Elliptic curve data - 70560.l4

Formats: - HTML - YAML - JSON - 2024-04-28T11:13:15.482968

• 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': '70560do', 'Clabel': '70560do2', 'Cnumber': 2, 'abc_quality': 1.0153915089943955, 'absD': 38446458459514176960000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 0, 0, -7680603, -12494843102], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 70560, 'degree': 5898240, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0325182562223712217543804309', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 4], 'jinv': [-1141100604753992, 875529151875], 'lmfdb_iso': '70560.l', 'lmfdb_label': '70560.l4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -17416, -1343384], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.v.1', '28.12.0-4.c.1.1', '40.12.0.bb.1', '120.24.0.?', '168.24.0.?', '280.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.99039665194070074144115734962', 'prec': 103}, 'szpiro_ratio': 5.376131629909178, '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, -4, 0, 6, 0, 0, 0, 6, 0, 0, 0], 'aplist': [0, 0, -1, 0, -4, 6, 6, 0, 4, 6, 0, 2, 2, 4, 4, 6, 12, 10, 4, -8, 14, 8, -12, -6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 70560, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '70560.l', 'trace_hash': 1079013455634318296}
• 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': '0.0023226732065045898643553256906', 'prec': 110}, 'conductor': 70560, 'gens': [], 'heights': [], 'lmfdb_label': '70560.l4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.043888089904965514309743904056', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1599424731575170303015610920708424728', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[3374, 0, 1]], 'xcoord_integral_points': [3374]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': 'a'}, 'iwp0': 5, 'lmfdb_label': '70560.l4'}
• ec_torsion_growth •

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

  
  
  • id: 3354269
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [4]}
  • id: 3354268
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [2, 2]}
  • id: 3354270
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [4]}
  • id: 3354271
    {'degree': 4, 'field': [81, 0, 24, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [2, 4]}
  • id: 3354275
    {'degree': 8, 'field': [-2490, 5532, -1860, 960, -24, -12, 22, -4, 1], 'lmfdb_label': '70560.l4', 'torsion': [6]}
  • id: 3354272
    {'degree': 8, 'field': [616, 448, -376, -152, 97, -28, 14, -4, 1], 'lmfdb_label': '70560.l4', 'torsion': [2, 4]}
  • id: 3354273
    {'degree': 8, 'field': [1096, 3600, 3356, 1920, 357, -120, -46, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [8]}
  • id: 3354274
    {'degree': 8, 'field': [15376, 0, -512, 0, 288, 0, -32, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [8]}
  • id: 3354280
    {'degree': 16, 'field': [441, 0, -1707552, 0, -1162476, 0, 170016, 0, -80850, 0, 8736, 0, 4, 0, -32, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [12]}
  • id: 3354276
    {'degree': 16, 'field': [2116, 0, 8016, 0, 20572, 0, -3888, 0, 3045, 0, -324, 0, 46, 0, -12, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [4, 4]}
  • id: 3354278
    {'degree': 16, 'field': [52794, -6552, 9900, -8856, 13686, -22008, 25872, -16884, 5995, -1916, 964, -140, -98, 28, 16, -8, 1], 'lmfdb_label': '70560.l4', 'torsion': [2, 8]}
  • id: 3354277
    {'degree': 16, 'field': [62001, 0, 96000, 0, 92752, 0, -261552, 0, 119154, 0, -13312, 0, 1104, 0, -48, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [2, 8]}
  • id: 3354279
    {'degree': 16, 'field': [11088900, 0, 6704304, 0, -410480, 0, 592872, 0, -14868, 0, 560, 0, 420, 0, 12, 0, 1], 'lmfdb_label': '70560.l4', 'torsion': [2, 6]}
  • id: 3354281
    {'degree': 16, 'field': [37265284, -90062000, -66515568, 122234336, 163222976, -7295568, -18326952, 953568, 681564, -65240, -9680, 2880, -684, -120, 60, -8, 1], 'lmfdb_label': '70560.l4', '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: 1710880
    {'conductor': 70560, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '70560.l4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1710881
    {'conductor': 70560, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '70560.l4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1710882
    {'conductor': 70560, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '70560.l4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1710883
    {'conductor': 70560, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '70560.l4', 'prime': 7, '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: 2131074
    {'adelic_gens': [[337, 728, 28, 393], [833, 8, 832, 9], [7, 6, 834, 835], [1, 0, 8, 1], [272, 357, 35, 118], [671, 672, 602, 545], [288, 833, 427, 414], [599, 0, 0, 839], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '840.48.0.?', 'conductor': 70560, 'lmfdb_label': '70560.l4', 'prime': 0}
  • id: 294090
    {'conductor': 70560, 'elladic_image': '4.6.0.1', 'lmfdb_label': '70560.l4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 70560.l does not appear in ec_padic