Elliptic curve data - 68544.bq3

Formats: - HTML - YAML - JSON - 2025-10-06T01:01:54.409166

• 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': '68544ca', 'Clabel': '68544ca5', 'Cnumber': 5, 'abc_quality': 1.0817271650752718, 'absD': 40117282902307747339601707008, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 816, 'ainvs': [0, 0, 0, -168539916, 9673331343856], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 68544, 'degree': 47185920, 'elladic_images': ['16.48.0.204'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.1681558844969905723582779218', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 42, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-2770540998624539614657, 209924951154647363208], 'lmfdb_iso': '68544.bq', 'lmfdb_label': '68544.bq3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -292604, -699871003], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.k.1', '12.12.0-4.c.1.2', '16.48.0.e.1', '24.48.0-8.k.1.5', '48.96.0-16.e.1.3', '136.48.0.?', '272.96.1.?', '408.96.0.?', '816.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '24.119111190970408251151928543', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 8, 7616], [7, 8, 9792], [17, 18, 4032]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.5791289693230177625348071212', 'prec': 100}, 'szpiro_ratio': 6.5848595563853545, '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, 0, 0, -2, 0, 1, 0, 0, 0, 4, 0, 2, 0, 0, 0, -1, 0, -4, 0], 'aplist': [0, 0, -2, 1, 4, 2, -1, -4, -8, 6, 0, 2, -10, 4, 0, 6, -4, -6, 12, 8, -6, 0, -12, 6, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 68544, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '68544.bq', 'trace_hash': 1626160513495575455}
• 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': '0.00023965461650980362574879322534', 'prec': 113}, 'conductor': 68544, 'gens': [[78870661413, 22149962544281495, 79]], 'heights': [{'__RealLiteral__': 0, 'data': '24.119111190970408251151928543', 'prec': 100}], 'lmfdb_label': '68544.bq3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.029932937554508479809824457615', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.7756467931965110393210928500233297968', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-23932, 0, 1]], 'xcoord_integral_points': [-23932]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 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': '68544.bq3'}
• ec_torsion_growth •

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

  
  
  • id: 3261101
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [4]}
  • id: 3261102
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '68544.bq3', 'torsion': [4]}
  • id: 3261100
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [2, 2]}
  • id: 3261103
    {'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [2, 4]}
  • id: 3261104
    {'degree': 4, 'field': [49, 0, -20, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [8]}
  • id: 3261105
    {'degree': 4, 'field': [529, 0, 22, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [8]}
  • id: 3261110
    {'degree': 8, 'field': [-37632, 0, -7008, 0, 1620, 0, -52, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [6]}
  • id: 3261109
    {'degree': 8, 'field': [3753, -108, -756, -324, 720, -108, 52, -4, 1], 'lmfdb_label': '68544.bq3', 'torsion': [16]}
  • id: 3261108
    {'degree': 8, 'field': [6561, 0, 1296, 0, 175, 0, 16, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [2, 8]}
  • id: 3261107
    {'degree': 8, 'field': [9604, 0, 0, 0, 98, 0, 0, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [8]}
  • id: 3261106
    {'degree': 8, 'field': [802532193, -26957784, -226568, 1904, 56662, -952, 8, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [2, 4]}
  • id: 3261115
    {'degree': 16, 'field': [6561, -40500, 106468, -779080, 2741944, -340212, -1109160, -116916, 516079, -39268, -32072, -1860, 2232, 24, -44, -4, 1], 'lmfdb_label': '68544.bq3', 'torsion': [2, 16]}
  • id: 3261112
    {'degree': 16, 'field': [5764801, 0, -3294172, 0, 941192, 0, -403368, 0, 112847, 0, -8232, 0, 392, 0, -28, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [2, 8]}
  • id: 3261116
    {'degree': 16, 'field': [7160976, 0, 15894464, 0, 4535896, 0, 1793184, 0, 274361, 0, 30004, 0, 2118, 0, 68, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [2, 6]}
  • id: 3261117
    {'degree': 16, 'field': [51581124, 0, -48074148, 0, 7124841, 0, -1610280, 0, 138564, 0, -15894, 0, 792, 0, -48, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [12]}
  • id: 3261118
    {'degree': 16, 'field': [241864704, 0, 75022848, 0, 16552512, 0, 2083968, 0, 202176, 0, 9648, 0, 432, 0, 0, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [12]}
  • id: 3261114
    {'degree': 16, 'field': [802135684, 0, 0, 0, 15860320, 0, 0, 0, 341922, 0, 0, 0, -560, 0, 0, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [16]}
  • id: 3261113
    {'degree': 16, 'field': [7703711109136, 0, 8804241267584, 0, -212707509616, 0, -75306385392, 0, -2319670927, 0, -4758096, 0, 243236, 0, -952, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [16]}
  • id: 3261111
    {'degree': 16, 'field': [40213853471634241, 0, -1351726167113756, 0, 22718086842248, 0, -572724878376, 0, 9425094287, 0, -40443816, 0, 113288, 0, -476, 0, 1], 'lmfdb_label': '68544.bq3', 'torsion': [4, 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: 1658676
    {'conductor': 68544, 'conductor_valuation': 6, 'discriminant_valuation': 21, 'j_denominator_valuation': 3, 'kodaira_symbol': -15, 'lmfdb_label': '68544.bq3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1658677
    {'conductor': 68544, 'conductor_valuation': 2, 'discriminant_valuation': 38, 'j_denominator_valuation': 32, 'kodaira_symbol': -36, 'lmfdb_label': '68544.bq3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1658678
    {'conductor': 68544, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '68544.bq3', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1658679
    {'conductor': 68544, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '68544.bq3', 'prime': 17, '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: 2117511
    {'adelic_gens': [[5, 4, 812, 813], [1, 16, 0, 1], [271, 0, 0, 815], [15, 2, 718, 803], [188, 747, 249, 398], [685, 288, 48, 229], [1, 0, 16, 1], [801, 16, 800, 17], [382, 69, 249, 418]], 'adelic_image': '816.192.1.?', 'conductor': 68544, 'lmfdb_label': '68544.bq3', 'prime': 0}
  • id: 286163
    {'conductor': 68544, 'elladic_image': '16.48.0.204', 'lmfdb_label': '68544.bq3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3506177
    {'lmfdb_iso': '68544.bq', 'p': 5, 'prec': 20, 'unit': 267147246843, 'val': 1}
  • id: 3506183
    {'lmfdb_iso': '68544.bq', 'p': 11, 'prec': 20, 'unit': 30050572156263188532, 'val': 1}
  • id: 3506181
    {'lmfdb_iso': '68544.bq', 'p': 13, 'prec': 20, 'unit': 1326574875053058831907, 'val': 1}
  • id: 3506184
    {'lmfdb_iso': '68544.bq', 'p': 19, 'prec': 20, 'unit': 1507767466450445464758043, 'val': 1}
  • id: 3506187
    {'lmfdb_iso': '68544.bq', 'p': 23, 'prec': 20, 'unit': 60210303069793889802218094, 'val': 1}
  • id: 3506182
    {'lmfdb_iso': '68544.bq', 'p': 29, 'prec': 20, 'unit': 5653534159123909446089557070, 'val': 1}
  • id: 3506191
    {'lmfdb_iso': '68544.bq', 'p': 37, 'prec': 20, 'unit': 241072516468501745605126401824, 'val': 1}
  • id: 3506179
    {'lmfdb_iso': '68544.bq', 'p': 41, 'prec': 20, 'unit': 926829382571324497239588367476, 'val': 1}
  • id: 3506180
    {'lmfdb_iso': '68544.bq', 'p': 43, 'prec': 20, 'unit': 10644114865747584102748168997246, 'val': 1}
  • id: 3506185
    {'lmfdb_iso': '68544.bq', 'p': 53, 'prec': 20, 'unit': 417708293558777249967522435398755, 'val': 1}
  • id: 3506189
    {'lmfdb_iso': '68544.bq', 'p': 59, 'prec': 20, 'unit': 4396491696699369052241782501203598, 'val': 1}
  • id: 3506190
    {'lmfdb_iso': '68544.bq', 'p': 61, 'prec': 20, 'unit': 7356283752581740650853587260814333, 'val': 1}
  • id: 3506176
    {'lmfdb_iso': '68544.bq', 'p': 67, 'prec': 20, 'unit': 35241716345465116970185118895805490, 'val': 1}
  • id: 3506178
    {'lmfdb_iso': '68544.bq', 'p': 71, 'prec': 20, 'unit': 51178747146503731838090468460680726, 'val': 1}
  • id: 3506186
    {'lmfdb_iso': '68544.bq', 'p': 73, 'prec': 20, 'unit': 215621843544317159008084377228579410, 'val': 1}
  • id: 3506175
    {'lmfdb_iso': '68544.bq', 'p': 83, 'prec': 20, 'unit': 1752263365125592446250740863597734391, 'val': 1}
  • id: 3506188
    {'lmfdb_iso': '68544.bq', 'p': 89, 'prec': 20, 'unit': 6853514604462097685054726813516499330, 'val': 1}
  • id: 3506174
    {'lmfdb_iso': '68544.bq', 'p': 97, 'prec': 20, 'unit': 52577230346003483058614241913339364187, 'val': 1}