Elliptic curve data - 6930.bc4

Formats: - HTML - YAML - JSON - 2024-05-07T12:12:36.846625

• 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': '6930be', 'Clabel': '6930be4', 'Cnumber': 4, 'abc_quality': 1.08149704374976, 'absD': 65644741076190701040000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [1, -1, 1, 10074073, 697965279], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6930, 'degree': 802816, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0676623395609213854547356811', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2, 4], 'jinv': [155099895405729262880471, 90047655797243760000], 'lmfdb_iso': '6930.bc', 'lmfdb_label': '6930.bc4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 1119342, -25477452], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '24.24.0-24.v.1.1', '280.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.5183561952268665397571130626', 'prec': 100}, 'szpiro_ratio': 6.783428434568442, '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, -1, 1, 0, 1, -1, 0, 6, -1, 0, 1, -2, 0, 0, 1], 'aplist': [1, 0, 1, -1, -1, 6, -2, 0, 0, 6, -8, 10, 2, -8, -4, 6, 12, 10, 8, -4, 10, 8, -12, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 6930, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '6930.bc', 'trace_hash': 15104955255375736}
• 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': '0.0021650221662621194073626711872', 'prec': 110}, 'conductor': 6930, 'gens': [], 'heights': [], 'lmfdb_label': '6930.bc4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.066298520276490342837916309271', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.7127171354834591989233133191536420568', 'prec': 130}, 'tamagawa_product': 224, 'torsion_generators': [[-277, 273, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 2], '3': 'a', '5': [1, 0], '7': [2, 0], '11': [0, 0]}, 'iwp0': 11, 'lmfdb_label': '6930.bc4'}
• ec_torsion_growth •

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

  
  
  • id: 364585
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [4]}
  • id: 364586
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [4]}
  • id: 364584
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [2, 2]}
  • id: 364587
    {'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [2, 4]}
  • id: 364588
    {'degree': 4, 'field': [24, 0, 0, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [2, 4]}
  • id: 364592
    {'degree': 8, 'field': [-69670, 4820, -4730, -197, 142, -55, 23, -4, 1], 'lmfdb_label': '6930.bc4', 'torsion': [6]}
  • id: 364589
    {'degree': 8, 'field': [25, 0, 76, 0, -6, 0, 4, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [4, 4]}
  • id: 364591
    {'degree': 8, 'field': [676, 0, 160, 0, -27, 0, 10, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [8]}
  • id: 364590
    {'degree': 8, 'field': [4096, 0, 0, 0, -152, 0, 0, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [8]}
  • id: 364593
    {'degree': 16, 'field': [400, -4000, 20000, -51840, 85484, -99584, 80872, -43188, 15193, -5292, 3496, -1444, 362, -84, 32, -8, 1], 'lmfdb_label': '6930.bc4', 'torsion': [2, 8]}
  • id: 364594
    {'degree': 16, 'field': [87025, 0, -125440, 0, 62696, 0, -10632, 0, 734, 0, -96, 0, 104, 0, 8, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [2, 8]}
  • id: 364595
    {'degree': 16, 'field': [147456, 0, 0, 0, -73728, 0, 0, 0, 8544, 0, 0, 0, 192, 0, 0, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [2, 8]}
  • id: 364596
    {'degree': 16, 'field': [1731260476, -924274696, 834656420, 149126348, 1428030, -93219640, 34538149, -3140504, 1016604, -183410, 66965, -18052, 4313, -630, 110, -8, 1], 'lmfdb_label': '6930.bc4', 'torsion': [2, 6]}
  • id: 364598
    {'degree': 16, 'field': [4853908900, 0, -635845800, 0, 4485700, 0, 4056749, 0, -319866, 0, 7529, 0, 373, 0, -30, 0, 1], 'lmfdb_label': '6930.bc4', 'torsion': [12]}
  • id: 364597
    {'degree': 16, 'field': [7508599660, 2537572520, -2988885820, 929183564, -531994422, 83727464, -32696171, 4194856, -1160352, 69886, -9619, -2164, 209, 42, 14, -8, 1], 'lmfdb_label': '6930.bc4', '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: 141687
    {'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '6930.bc4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 141688
    {'conductor': 6930, 'conductor_valuation': 2, 'discriminant_valuation': 13, 'j_denominator_valuation': 7, 'kodaira_symbol': -11, 'lmfdb_label': '6930.bc4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 141689
    {'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6930.bc4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 141690
    {'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6930.bc4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 141691
    {'conductor': 6930, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '6930.bc4', 'prime': 11, '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: 1709724
    {'adelic_gens': [[556, 839, 257, 834], [833, 8, 832, 9], [7, 6, 834, 835], [1, 0, 8, 1], [736, 323, 529, 558], [739, 736, 338, 741], [337, 8, 508, 33], [241, 8, 124, 33], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '840.48.0.?', 'conductor': 6930, 'lmfdb_label': '6930.bc4', 'prime': 0}
  • id: 34155
    {'conductor': 6930, 'elladic_image': '4.12.0.8', 'lmfdb_label': '6930.bc4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6930.bc does not appear in ec_padic