Elliptic curve data - 3960.b3

Formats: - HTML - YAML - JSON - 2025-10-15T01:14:47.431687

• 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': '3960f', 'Clabel': '3960f2', 'Cnumber': 2, 'abc_quality': 0.9352092820152678, 'absD': 45727545600, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 660, 'ainvs': [0, 0, 0, -903, -1798], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3960, 'degree': 4096, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.73564597201901585493453621772', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [436334416, 245025], 'lmfdb_iso': '3960.b', 'lmfdb_label': '3960.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -100, 100], 'min_quad_twist_disc': -3, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0-2.a.1.1', '20.12.0.b.1', '44.12.0.b.1', '60.24.0-20.b.1.2', '132.24.0.?', '220.24.0.?', '660.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 11, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6423624534583200320187817831', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 440], [5, 6, 792], [11, 12, 360]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27575829268833586370790781505', 'prec': 107}, 'szpiro_ratio': 3.866582977203698, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 0, -1, 0, -4, 0, 0, 0, 1, 0, 2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, -1, -4, 1, 2, -6, 4, 8, 10, 0, -10, 6, -8, 0, 2, -12, -2, -12, -8, -2, -8, 8, 6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 3960, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3960.b', 'trace_hash': 463883355665375430}
• 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': '0.22962862613088006875871695210', 'prec': 103}, 'conductor': 3960, 'gens': [[-14, 90, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6423624534583200320187817831', 'prec': 100}], 'lmfdb_label': '3960.b3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.93668563723270935804141734183', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0767546425693649287139716640534521953', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-2, 0, 1], [31, 0, 1]], 'xcoord_integral_points': [-29, -14, -13, -2, 31, 79, 31711]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [3, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '3960.b3'}
• ec_torsion_growth •

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

  
  
  • id: 206166
    {'degree': 4, 'field': [1, 1, 2, -1, 1], 'lmfdb_label': '3960.b3', 'torsion': [2, 4]}
  • id: 206165
    {'degree': 4, 'field': [33, 0, 1, -2, 1], 'lmfdb_label': '3960.b3', 'torsion': [2, 4]}
  • id: 206164
    {'degree': 4, 'field': [100, 0, -35, 0, 1], 'lmfdb_label': '3960.b3', 'torsion': [2, 4]}
  • id: 206167
    {'degree': 8, 'field': [-243, 0, 744, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '3960.b3', 'torsion': [2, 6]}
  • id: 206168
    {'degree': 16, 'field': [256, 0, 368, 0, 9473, 0, -7740, 0, 5156, 0, -1710, 0, 308, 0, -28, 0, 1], 'lmfdb_label': '3960.b3', 'torsion': [4, 4]}
  • id: 206171
    {'degree': 16, 'field': [625, 0, 5000, 0, 37625, 0, 18000, 0, 5000, 0, 1500, 0, 305, 0, 20, 0, 1], 'lmfdb_label': '3960.b3', 'torsion': [2, 8]}
  • id: 206169
    {'degree': 16, 'field': [65536, 0, -188416, 0, 282880, 0, -223744, 0, 82564, 0, -13984, 0, 1105, 0, -46, 0, 1], 'lmfdb_label': '3960.b3', 'torsion': [2, 8]}
  • id: 206170
    {'degree': 16, 'field': [110889, 0, -48276, 0, 18990, 0, -50076, 0, 25243, 0, -3468, 0, 610, 0, -24, 0, 1], 'lmfdb_label': '3960.b3', 'torsion': [2, 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: 73820
    {'conductor': 3960, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '3960.b3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 73821
    {'conductor': 3960, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '3960.b3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 73822
    {'conductor': 3960, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3960.b3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 73823
    {'conductor': 3960, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3960.b3', '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: 1689694
    {'adelic_gens': [[1, 0, 4, 1], [331, 444, 0, 1], [439, 0, 0, 659], [1, 4, 0, 1], [397, 222, 0, 1], [657, 4, 656, 5], [541, 444, 642, 229]], 'adelic_image': '660.48.0.?', 'conductor': 3960, 'lmfdb_label': '3960.b3', 'prime': 0}
  • id: 19606
    {'conductor': 3960, 'elladic_image': '2.6.0.1', 'lmfdb_label': '3960.b3', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 138274
    {'lmfdb_iso': '3960.b', 'p': 7, 'prec': 20, 'unit': 7829510067328890, 'val': 1}
  • id: 138278
    {'lmfdb_iso': '3960.b', 'p': 13, 'prec': 20, 'unit': 1010330406485411802795, 'val': 1}
  • id: 138280
    {'lmfdb_iso': '3960.b', 'p': 17, 'prec': 20, 'unit': 5496948620850829671742, 'val': 2}
  • id: 138270
    {'lmfdb_iso': '3960.b', 'p': 19, 'prec': 20, 'unit': 1812876951136796296192549, 'val': 1}
  • id: 138284
    {'lmfdb_iso': '3960.b', 'p': 23, 'prec': 20, 'unit': 74456591685852806569972536, 'val': 1}
  • id: 138277
    {'lmfdb_iso': '3960.b', 'p': 29, 'prec': 20, 'unit': 3148257169303023575075996203, 'val': 1}
  • id: 138273
    {'lmfdb_iso': '3960.b', 'p': 37, 'prec': 20, 'unit': 609166816107453415180130023987, 'val': 1}
  • id: 138275
    {'lmfdb_iso': '3960.b', 'p': 41, 'prec': 20, 'unit': 3830588387150963841403091920618, 'val': 1}
  • id: 138276
    {'lmfdb_iso': '3960.b', 'p': 43, 'prec': 20, 'unit': 9798323778578812223346310784324, 'val': 1}
  • id: 138282
    {'lmfdb_iso': '3960.b', 'p': 53, 'prec': 20, 'unit': 6864885817063055633378983072134, 'val': 1}
  • id: 138287
    {'lmfdb_iso': '3960.b', 'p': 59, 'prec': 20, 'unit': 2628399252662591098088181788347313, 'val': 1}
  • id: 138288
    {'lmfdb_iso': '3960.b', 'p': 61, 'prec': 20, 'unit': 6235623727078103731986740100285369, 'val': 1}
  • id: 138272
    {'lmfdb_iso': '3960.b', 'p': 67, 'prec': 20, 'unit': 19887403971959046128171454734226225, 'val': 1}
  • id: 138286
    {'lmfdb_iso': '3960.b', 'p': 71, 'prec': 20, 'unit': 140219747898338885846152050678938287, 'val': 1}
  • id: 138283
    {'lmfdb_iso': '3960.b', 'p': 73, 'prec': 20, 'unit': 91726369498853929702642653109425320, 'val': 1}
  • id: 138279
    {'lmfdb_iso': '3960.b', 'p': 79, 'prec': 20, 'unit': 15545779932803378509212330016708044, 'val': 1}
  • id: 138281
    {'lmfdb_iso': '3960.b', 'p': 83, 'prec': 20, 'unit': 1275025698166345165674154807506223856, 'val': 1}
  • id: 138285
    {'lmfdb_iso': '3960.b', 'p': 89, 'prec': 20, 'unit': 7182054848177979939467213530295405705, 'val': 1}
  • id: 138271
    {'lmfdb_iso': '3960.b', 'p': 97, 'prec': 20, 'unit': 30507722890953437578180911031962481300, 'val': 1}