Elliptic curve data - 70560.j3

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• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '70560dk', 'Clabel': '70560dk1', 'Cnumber': 1, 'abc_quality': 1.02660573918469, 'absD': 248155780267521000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 0, 0, -8937453, 10256192548], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 70560, 'degree': 2949120, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7805752655718886892313391165', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2], 'jinv': [14383655824793536, 45209390625], 'lmfdb_iso': '70560.j', 'lmfdb_label': '70560.j3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -20266, 1114216], 'min_quad_twist_disc': 21, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0-2.a.1.1', '28.12.0-2.a.1.1', '40.12.0-2.a.1.2', '84.24.0.?', '120.24.0.?', '280.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 441], [3, 8, 1568], [5, 6, 14112], [7, 32, 1440]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.91174045643020453627242406559', 'prec': 103}, 'szpiro_ratio': 5.341250320023601, '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, 0, 0, 0, -1, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, 0, -1, 0, -4, 2, -2, 4, 0, -10, 0, 6, -10, -8, -4, -6, 0, -10, -8, 8, 2, 4, -12, 6, -6], '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.j', 'trace_hash': 1969461805375224216}
• 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': '0.0038443508068778264030017385062', 'prec': 110}, 'conductor': 70560, 'gens': [], 'heights': [], 'lmfdb_label': '70560.j3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.17607788995102197159658312571', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.70431155980408788638633250285083621532', 'prec': 133}, 'tamagawa_product': 64, 'torsion_generators': [[1652, 0, 1], [1799, 0, 1]], 'xcoord_integral_points': [-3451, 1652, 1799]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '70560.j3'}
• ec_torsion_growth •

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

  
  
  • id: 3354061
    {'degree': 4, 'field': [49, 0, 7, 0, 1], 'lmfdb_label': '70560.j3', 'torsion': [2, 4]}
  • id: 3354062
    {'degree': 4, 'field': [994, 56, -55, -2, 1], 'lmfdb_label': '70560.j3', 'torsion': [2, 4]}
  • id: 3354060
    {'degree': 4, 'field': [1225, 0, -140, 0, 1], 'lmfdb_label': '70560.j3', 'torsion': [2, 4]}
  • id: 3354063
    {'degree': 8, 'field': [-11907, 0, 3024, 0, -378, 0, 0, 0, 1], 'lmfdb_label': '70560.j3', 'torsion': [2, 6]}
  • id: 3354064
    {'degree': 16, 'field': [365481, -171900, -40716, -481080, 465079, -62260, -11434, -480, -6396, -140, 104, 280, 119, -20, 6, 0, 1], 'lmfdb_label': '70560.j3', 'torsion': [4, 4]}
  • id: 3354066
    {'degree': 16, 'field': [390625, 0, 212500, 0, 74350, 0, 47440, 0, 10531, 0, -2000, 0, 334, 0, -20, 0, 1], 'lmfdb_label': '70560.j3', 'torsion': [2, 8]}
  • id: 3354065
    {'degree': 16, 'field': [2722500, 0, -11190000, 0, -3425000, 0, -278000, 0, 10400, 0, -200, 0, 1100, 0, -80, 0, 1], 'lmfdb_label': '70560.j3', 'torsion': [2, 8]}
  • id: 3354067
    {'degree': 16, 'field': [203775625, 0, 52520000, 0, -5882000, 0, -751000, 0, 187750, 0, -18400, 0, 1120, 0, -40, 0, 1], 'lmfdb_label': '70560.j3', '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: 1710812
    {'conductor': 70560, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '70560.j3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1710813
    {'conductor': 70560, 'conductor_valuation': 2, 'discriminant_valuation': 16, 'j_denominator_valuation': 10, 'kodaira_symbol': -14, 'lmfdb_label': '70560.j3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1710814
    {'conductor': 70560, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '70560.j3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1710815
    {'conductor': 70560, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '70560.j3', '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: 2131067
    {'adelic_gens': [[837, 4, 836, 5], [599, 836, 358, 831], [837, 838, 562, 1], [1, 4, 0, 1], [631, 2, 422, 5], [421, 2, 0, 1], [1, 0, 4, 1], [337, 2, 0, 1]], 'adelic_image': '840.48.0.?', 'conductor': 70560, 'lmfdb_label': '70560.j3', 'prime': 0}
  • id: 294083
    {'conductor': 70560, 'elladic_image': '2.6.0.1', 'lmfdb_label': '70560.j3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 70560.j does not appear in ec_padic