Elliptic curve data - 177870.ff6

Formats: - HTML - YAML - JSON - 2024-05-16T06:52:51.990860

• 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': '177870dy', 'Clabel': '177870dy2', 'Cnumber': 2, 'abc_quality': 1.0136164980344768, 'absD': 1861263959789792250000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 4620, 'ainvs': [1, 1, 1, -3424121, 1278863543], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 177870, 'degree': 13271040, 'elladic_images': ['2.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7782879826232631048541656865', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 135, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [21302308926361, 8930250000], 'lmfdb_iso': '177870.ff', 'lmfdb_label': '177870.ff6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -578, 2756], 'min_quad_twist_disc': 77, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1', '12.48.0.a.1', '20.12.0.a.1', '60.96.1.e.4', '84.96.1.?', '132.96.0.?', '231.8.0.?', '308.12.0.?', '420.192.5.?', '462.48.0.?', '660.192.1.?', '924.192.1.?', '1540.24.0.?', '4620.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.60638527169642118027051752580', 'prec': 103}, 'szpiro_ratio': 4.694645498229417, '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, 0, -1, 2, 0, 1, 1, -6, 1, 8, -1], 'aplist': [1, -1, -1, 0, 0, 2, -6, 8, 0, -6, 4, -10, -6, 4, 0, -6, 12, -10, -4, 12, -10, -8, 12, 6, 10], 'class_deg': 12, 'class_size': 8, 'conductor': 177870, 'isogeny_matrix': [[1, 2, 4, 3, 4, 6, 12, 12], [2, 1, 2, 6, 2, 3, 6, 6], [4, 2, 1, 12, 4, 6, 12, 3], [3, 6, 12, 1, 12, 2, 4, 4], [4, 2, 4, 12, 1, 6, 3, 12], [6, 3, 6, 2, 6, 1, 2, 2], [12, 6, 12, 4, 3, 2, 1, 4], [12, 6, 3, 4, 12, 2, 4, 1]], 'lmfdb_iso': '177870.ff', 'trace_hash': 454430687282175800}
• 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': '0.0038619773290810530900027102767', 'prec': 110}, 'conductor': 177870, 'gens': [], 'heights': [], 'lmfdb_label': '177870.ff6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.13409320228506364735813348252', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1454912365610183577301357202950304173', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[391, -196, 1], [1623, -812, 1]], 'xcoord_integral_points': [391, 1623]}
• lmfdb_label 177870.ff6 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7880250
    {'degree': 2, 'field': [-19, -1, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 6]}
  • id: 7880252
    {'degree': 4, 'field': [-17, 37, -16, -1, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 12]}
  • id: 7880253
    {'degree': 4, 'field': [324, 0, 41, 0, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 4]}
  • id: 7880251
    {'degree': 4, 'field': [3514, -14, 15, -2, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 4]}
  • id: 7880254
    {'degree': 6, 'field': [652, -148, 162, -71, 15, -1, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 6]}
  • id: 7880256
    {'degree': 8, 'field': [10201, 0, 6386, 0, 1167, 0, 74, 0, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 12]}
  • id: 7880255
    {'degree': 8, 'field': [176724, 29820, -27754, -4062, 1857, 206, -64, -4, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 12]}
  • id: 7880257
    {'degree': 12, 'field': [85849, 111926, 136255, -8490, -13542, -518, -153, -406, -30, 78, 7, -2, 1], 'lmfdb_label': '177870.ff6', 'torsion': [6, 6]}
  • id: 7880260
    {'degree': 16, 'field': [-8291, -224492, 1353876, -2935912, 2896077, -961764, -592556, 791564, -336054, 2704, 54862, -20088, 1467, 616, -102, -4, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 24]}
  • id: 7880258
    {'degree': 16, 'field': [26896, 0, 168904, 0, 337409, 0, 297036, 0, 122564, 0, 22674, 0, 1964, 0, 76, 0, 1], 'lmfdb_label': '177870.ff6', 'torsion': [4, 12]}
  • id: 7880261
    {'degree': 16, 'field': [123063416, 141540112, 60604896, 48070168, 13636276, -8731464, -991416, 584664, 82422, -63996, 24204, -3474, -169, -62, 36, -8, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 8]}
  • id: 7880259
    {'degree': 16, 'field': [1424241749056, 0, 288245041728, 0, 24574185748, 0, 867109236, 0, 14066865, 0, 146016, 0, 4318, 0, 108, 0, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 8]}
  • id: 7880262
    {'degree': 18, 'field': [1473452817307, 1825341078216, 260131999314, -355654781669, -79665885477, 31574148468, 7986279954, -1447978839, -470453298, 20777493, 19057143, 979269, -560109, -49083, 12033, 806, -177, -3, 1], 'lmfdb_label': '177870.ff6', 'torsion': [2, 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: 4402505
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '177870.ff6', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4402506
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '177870.ff6', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4402507
    {'conductor': 177870, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '177870.ff6', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4402508
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '177870.ff6', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4402509
    {'conductor': 177870, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '177870.ff6', 'prime': 11, '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: 2809622
    {'adelic_gens': [[4609, 12, 4608, 13], [3697, 2112, 2442, 3433], [1827, 2530, 2662, 4203], [2311, 2112, 0, 1], [1, 0, 12, 1], [2099, 0, 0, 4619], [1253, 1254, 2706, 3365], [1, 12, 0, 1], [9, 4, 4604, 4613]], 'adelic_image': '4620.384.5.?', 'conductor': 177870, 'lmfdb_label': '177870.ff6', 'prime': 0}
  • id: 668597
    {'conductor': 177870, 'elladic_image': '2.6.0.1', 'lmfdb_label': '177870.ff6', 'modell_image': '2Cs', 'prime': 2}
  • id: 668598
    {'conductor': 177870, 'elladic_image': '3.4.0.1', 'lmfdb_label': '177870.ff6', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 177870.ff does not appear in ec_padic