Elliptic curve data - 342720.bw8

Formats: - HTML - YAML - JSON - 2024-05-21T15:13:39.848665

• 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': '342720bw', 'Clabel': '342720bw3', 'Cnumber': 3, 'abc_quality': 1.0201278670329077, 'absD': 181146881212416000000000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 14280, 'ainvs': [0, 0, 0, 133997172, -250767224048], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 342720, 'degree': 84934656, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7270969089915583663398503455', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 48, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [1392333139184610040991, 947901937500000000], 'lmfdb_iso': '342720.bw', 'lmfdb_label': '342720.bw8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 232634, -18120604], 'min_quad_twist_disc': 24, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.48.0-12.g.1.27', '84.48.0.?', '120.96.0.?', '168.96.0.?', '204.48.0.?', '238.6.0.?', '280.12.0.?', '408.96.0.?', '476.12.0.?', '680.12.0.?', '714.24.0.?', '840.192.1.?', '1428.96.1.?', '2040.192.1.?', '2856.192.1.?', '4760.24.0.?', '14280.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1380699938175855565163795449', 'prec': 100}, 'szpiro_ratio': 5.316229902888269, '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, -1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, -4, 0], 'aplist': [0, 0, -1, -1, 0, -2, 1, -4, 0, 6, -8, -2, -6, -4, 12, 6, -12, -2, -4, -12, -10, 4, 0, 6, 14], 'class_deg': 12, 'class_size': 8, 'conductor': 342720, 'isogeny_matrix': [[1, 4, 12, 2, 3, 6, 12, 4], [4, 1, 3, 2, 12, 6, 12, 4], [12, 3, 1, 6, 4, 2, 4, 12], [2, 2, 6, 1, 6, 3, 6, 2], [3, 12, 4, 6, 1, 2, 4, 12], [6, 6, 2, 3, 2, 1, 2, 6], [12, 12, 4, 6, 4, 2, 1, 3], [4, 4, 12, 2, 12, 6, 3, 1]], 'lmfdb_iso': '342720.bw', 'trace_hash': 1319316593445676921}
• 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': '0.00057900825799321516714831019637', 'prec': 113}, 'conductor': 342720, 'gens': [], 'heights': [], 'lmfdb_label': '342720.bw8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.032276353823809021476336715581', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.77463249177141651543208117394602565190', 'prec': 133}, 'tamagawa_product': 96, 'torsion_generators': [[1826, 0, 1]], 'xcoord_integral_points': [1826]}
• lmfdb_label 342720.bw8 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 14322086
    {'degree': 2, 'field': [-102, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [4]}
  • id: 14322088
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [6]}
  • id: 14322085
    {'degree': 2, 'field': [30, -1, 1], 'lmfdb_label': '342720.bw8', 'torsion': [2, 2]}
  • id: 14322087
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [4]}
  • id: 14322092
    {'degree': 4, 'field': [51, 6, -5, -2, 1], 'lmfdb_label': '342720.bw8', 'torsion': [12]}
  • id: 14322091
    {'degree': 4, 'field': [123, -30, 31, -2, 1], 'lmfdb_label': '342720.bw8', 'torsion': [12]}
  • id: 14322090
    {'degree': 4, 'field': [786, -64, 65, -2, 1], 'lmfdb_label': '342720.bw8', 'torsion': [2, 6]}
  • id: 14322089
    {'degree': 4, 'field': [1296, 0, -30, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [2, 4]}
  • id: 14322093
    {'degree': 6, 'field': [-6, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [6]}
  • id: 14322097
    {'degree': 8, 'field': [6084, -8736, 5092, -1916, 695, -158, 47, -2, 1], 'lmfdb_label': '342720.bw8', 'torsion': [2, 12]}
  • id: 14322094
    {'degree': 8, 'field': [19600, 0, -882, 0, 721, 0, -42, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [2, 4]}
  • id: 14322096
    {'degree': 8, 'field': [33856, 0, 14592, 0, 404, 0, -12, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [8]}
  • id: 14322095
    {'degree': 8, 'field': [569275, -115450, -83255, -2410, 5706, 262, -131, -2, 1], 'lmfdb_label': '342720.bw8', 'torsion': [8]}
  • id: 14322098
    {'degree': 12, 'field': [25, 30, 111, -290, 180, -90, 129, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '342720.bw8', 'torsion': [3, 6]}
  • id: 14322101
    {'degree': 12, 'field': [2304, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [12]}
  • id: 14322100
    {'degree': 12, 'field': [2350, 9780, -6714, -4840, -570, 2940, 29, -726, 15, 100, -9, -6, 1], 'lmfdb_label': '342720.bw8', 'torsion': [12]}
  • id: 14322099
    {'degree': 12, 'field': [729276510, -145643364, 157798710, -24850680, 13788810, -1674144, 621889, -55806, 15315, -920, 195, -6, 1], 'lmfdb_label': '342720.bw8', 'torsion': [2, 6]}
  • id: 14322106
    {'degree': 16, 'field': [226576, 0, 194208, 0, -3128, 0, 47328, 0, 36753, 0, 8814, 0, 1183, 0, 66, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [24]}
  • id: 14322102
    {'degree': 16, 'field': [813604, 0, 13468808, 0, 12510704, 0, 4172964, 0, 633029, 0, 55452, 0, 2894, 0, 80, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [4, 4]}
  • id: 14322107
    {'degree': 16, 'field': [37650496, 0, 2709952, 0, 4085120, 0, -148008, 0, 84689, 0, -1932, 0, 470, 0, 28, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [24]}
  • id: 14322104
    {'degree': 16, 'field': [63361600, 0, 332252160, 0, 624739124, 0, 5776788, 0, -816495, 0, 33960, 0, 590, 0, -12, 0, 1], 'lmfdb_label': '342720.bw8', 'torsion': [2, 8]}
  • id: 14322105
    {'degree': 16, 'field': [288598872, -369222624, 302496004, -95107348, 25039001, 2997236, 940960, -487056, 243380, -122408, 39650, -6396, 2020, -280, 68, -4, 1], 'lmfdb_label': '342720.bw8', 'torsion': [2, 12]}
  • id: 14322103
    {'degree': 16, 'field': [6211259404, 2166583608, -1458963394, -1387258768, 622749065, 87618852, -33381904, 3380076, -576458, -210288, 74182, -18656, 4080, -476, 88, -8, 1], 'lmfdb_label': '342720.bw8', 'torsion': [2, 8]}
  • id: 14322108
    {'degree': 18, 'field': [7969233843427632, 9620695920031200, 5586212491750416, 1844743105207760, 403835103408024, 61250539407360, 8393647052380, 759763965720, 94945551756, 904146020, 38198688, -26638620, -7579385, -106770, -31563, -250, 192, 0, 1], 'lmfdb_label': '342720.bw8', '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: 8479422
    {'conductor': 342720, 'conductor_valuation': 6, 'discriminant_valuation': 26, 'j_denominator_valuation': 8, 'kodaira_symbol': -20, 'lmfdb_label': '342720.bw8', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8479423
    {'conductor': 342720, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '342720.bw8', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8479424
    {'conductor': 342720, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '342720.bw8', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8479425
    {'conductor': 342720, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '342720.bw8', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 8479426
    {'conductor': 342720, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '342720.bw8', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 3804787
    {'adelic_gens': [[1, 24, 0, 1], [1, 0, 24, 1], [7719, 10112, 11764, 13771], [12256, 21, 11955, 13906], [10703, 14256, 10806, 329], [1, 12, 12, 145], [15, 106, 12974, 5051], [5896, 3, 13821, 14194], [14257, 24, 14256, 25], [2379, 4756, 14260, 7059], [2857, 24, 5724, 289]], 'adelic_image': '14280.384.5.?', 'conductor': 342720, 'lmfdb_label': '342720.bw8', 'prime': 0}
  • id: 1187705
    {'conductor': 342720, 'elladic_image': '4.6.0.1', 'lmfdb_label': '342720.bw8', 'modell_image': '2B', 'prime': 2}
  • id: 1187706
    {'conductor': 342720, 'elladic_image': '3.4.0.1', 'lmfdb_label': '342720.bw8', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 342720.bw does not appear in ec_padic