Elliptic curve data - 15680.y2

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• 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': '15680co', 'Clabel': '15680co1', 'Cnumber': 1, 'abc_quality': 0.9725629972122254, 'absD': 256901120, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 840, 'ainvs': [0, -1, 0, 159, 1], 'analytic_rank': 1, 'bad_primes': [2, 5, 7], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 15680, 'degree': 4608, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.30312514807164693045650862353', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 24, 'isogeny_degrees': [1, 3], 'jinv': [34391, 20], 'lmfdb_iso': '15680.y', 'lmfdb_label': '15680.y2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 3, 1], 'min_quad_twist_disc': -8, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '20.2.0.a.1', '60.8.0.a.1', '168.8.0.?', '840.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.63367692827670178780489786928', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 245], [5, 6, 3136], [7, 14, 320]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0609139809441565845202316826', 'prec': 103}, 'szpiro_ratio': 2.7757378400182815, '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, -1, 0, 0, 0, -2, 0, -6, 0, -4, 0, 1, 0, 0, 0, -2, 0], 'aplist': [0, -1, -1, 0, -6, -4, 0, -2, 3, 3, 8, 4, -9, -7, 0, 6, 6, 5, 5, 6, 16, -2, -3, 15, -14], 'class_deg': 3, 'class_size': 2, 'conductor': 15680, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '15680.y', 'trace_hash': 181233654210262758}
• 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': '0.54539209853511610063898181529', 'prec': 103}, 'conductor': 15680, 'gens': [[13, 64, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.63367692827670178780489786928', 'prec': 103}], 'lmfdb_label': '15680.y2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0540950106396960260955102498', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6718227538158394665209500053911873502', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [0, 13]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '15680.y2'}
• ec_torsion_growth •

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

  
  
  • id: 805810
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '15680.y2', 'torsion': [3]}
  • id: 805811
    {'degree': 3, 'field': [-13, 5, -1, 1], 'lmfdb_label': '15680.y2', 'torsion': [2]}
  • id: 805814
    {'degree': 6, 'field': [-14, 0, 49, 0, 14, 0, 1], 'lmfdb_label': '15680.y2', 'torsion': [6]}
  • id: 805812
    {'degree': 6, 'field': [20, 0, -4, 0, -3, 0, 1], 'lmfdb_label': '15680.y2', 'torsion': [2, 2]}
  • id: 805813
    {'degree': 6, 'field': [42, 0, 112, 0, 14, 0, 1], 'lmfdb_label': '15680.y2', 'torsion': [3]}
  • id: 805815
    {'degree': 12, 'field': [-24500, 0, -37240, 0, -13279, 0, -1428, 0, 154, 0, 28, 0, 1], 'lmfdb_label': '15680.y2', 'torsion': [4]}
  • id: 805816
    {'degree': 12, 'field': [1764, 0, -4704, 0, 11956, 0, -1484, 0, 84, 0, -14, 0, 1], 'lmfdb_label': '15680.y2', 'torsion': [3, 3]}
  • id: 805817
    {'degree': 12, 'field': [78400, 0, -31360, 0, 4116, 0, -420, 0, 133, 0, 0, 0, 1], 'lmfdb_label': '15680.y2', 'torsion': [2, 6]}
  • id: 805818
    {'degree': 18, 'field': [249187, -326490, 327189, -555364, -182709, 78744, 92315, 50124, 20877, 6248, -4488, -3648, -1750, -498, -33, -20, -18, 0, 1], 'lmfdb_label': '15680.y2', 'torsion': [9]}
  • id: 805819
    {'degree': 18, 'field': [40915098, 0, -11742948, 0, 3992520, 0, -75803, 0, -64288, 0, -11221, 0, 3276, 0, -105, 0, -14, 0, 1], 'lmfdb_label': '15680.y2', '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: 347500
    {'conductor': 15680, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '15680.y2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 347501
    {'conductor': 15680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15680.y2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 347502
    {'conductor': 15680, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '15680.y2', 'prime': 7, 'reduction_type': 0, '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: 1768527
    {'adelic_gens': [[4, 3, 9, 7], [835, 6, 834, 7], [337, 6, 171, 19], [211, 6, 213, 19], [419, 0, 0, 839], [537, 838, 530, 833], [425, 834, 426, 833], [1, 6, 0, 1], [3, 4, 8, 11], [594, 659, 455, 489], [1, 0, 6, 1]], 'adelic_image': '840.16.0.?', 'conductor': 15680, 'lmfdb_label': '15680.y2', 'prime': 0}
  • id: 73969
    {'conductor': 15680, 'elladic_image': '3.4.0.1', 'lmfdb_label': '15680.y2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 707390
    {'lmfdb_iso': '15680.y', 'p': 11, 'prec': 20, 'unit': 47005718935286863731, 'val': 1}
  • id: 707388
    {'lmfdb_iso': '15680.y', 'p': 13, 'prec': 20, 'unit': 1262401394523629769882, 'val': 1}
  • id: 707391
    {'lmfdb_iso': '15680.y', 'p': 19, 'prec': 20, 'unit': 1474814610205560605918051, 'val': 1}
  • id: 707394
    {'lmfdb_iso': '15680.y', 'p': 23, 'prec': 20, 'unit': 71440258769622946733630738, 'val': 1}
  • id: 707387
    {'lmfdb_iso': '15680.y', 'p': 29, 'prec': 20, 'unit': 3519650527994298017378733285, 'val': 1}
  • id: 707398
    {'lmfdb_iso': '15680.y', 'p': 31, 'prec': 20, 'unit': 16348871081959819104031947080, 'val': 1}
  • id: 707383
    {'lmfdb_iso': '15680.y', 'p': 37, 'prec': 20, 'unit': 559896303992110563395853274518, 'val': 1}
  • id: 707385
    {'lmfdb_iso': '15680.y', 'p': 41, 'prec': 20, 'unit': 43520719268036252208417400499, 'val': 1}
  • id: 707386
    {'lmfdb_iso': '15680.y', 'p': 43, 'prec': 20, 'unit': 10761073936674297750070402037551, 'val': 1}
  • id: 707392
    {'lmfdb_iso': '15680.y', 'p': 53, 'prec': 20, 'unit': 511969523924534349176702802133895, 'val': 1}
  • id: 707396
    {'lmfdb_iso': '15680.y', 'p': 59, 'prec': 20, 'unit': 725920526565014141861699194763496, 'val': 1}
  • id: 707397
    {'lmfdb_iso': '15680.y', 'p': 61, 'prec': 20, 'unit': 7170176213493260862783230912482415, 'val': 1}
  • id: 707382
    {'lmfdb_iso': '15680.y', 'p': 67, 'prec': 20, 'unit': 19531140261809003385466802985561655, 'val': 1}
  • id: 707384
    {'lmfdb_iso': '15680.y', 'p': 71, 'prec': 20, 'unit': 73144302204682095268259195533082821, 'val': 1}
  • id: 707393
    {'lmfdb_iso': '15680.y', 'p': 73, 'prec': 20, 'unit': 193848941200287228416240000017478488, 'val': 1}
  • id: 707389
    {'lmfdb_iso': '15680.y', 'p': 79, 'prec': 20, 'unit': 865559054977507098615958415234673960, 'val': 1}
  • id: 707381
    {'lmfdb_iso': '15680.y', 'p': 83, 'prec': 20, 'unit': 943477993222026728145391988426433577, 'val': 1}
  • id: 707395
    {'lmfdb_iso': '15680.y', 'p': 89, 'prec': 20, 'unit': 1391073460086163286271890167738882193, 'val': 1}
  • id: 707380
    {'lmfdb_iso': '15680.y', 'p': 97, 'prec': 20, 'unit': 6818948185068829436400408694579919765, 'val': 1}