Elliptic curve data - 25168.bh1

Formats: - HTML - YAML - JSON - 2025-10-22T23:24:13.543673

• 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': '25168t', 'Clabel': '25168t1', 'Cnumber': 1, 'abc_quality': 0.9016746280716706, 'absD': 46752488224718848, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 26, 'ainvs': [0, 1, 0, -260432, 49999508], 'analytic_rank': 1, 'bad_primes': [2, 11, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 25168, 'degree': 152064, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9834563828922099207933633182', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 33, 'isogeny_degrees': [1], 'jinv': [2224882033, 53248], 'lmfdb_iso': '25168.bh', 'lmfdb_label': '25168.bh1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -134, 532], 'min_quad_twist_disc': 44, 'modell_images': [], 'modm_images': ['26.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.3675124134321943583012389703', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1573], [11, 52, 208], [13, 14, 1936]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.30828764619998241799849785523', 'prec': 107}, 'szpiro_ratio': 4.8378869268090074, '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, 1, 0, 2, 0, 2, 0, -2, 0, 0, 0, -1, 0, 2, 0, -1, 0, -2, 0], 'aplist': [0, 1, 2, 2, 0, -1, -1, -2, 5, 1, 6, -2, -2, -5, -2, -13, 4, -5, 10, -6, -4, 1, -12, -10, -10], 'class_deg': 1, 'class_size': 1, 'conductor': 25168, 'isogeny_matrix': [[1]], 'lmfdb_iso': '25168.bh', 'trace_hash': 687464059371947369}
• 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': '0.018931789877808203969347665967', 'prec': 107}, 'conductor': 25168, 'gens': [[8594, 137728, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '5.3675124134321943583012389703', 'prec': 100}], 'lmfdb_label': '25168.bh1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.35780180886298449535135788675', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.6820226024822504728220575838026103952', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '25168.bh1'}
• ec_torsion_growth •

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

  
  
  • id: 1265217
    {'degree': 3, 'field': [2, -7, -1, 1], 'lmfdb_label': '25168.bh1', 'torsion': [2]}
  • id: 1265218
    {'degree': 6, 'field': [-4, -20, 5, 29, -12, -3, 1], 'lmfdb_label': '25168.bh1', 'torsion': [2, 2]}
  • id: 1265219
    {'degree': 8, 'field': [-48, 0, 233, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '25168.bh1', 'torsion': [3]}
  • id: 1265220
    {'degree': 12, 'field': [-1040, -988, 1108, 737, -705, -420, 296, 184, -56, -4, -16, -1, 1], 'lmfdb_label': '25168.bh1', '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: 577502
    {'conductor': 25168, 'conductor_valuation': 4, 'discriminant_valuation': 24, 'j_denominator_valuation': 12, 'kodaira_symbol': -20, 'lmfdb_label': '25168.bh1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 577503
    {'conductor': 25168, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '25168.bh1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 577504
    {'conductor': 25168, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '25168.bh1', 'prime': 13, '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': [[25, 2, 24, 3], [1, 2, 0, 1], [1, 0, 2, 1], [15, 2, 15, 3], [1, 1, 25, 0]], 'adelic_image': '26.2.0.?', 'conductor': 25168, 'lmfdb_label': '25168.bh1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 1197252
    {'lmfdb_iso': '25168.bh', 'p': 5, 'prec': 20, 'unit': 783320825311, 'val': 1}
  • id: 1197253
    {'lmfdb_iso': '25168.bh', 'p': 7, 'prec': 20, 'unit': 1757690422992793, 'val': 1}
  • id: 1197259
    {'lmfdb_iso': '25168.bh', 'p': 17, 'prec': 20, 'unit': 124683732291338996423768, 'val': 1}
  • id: 1197249
    {'lmfdb_iso': '25168.bh', 'p': 19, 'prec': 20, 'unit': 1895907901448944602482379, 'val': 1}
  • id: 1197264
    {'lmfdb_iso': '25168.bh', 'p': 23, 'prec': 20, 'unit': 4648500729260602928541491, 'val': 1}
  • id: 1197257
    {'lmfdb_iso': '25168.bh', 'p': 29, 'prec': 20, 'unit': 131316735995130313042170572632, 'val': -1}
  • id: 1197254
    {'lmfdb_iso': '25168.bh', 'p': 31, 'prec': 20, 'unit': 11385245590244806710275601294, 'val': 1}
  • id: 1197269
    {'lmfdb_iso': '25168.bh', 'p': 37, 'prec': 20, 'unit': 507905923314665808004151507844, 'val': 1}
  • id: 1197255
    {'lmfdb_iso': '25168.bh', 'p': 41, 'prec': 20, 'unit': 34372534479890025614235411424, 'val': 2}
  • id: 1197256
    {'lmfdb_iso': '25168.bh', 'p': 43, 'prec': 20, 'unit': 6729109634375272788043688432728, 'val': 1}
  • id: 1197267
    {'lmfdb_iso': '25168.bh', 'p': 47, 'prec': 20, 'unit': 12968738863767030246470138885961, 'val': 1}
  • id: 1197261
    {'lmfdb_iso': '25168.bh', 'p': 53, 'prec': 20, 'unit': 4912445635841375723421653655292, 'val': 1}
  • id: 1197262
    {'lmfdb_iso': '25168.bh', 'p': 59, 'prec': 20, 'unit': 4420582424996203060728936643068543, 'val': 1}
  • id: 1197268
    {'lmfdb_iso': '25168.bh', 'p': 61, 'prec': 20, 'unit': 3855359300895893633103785138235267, 'val': 1}
  • id: 1197251
    {'lmfdb_iso': '25168.bh', 'p': 67, 'prec': 20, 'unit': 42589996479093017296587652319956892, 'val': 1}
  • id: 1197266
    {'lmfdb_iso': '25168.bh', 'p': 71, 'prec': 20, 'unit': 80468284333802213885655134165123890, 'val': 1}
  • id: 1197263
    {'lmfdb_iso': '25168.bh', 'p': 73, 'prec': 20, 'unit': 230680562871026132981609426199537151, 'val': 1}
  • id: 1197258
    {'lmfdb_iso': '25168.bh', 'p': 79, 'prec': 20, 'unit': 40924065467701283027485110771179956497, 'val': -1}
  • id: 1197260
    {'lmfdb_iso': '25168.bh', 'p': 83, 'prec': 20, 'unit': 944359459890038780079421537663829236, 'val': 1}
  • id: 1197265
    {'lmfdb_iso': '25168.bh', 'p': 89, 'prec': 20, 'unit': 4972500872717200323661701168608035568, 'val': 1}
  • id: 1197250
    {'lmfdb_iso': '25168.bh', 'p': 97, 'prec': 20, 'unit': 16602821843359009995154340593837090411, 'val': 1}