Elliptic curve data - 8670.v5

Formats: - HTML - YAML - JSON - 2024-06-07T06:14:14.668784

• 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': '8670v', 'Clabel': '8670v2', 'Cnumber': 2, 'abc_quality': 0.9796429838987872, 'absD': 401803628601600, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 4080, 'ainvs': [1, 0, 0, -393046, 94807076], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 73728, 'elladic_images': ['16.96.0.36'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8636257781013267208905741359', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [278202094583041, 16646400], 'lmfdb_iso': '8670.v', 'lmfdb_label': '8670.v5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1360, 18737], 'min_quad_twist_disc': 17, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.i.1.3', '16.96.0-16.d.1.3', '60.24.0-4.b.1.2', '68.24.0-4.b.1.3', '120.96.0.?', '136.96.0.?', '240.192.1.?', '272.192.1.?', '816.384.5.?', '1020.48.0.?', '1360.384.5.?', '2040.192.1.?', '4080.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7314743641565178816818754154', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.44701910607321868076580682696', 'prec': 103}, 'szpiro_ratio': 5.542648063268354, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 1, 1, -1, 1, 0, 1, 1, -1, -4, 1, -2, 0, -1, 1, 0, 1, 4, -1], 'aplist': [1, 1, -1, 0, -4, -2, 0, 4, 0, 2, -8, -6, 6, -4, 0, -10, -4, 2, 4, 0, 6, -8, -12, -6, 14], 'class_deg': 16, 'class_size': 8, 'conductor': 8670, 'isogeny_matrix': [[1, 16, 2, 4, 8, 16, 8, 4], [16, 1, 8, 4, 2, 4, 8, 16], [2, 8, 1, 2, 4, 8, 4, 2], [4, 4, 2, 1, 2, 4, 2, 4], [8, 2, 4, 2, 1, 2, 4, 8], [16, 4, 8, 4, 2, 1, 8, 16], [8, 8, 4, 2, 4, 8, 1, 8], [4, 16, 2, 4, 8, 16, 8, 1]], 'lmfdb_iso': '8670.v', 'trace_hash': 48406145217345363}
• 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': '0.024058869500884818581464442226', 'prec': 107}, 'conductor': 8670, 'gens': [[356, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7314743641565178816818754154', 'prec': 100}], 'lmfdb_label': '8670.v5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.50471352733979089769094250615', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.9911882706548619890226010306118662403', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-724, 362, 1], [364, -182, 1]], 'xcoord_integral_points': [-724, -214, 356, 364, 1588]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [2, 0], '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [3, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '8670.v5'}
• ec_torsion_growth •

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

  
  
  • id: 452795
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '8670.v5', 'torsion': [2, 8]}
  • id: 452796
    {'degree': 4, 'field': [64, 0, 1, 0, 1], 'lmfdb_label': '8670.v5', 'torsion': [2, 4]}
  • id: 452797
    {'degree': 4, 'field': [186, -42, 43, -2, 1], 'lmfdb_label': '8670.v5', 'torsion': [2, 4]}
  • id: 452801
    {'degree': 8, 'field': [-900, -288, 180, 215, -104, -7, 7, -4, 1], 'lmfdb_label': '8670.v5', 'torsion': [2, 6]}
  • id: 452798
    {'degree': 8, 'field': [64, -272, 562, -614, 393, -106, 40, -4, 1], 'lmfdb_label': '8670.v5', 'torsion': [4, 8]}
  • id: 452799
    {'degree': 8, 'field': [1174, 644, 337, -202, 297, -32, 31, -2, 1], 'lmfdb_label': '8670.v5', 'torsion': [2, 16]}
  • id: 452800
    {'degree': 8, 'field': [1934, -592, -3843, -418, 809, 60, -53, -2, 1], 'lmfdb_label': '8670.v5', 'torsion': [2, 16]}
  • id: 452805
    {'degree': 16, 'field': [2304, 0, -779904, 0, 310320, 0, -46913, 0, 16010, 0, -4433, 0, 505, 0, -34, 0, 1], 'lmfdb_label': '8670.v5', 'torsion': [2, 24]}
  • id: 452804
    {'degree': 16, 'field': [18496, 0, 49776, 0, 449020, 0, -14931, 0, 23829, 0, -246, 0, 430, 0, -39, 0, 1], 'lmfdb_label': '8670.v5', 'torsion': [4, 16]}
  • id: 452802
    {'degree': 16, 'field': [65025, 0, 520200, 0, 1562640, 0, 2082840, 0, 1040926, 0, 2072, 0, 2064, 0, 8, 0, 1], 'lmfdb_label': '8670.v5', 'torsion': [2, 8]}
  • id: 452803
    {'degree': 16, 'field': [8856576, 0, -7391232, 0, 2959140, 0, -684492, 0, 100249, 0, -9448, 0, 630, 0, -28, 0, 1], 'lmfdb_label': '8670.v5', 'torsion': [2, 8]}
• 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: 180971
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '8670.v5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 180972
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8670.v5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 180973
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8670.v5', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 180974
    {'conductor': 8670, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '8670.v5', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1721300
    {'adelic_gens': [[4065, 16, 4064, 17], [13, 8, 320, 3257], [15, 16, 74, 3649], [3273, 16, 3458, 345], [1361, 16, 6, 97], [1, 16, 0, 1], [1, 0, 16, 1], [1, 16, 4, 65], [2875, 4072, 3442, 131]], 'adelic_image': '4080.768.13.?', 'conductor': 8670, 'lmfdb_label': '8670.v5', 'prime': 0}
  • id: 42425
    {'conductor': 8670, 'elladic_image': '16.96.0.36', 'lmfdb_label': '8670.v5', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 359571
    {'lmfdb_iso': '8670.v', 'p': 11, 'prec': 20, 'unit': 13996202793224408928, 'val': 1}
  • id: 359569
    {'lmfdb_iso': '8670.v', 'p': 13, 'prec': 20, 'unit': 675068187442049791604, 'val': 1}
  • id: 359572
    {'lmfdb_iso': '8670.v', 'p': 19, 'prec': 20, 'unit': 150846914049377824542958, 'val': 1}
  • id: 359568
    {'lmfdb_iso': '8670.v', 'p': 29, 'prec': 20, 'unit': 5789923948311056993965520889, 'val': 1}
  • id: 359578
    {'lmfdb_iso': '8670.v', 'p': 31, 'prec': 20, 'unit': 15795778693296627642411827908, 'val': 1}
  • id: 359565
    {'lmfdb_iso': '8670.v', 'p': 37, 'prec': 20, 'unit': 5834886356063184146421215772, 'val': 2}
  • id: 359566
    {'lmfdb_iso': '8670.v', 'p': 41, 'prec': 20, 'unit': 1450145482935207596653135955755, 'val': 1}
  • id: 359567
    {'lmfdb_iso': '8670.v', 'p': 43, 'prec': 20, 'unit': 8245995097187571479617816076888, 'val': 1}
  • id: 359573
    {'lmfdb_iso': '8670.v', 'p': 53, 'prec': 20, 'unit': 264070251959860975164248823743520, 'val': 1}
  • id: 359576
    {'lmfdb_iso': '8670.v', 'p': 59, 'prec': 20, 'unit': 3279687491870816483027866444936426, 'val': 1}
  • id: 359577
    {'lmfdb_iso': '8670.v', 'p': 61, 'prec': 20, 'unit': 256136801749568211848430033645817, 'val': 1}
  • id: 359564
    {'lmfdb_iso': '8670.v', 'p': 67, 'prec': 20, 'unit': 23635108252040992123365229060653862, 'val': 1}
  • id: 359574
    {'lmfdb_iso': '8670.v', 'p': 73, 'prec': 20, 'unit': 28099545204390546499413866502358957, 'val': 1}
  • id: 359570
    {'lmfdb_iso': '8670.v', 'p': 79, 'prec': 20, 'unit': 803151841496943099698749224441788342, 'val': 1}
  • id: 359563
    {'lmfdb_iso': '8670.v', 'p': 83, 'prec': 20, 'unit': 2474403757319322642195420704007025252, 'val': 1}
  • id: 359575
    {'lmfdb_iso': '8670.v', 'p': 89, 'prec': 20, 'unit': 3759971848594044952531598369022040259, 'val': 1}
  • id: 359562
    {'lmfdb_iso': '8670.v', 'p': 97, 'prec': 20, 'unit': 2323263223297366656883352925489279965, 'val': 1}