Elliptic curve data - 5070.j1

Formats: - HTML - YAML - JSON - 2025-10-14T10:53:01.680931

• 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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '5070i', 'Clabel': '5070i1', 'Cnumber': 1, 'abc_quality': 0.9704956863834545, 'absD': 192786750, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 120, 'ainvs': [1, 0, 1, -849, 9466], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 5070, 'degree': 3024, 'elladic_images': ['3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.46139175674121584845443095529', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 3], 'jinv': [-2365581049, 6750], 'lmfdb_iso': '5070.j', 'lmfdb_label': '5070.j1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -849, 9466], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.1'], 'modm_images': ['3.8.0-3.a.1.2', '120.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2535], [3, 4, 338], [5, 6, 1014], [13, 62, 30]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.39359136241262973023006485857', 'prec': 107}, 'szpiro_ratio': 3.73328411507609, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, 2, -1, 1, 1, -3, 1, 0, -2, -1, 1, 6, -1, 2, -1], 'aplist': [-1, 1, -1, 2, -3, 0, 6, 2, 3, 3, 5, -7, 6, -1, -3, -6, -9, 2, 8, -12, 14, 5, -6, -18, 14], 'class_deg': 3, 'class_size': 2, 'conductor': 5070, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '5070.j', 'trace_hash': 1638615012346348258}
• 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': '0.39741130038146695187022517219', 'prec': 103}, 'conductor': 5070, 'gens': [], 'heights': [], 'lmfdb_label': '5070.j1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.7973824456475800369311551904', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7973824456475800369311551903848833170', 'prec': 130}, 'tamagawa_product': 9, 'torsion_generators': [[14, 12, 1]], 'xcoord_integral_points': [14]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 0], '5': [0, 0], '13': 'a'}, 'iwp0': 5, 'lmfdb_label': '5070.j1'}
• ec_torsion_growth •

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

  
  
  • id: 265491
    {'degree': 3, 'field': [51, 9, -1, 1], 'lmfdb_label': '5070.j1', 'torsion': [6]}
  • id: 265493
    {'degree': 6, 'field': [27, 0, -17, 0, 1, 0, 1], 'lmfdb_label': '5070.j1', 'torsion': [3, 3]}
  • id: 265492
    {'degree': 6, 'field': [4896, -4272, 1618, -224, 3, -2, 1], 'lmfdb_label': '5070.j1', 'torsion': [2, 6]}
  • id: 265494
    {'degree': 9, 'field': [27, 0, -27, 66, -108, 99, -31, 3, -3, 1], 'lmfdb_label': '5070.j1', 'torsion': [9]}
  • id: 265495
    {'degree': 12, 'field': [-520677, -895608, -479616, -95940, -37941, -21360, -1232, 200, -359, 40, 16, -4, 1], 'lmfdb_label': '5070.j1', 'torsion': [12]}
  • id: 265496
    {'degree': 18, 'field': [729, 243, 81, 1620, 108, -324, 1296, -18, -51, 231, 139, -6, 26, -18, 42, -24, 5, -3, 1], 'lmfdb_label': '5070.j1', 'torsion': [3, 6]}
• 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: 98477
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5070.j1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 98478
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5070.j1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 98479
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5070.j1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 98480
    {'conductor': 5070, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '5070.j1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1697106
    {'adelic_gens': [[97, 6, 51, 19], [61, 6, 63, 19], [1, 0, 6, 1], [4, 3, 9, 7], [115, 6, 114, 7], [31, 6, 0, 1], [3, 4, 8, 11], [6, 1, 43, 54], [1, 6, 0, 1]], 'adelic_image': '120.16.0.?', 'conductor': 5070, 'lmfdb_label': '5070.j1', 'prime': 0}
  • id: 25202
    {'conductor': 5070, 'elladic_image': '3.8.0.1', 'lmfdb_label': '5070.j1', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 5070.j does not appear in ec_padic