Elliptic curve data - 16830.bk4

Formats: - HTML - YAML - JSON - 2024-04-25T04:42:24.066380

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '16830cd', 'Clabel': '16830cd5', 'Cnumber': 5, 'abc_quality': 1.0120982194921988, 'absD': 1050152657562990531000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 22440, 'ainvs': [1, -1, 1, -22364168, 40683483731], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 16830, 'degree': 1769472, 'elladic_images': ['8.12.0.8', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9607874489120620788144189750', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 36, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [1696892787277117093383481, 1440538624914939000], 'lmfdb_iso': '16830.bk', 'lmfdb_label': '16830.bk4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -2484908, -1506795694], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '8.12.0-4.c.1.4', '12.48.0-12.g.1.10', '24.96.0-24.bu.4.24', '264.192.1.?', '1020.96.0.?', '2040.192.1.?', '7480.24.0.?', '22440.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4114813045780072331167963565', 'prec': 100}, 'szpiro_ratio': 6.410753120029688, '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, 0, 1, -1, 0, -4, 1, 0, -1, -1, 0, 2, -4, 0, 1, 1, 0, -4, -1], 'aplist': [1, 0, -1, -4, -1, 2, 1, -4, 0, 6, 8, -10, -6, -4, -12, -6, -12, 2, 8, 12, 2, 8, 12, 6, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 16830, 'isogeny_matrix': [[1, 4, 2, 3, 12, 4, 6, 12], [4, 1, 2, 12, 3, 4, 6, 12], [2, 2, 1, 6, 6, 2, 3, 6], [3, 12, 6, 1, 4, 12, 2, 4], [12, 3, 6, 4, 1, 12, 2, 4], [4, 4, 2, 12, 12, 1, 6, 3], [6, 6, 3, 2, 2, 6, 1, 2], [12, 12, 6, 4, 4, 3, 2, 1]], 'lmfdb_iso': '16830.bk', 'trace_hash': 84194083118469295}
• 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': '0.0026809745893455576352721874716', 'prec': 110}, 'conductor': 16830, 'gens': [], 'heights': [], 'lmfdb_label': '16830.bk4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.15446112241278367685600282863', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8535334689534041222720339435407928774', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[11163, -11167, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': 'a', '5': [0, 0], '11': [0, 0], '17': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '16830.bk4'}
• ec_torsion_growth •

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

  
  
  • id: 863577
    {'degree': 2, 'field': [-510, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 2]}
  • id: 863579
    {'degree': 2, 'field': [-255, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [4]}
  • id: 863578
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [4]}
  • id: 863580
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '16830.bk4', 'torsion': [6]}
  • id: 863581
    {'degree': 3, 'field': [-12, 6, -1, 1], 'lmfdb_label': '16830.bk4', 'torsion': [6]}
  • id: 863584
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [12]}
  • id: 863585
    {'degree': 4, 'field': [7225, 0, -85, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [12]}
  • id: 863582
    {'degree': 4, 'field': [16129, 0, -256, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 4]}
  • id: 863583
    {'degree': 4, 'field': [28900, 0, -170, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 6]}
  • id: 863587
    {'degree': 6, 'field': [-204000, 0, 8500, 0, -170, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 6]}
  • id: 863589
    {'degree': 6, 'field': [-25500, 0, 2125, 0, -85, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [12]}
  • id: 863586
    {'degree': 6, 'field': [12, 0, -11, 0, 1, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [3, 6]}
  • id: 863588
    {'degree': 6, 'field': [68, -272, 68, -28, 7, -2, 1], 'lmfdb_label': '16830.bk4', 'torsion': [12]}
  • id: 863591
    {'degree': 8, 'field': [1040400, 0, -269280, 0, 19014, 0, -264, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [8]}
  • id: 863593
    {'degree': 8, 'field': [3418801, 0, -155316, 0, 5207, 0, -84, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 12]}
  • id: 863592
    {'degree': 8, 'field': [21080016, -3493008, 2077680, -133728, 54094, -1442, 495, -2, 1], 'lmfdb_label': '16830.bk4', 'torsion': [8]}
  • id: 863590
    {'degree': 8, 'field': [162460516, 0, 306032, 0, -25476, 0, 8, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 4]}
  • id: 863595
    {'degree': 12, 'field': [1348, -3336, 2054, 864, -1335, 606, -221, -54, 114, -54, 23, -6, 1], 'lmfdb_label': '16830.bk4', 'torsion': [3, 12]}
  • id: 863597
    {'degree': 12, 'field': [4088484, 0, -1534188, 0, 302173, 0, -46260, 0, 3347, 0, -108, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 12]}
  • id: 863596
    {'degree': 12, 'field': [4519876, -12756, -31854, 84950, -31785, -12876, 4391, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '16830.bk4', 'torsion': [3, 12]}
  • id: 863594
    {'degree': 12, 'field': [289034001, -102006, -254979, 679950, -254910, -102126, 34141, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '16830.bk4', 'torsion': [6, 6]}
  • id: 863600
    {'degree': 16, 'field': [3662186256, 0, -5625083232, 0, 2599566048, 0, -530611560, 0, 52197921, 0, -2423340, 0, 52488, 0, -468, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 8]}
  • id: 863599
    {'degree': 16, 'field': [34947067907236, -5794272485200, 6269761517528, -974296626816, 546194551232, -72969387896, 27889559956, -3143915448, 895723885, -74765088, 16563928, -890368, 158162, -4536, 668, -8, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 8]}
  • id: 863603
    {'degree': 16, 'field': [46569173353921, 0, -4998057147596, 0, 274643551250, 0, -9387036924, 0, 229102259, 0, -3872724, 0, 43370, 0, -296, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [24]}
  • id: 863602
    {'degree': 16, 'field': [277102632960000, 0, -17930170368000, 0, 734605632000, 0, -18748350720, 0, 352614276, 0, -4595184, 0, 44130, 0, -264, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [24]}
  • id: 863598
    {'degree': 16, 'field': [1651660400390625, 0, 0, 0, 0, 0, 0, 0, 1381781250, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [4, 4]}
  • id: 863601
    {'degree': 16, 'field': [26443155585882256, 0, -49702495944512, 0, -8203568279360, 0, 6494339488, 0, 980985304, 0, -102128, 0, -50960, 0, -8, 0, 1], 'lmfdb_label': '16830.bk4', 'torsion': [2, 12]}
  • id: 863604
    {'degree': 18, 'field': [16136792522481, -70388861268573, 101325202481799, -4129256352501, 2255320754100, -132376512762, 65534944732, 9438884493, 2366967, -271413670, 54754812, -1840077, -354213, 64413, -11610, 74, -6, -3, 1], 'lmfdb_label': '16830.bk4', '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: 375241
    {'conductor': 16830, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '16830.bk4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 375242
    {'conductor': 16830, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '16830.bk4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 375243
    {'conductor': 16830, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '16830.bk4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 375244
    {'conductor': 16830, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '16830.bk4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 375245
    {'conductor': 16830, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '16830.bk4', '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: 1776132
    {'adelic_gens': [[7936, 21, 12915, 22066], [1, 12, 12, 145], [18361, 24, 18372, 289], [5614, 3, 5655, 34], [8992, 21, 22155, 22066], [15, 106, 21134, 13211], [22424, 11217, 19159, 15046], [22417, 24, 22416, 25], [1, 24, 0, 1], [17766, 21529, 12155, 15896], [1, 0, 24, 1]], 'adelic_image': '22440.384.5.?', 'conductor': 16830, 'lmfdb_label': '16830.bk4', 'prime': 0}
  • id: 79020
    {'conductor': 16830, 'elladic_image': '8.12.0.8', 'lmfdb_label': '16830.bk4', 'modell_image': '2B', 'prime': 2}
  • id: 79021
    {'conductor': 16830, 'elladic_image': '3.8.0.2', 'lmfdb_label': '16830.bk4', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 16830.bk does not appear in ec_padic