Elliptic curve data - 45968.t2

Formats: - HTML - YAML - JSON - 2025-10-28T07:24:59.549189

• 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': '45968k', 'Clabel': '45968k3', 'Cnumber': 3, 'abc_quality': 0.985640636788803, 'absD': 388532021116928, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 5304, 'ainvs': [0, -1, 0, -278568, 56675696], 'analytic_rank': 0, 'bad_primes': [2, 13, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 45968, 'degree': 331776, 'elladic_images': ['8.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8085356670763065364896102828', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [120920208625, 19652], 'lmfdb_iso': '45968.t', 'lmfdb_label': '45968.t2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -103, -411], 'min_quad_twist_disc': -52, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.c.1', '24.24.0.bw.1', '34.6.0.a.1', '102.24.0.?', '136.12.0.?', '156.24.0.?', '312.48.0.?', '408.48.1.?', '2652.48.0.?', '5304.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 2873], [3, 2, 2704], [13, 86, 272], [17, 18, 2704]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.16708619221440714095436555944', 'prec': 107}, 'szpiro_ratio': 4.585248792493754, '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, 0, 2, 0, 0, 0, -4, 0, 1, 0, 6, 0, 0, 0, 0, 0, -1, 0, -4, 0], 'aplist': [0, 2, 0, -4, 6, 0, -1, -4, 0, 0, -4, 4, -6, -8, 0, -6, 0, -4, 8, 0, -2, -8, 0, 6, -14], 'class_deg': 6, 'class_size': 4, 'conductor': 45968, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '45968.t', 'trace_hash': 781945371465542662}
• 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': '0.026861228973421703349200046138', 'prec': 107}, 'conductor': 45968, 'gens': [], 'heights': [], 'lmfdb_label': '45968.t2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.51702913508906903266200308115', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0681165403562761306480123245969685294', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[308, 0, 1]], 'xcoord_integral_points': [308]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '13': 'a', '17': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '45968.t2'}
• ec_torsion_growth •

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

  
  
  • id: 2244052
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '45968.t2', 'torsion': [6]}
  • id: 2244051
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '45968.t2', 'torsion': [2, 2]}
  • id: 2244053
    {'degree': 4, 'field': [686, -52, -66, 0, 1], 'lmfdb_label': '45968.t2', 'torsion': [4]}
  • id: 2244054
    {'degree': 4, 'field': [1186, 86, -85, -2, 1], 'lmfdb_label': '45968.t2', 'torsion': [2, 6]}
  • id: 2244055
    {'degree': 6, 'field': [686, 0, 0, -38, 0, 0, 1], 'lmfdb_label': '45968.t2', 'torsion': [6]}
  • id: 2244058
    {'degree': 8, 'field': [-4463, -9208, -4198, 1508, 1290, 72, -66, -4, 1], 'lmfdb_label': '45968.t2', 'torsion': [12]}
  • id: 2244056
    {'degree': 8, 'field': [361, 0, 337, 0, 182, 0, 41, 0, 1], 'lmfdb_label': '45968.t2', 'torsion': [2, 4]}
  • id: 2244057
    {'degree': 8, 'field': [1849, 0, -5834, 0, 1234, 0, -74, 0, 1], 'lmfdb_label': '45968.t2', 'torsion': [2, 4]}
  • id: 2244059
    {'degree': 12, 'field': [469225, -427440, 185277, -50544, 17352, -7512, 2963, -498, 6, -18, 15, -6, 1], 'lmfdb_label': '45968.t2', 'torsion': [3, 6]}
  • id: 2244060
    {'degree': 12, 'field': [893286, -1140768, 691830, -229866, 59562, 2094, 3655, -1410, 357, 24, -9, -6, 1], 'lmfdb_label': '45968.t2', 'torsion': [2, 6]}
  • id: 2244061
    {'degree': 16, 'field': [127742, -392312, 427956, -54424, -413578, 412184, -71872, -95096, 57447, -8168, -3552, 2248, -542, 8, 28, -8, 1], 'lmfdb_label': '45968.t2', 'torsion': [8]}
  • id: 2244062
    {'degree': 16, 'field': [1886353, -9405074, 17376292, -18131166, 14893074, -8031632, 4539450, -1867530, 826531, -272300, 88186, -19930, 4626, -630, 110, -8, 1], 'lmfdb_label': '45968.t2', 'torsion': [2, 12]}
  • id: 2244063
    {'degree': 16, 'field': [7204132, -38214280, 67059148, -31047952, -30330914, 31134680, -240874, -7310564, 1288659, 693812, -164110, -29968, 7733, 572, -150, -4, 1], 'lmfdb_label': '45968.t2', 'torsion': [2, 12]}
  • id: 2244064
    {'degree': 18, 'field': [-76789446026471, -24721941609438, -6421439590626, 377904487928, 75932265405, 33563293626, -8604696642, -941978262, 109983900, 11909770, 7750995, -444498, 61167, 8868, -2487, -58, -69, 0, 1], 'lmfdb_label': '45968.t2', 'torsion': [18]}
• 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: 1095600
    {'conductor': 45968, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '45968.t2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1095601
    {'conductor': 45968, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '45968.t2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1095602
    {'conductor': 45968, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '45968.t2', '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

  
  
  • id: 1970400
    {'adelic_gens': [[2653, 3276, 1638, 3745], [11, 2, 5254, 5295], [5293, 12, 5292, 13], [2039, 0, 0, 5303], [1, 0, 12, 1], [1, 6, 6, 37], [5266, 819, 429, 2848], [1, 12, 0, 1], [5277, 728, 4498, 4003], [1769, 3276, 4420, 1]], 'adelic_image': '5304.96.1.?', 'conductor': 45968, 'lmfdb_label': '45968.t2', 'prime': 0}
  • id: 199139
    {'conductor': 45968, 'elladic_image': '8.6.0.1', 'lmfdb_label': '45968.t2', 'modell_image': '2B', 'prime': 2}
  • id: 199140
    {'conductor': 45968, 'elladic_image': '3.4.0.1', 'lmfdb_label': '45968.t2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 45968.t does not appear in ec_padic