Elliptic curve data - 31680.dg3

Formats: - HTML - YAML - JSON - 2025-10-28T16:03:14.061251

• 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': '31680br', 'Clabel': '31680br1', 'Cnumber': 1, 'abc_quality': 1.0654161934626671, 'absD': 767521669921875000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [0, 0, 0, -2465607, 666270556], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 31680, 'degree': 983040, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7020960549488239482325173598', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 84, 'isogeny_degrees': [1, 2, 4], 'jinv': [35529391776305786176, 16450653076171875], 'lmfdb_iso': '31680.dg', 'lmfdb_label': '31680.dg3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1095825, -197048223], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '24.24.0-8.m.1.7', '44.12.0.h.1', '88.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 99], [3, 8, 320], [5, 6, 6336], [11, 12, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8062163203347964478262786806', 'prec': 100}, 'szpiro_ratio': 5.381171138971894, '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, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 0, 1, 0, 1, -2, 6, 4, 4, 10, 4, 2, -2, 4, 4, -2, -4, 14, 12, 4, 10, 0, -4, -10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 31680, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '31680.dg', 'trace_hash': 1843365040637272135}
• 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': '0.0044976865702527657584404488289', 'prec': 110}, 'conductor': 31680, 'gens': [], 'heights': [], 'lmfdb_label': '31680.dg3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14283527365290895047423041830', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4280465676698148113815300391744757126', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[1412, 0, 1]], 'xcoord_integral_points': [1412]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '11': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '31680.dg3'}
• ec_torsion_growth •

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

  
  
  • id: 1577694
    {'degree': 2, 'field': [-66, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [4]}
  • id: 1577693
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [2, 2]}
  • id: 1577695
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [4]}
  • id: 1577696
    {'degree': 4, 'field': [25, 0, -34, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [2, 4]}
  • id: 1577700
    {'degree': 8, 'field': [-108, 0, -168, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [6]}
  • id: 1577699
    {'degree': 8, 'field': [121, 0, 66, 0, 25, 0, 6, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [8]}
  • id: 1577697
    {'degree': 8, 'field': [625, 0, 1656, 0, 194, 0, 24, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [2, 4]}
  • id: 1577698
    {'degree': 8, 'field': [1764, 0, -3408, 0, 868, 0, -56, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [8]}
  • id: 1577704
    {'degree': 16, 'field': [-26885231, 27142860, 13952754, -10346540, 1541482, -239520, 569438, -410960, 85935, -53020, 7322, -3840, 688, -100, 36, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [2, 6]}
  • id: 1577706
    {'degree': 16, 'field': [-12150, 0, -8100, -12960, 4320, 1080, 108, 3744, 2124, -108, -780, -288, -54, -36, -12, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [12]}
  • id: 1577702
    {'degree': 16, 'field': [526, 10064, 30372, -21416, -104658, 53520, 99916, -56372, -35049, 22964, 4480, -4044, -54, 308, -24, -8, 1], 'lmfdb_label': '31680.dg3', 'torsion': [2, 8]}
  • id: 1577703
    {'degree': 16, 'field': [1444, 1216, 264, -4224, -4156, -2336, 1656, 3176, 3198, 2032, 1080, 464, 62, 0, 24, -4, 1], 'lmfdb_label': '31680.dg3', 'torsion': [2, 8]}
  • id: 1577701
    {'degree': 16, 'field': [5625, 0, 1200, 0, 4714, 0, 1820, 0, 1623, 0, 460, 0, 162, 0, 20, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [4, 4]}
  • id: 1577705
    {'degree': 16, 'field': [4294049841, 0, -3314188548, 0, 636069996, 0, -69636996, 0, 5186106, 0, -253044, 0, 7596, 0, -132, 0, 1], 'lmfdb_label': '31680.dg3', 'torsion': [12]}
• 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: 739439
    {'conductor': 31680, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '31680.dg3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 739440
    {'conductor': 31680, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '31680.dg3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 739441
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '31680.dg3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 739442
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '31680.dg3', 'prime': 11, '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: 1875658
    {'adelic_gens': [[175, 0, 0, 263], [52, 177, 255, 94], [1, 0, 8, 1], [257, 8, 256, 9], [232, 195, 99, 100], [245, 162, 6, 53], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 258, 259]], 'adelic_image': '264.48.0.?', 'conductor': 31680, 'lmfdb_label': '31680.dg3', 'prime': 0}
  • id: 141629
    {'conductor': 31680, 'elladic_image': '8.12.0.11', 'lmfdb_label': '31680.dg3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 31680.dg does not appear in ec_padic