', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.4393843723125422031886850885092812699', 'prec': 130}, 'tamagawa_product': 112, 'torsion_generators': [[172, -86, 1]], 'xcoord_integral_points': [172]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [1, 0], '5': [0, 0], '7': 'a', '11': [0, 0]}, 'iwp0': 11, 'lmfdb_label': '3234.v2'}
• ec_torsion_growth •

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

  
  
  • id: 169102
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '3234.v2', 'torsion': [2, 2]}
  • id: 169103
    {'degree': 4, 'field': [-6, 8, -7, -2, 1], 'lmfdb_label': '3234.v2', 'torsion': [4]}
  • id: 169105
    {'degree': 8, 'field': [28, 84, 28, -70, 95, -32, 12, -2, 1], 'lmfdb_label': '3234.v2', 'torsion': [2, 4]}
  • id: 169104
    {'degree': 8, 'field': [196, 0, 476, 0, 53, 0, -10, 0, 1], 'lmfdb_label': '3234.v2', 'torsion': [2, 4]}
  • id: 169106
    {'degree': 8, 'field': [288, -2448, 1176, -456, 60, -26, 6, 0, 1], 'lmfdb_label': '3234.v2', 'torsion': [6]}
  • id: 169108
    {'degree': 16, 'field': [36, 0, 2664, 0, 2196, 0, 331, 0, 326, 0, 319, 0, 85, 0, 14, 0, 1], 'lmfdb_label': '3234.v2', 'torsion': [2, 6]}
  • id: 169107
    {'degree': 16, 'field': [254016, 0, -178304, 0, -2148432, 0, 955824, 0, 356705, 0, 25700, 0, -330, 0, -12, 0, 1], 'lmfdb_label': '3234.v2', 'torsion': [8]}
• 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: 58702
    {'conductor': 3234, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '3234.v2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 14}
  • id: 58703
    {'conductor': 3234, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3234.v2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 58704
    {'conductor': 3234, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '3234.v2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 58705
    {'conductor': 3234, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3234.v2', 'prime': 11, '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: 1685068
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [613, 4, 612, 5], [90, 1, 263, 0], [1, 2, 2, 5], [1, 4, 0, 1], [309, 4, 2, 9], [57, 4, 114, 9], [81, 540, 384, 231]], 'adelic_image': '616.12.0.?', 'conductor': 3234, 'lmfdb_label': '3234.v2', 'prime': 0}
  • id: 16262
    {'conductor': 3234, 'elladic_image': '2.3.0.1', 'lmfdb_label': '3234.v2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3234.v does not appear in ec_padic