Elliptic curve data - 1600.j3

Formats: - HTML - YAML - JSON - 2024-04-28T04:34:46.120392

• 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': '1600j', 'Clabel': '1600j1', 'Cnumber': 1, 'abc_quality': 1.0904350906962674, 'absD': 327680000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, -1, 0, -33, -863], 'analytic_rank': 0, 'bad_primes': [2, 5], 'class_deg': 15, 'class_size': 4, 'cm': 0, 'conductor': 1600, 'degree': 384, 'elladic_images': ['8.2.0.1', '3.4.0.1', '5.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.31362117469603643137202280219', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 3, 5, 15], 'jinv': [-25, 2], 'lmfdb_iso': '1600.j', 'lmfdb_label': '1600.j3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -1, -2], 'min_quad_twist_disc': 8, 'modell_images': ['3B', '5B.4.2'], 'modm_images': ['3.4.0.a.1', '5.12.0.a.2', '8.2.0.a.1', '12.8.0-3.a.1.3', '15.96.1.a.2', '20.24.0-5.a.2.3', '24.16.0-24.a.1.2', '40.48.1-40.bx.2.2', '60.192.1-15.a.2.8', '120.384.9.?'], 'nonmax_primes': [2, 3, 5], 'nonmax_rad': 30, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2625789002885816576207451577', 'prec': 103}, 'szpiro_ratio': 3.6690648372147616, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 0, 0, 0, 2, 0, -2, 0, 3, 0, 4, 0, 0, 0, -3, 0, -5, 0], 'aplist': [0, -1, 0, 2, 3, 4, -3, -5, 6, 0, 2, -2, -3, 4, 12, -6, 0, -2, 13, 12, 11, -10, 9, 15, 2], 'class_deg': 15, 'class_size': 4, 'conductor': 1600, 'isogeny_matrix': [[1, 15, 3, 5], [15, 1, 5, 3], [3, 5, 1, 15], [5, 3, 15, 1]], 'lmfdb_iso': '1600.j', 'trace_hash': 2192776047517048661}
• 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': '0.53406253005712067829554158670', 'prec': 103}, 'conductor': 1600, 'gens': [], 'heights': [], 'lmfdb_label': '1600.j3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.75642569170909029483967555935', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5128513834181805896793511186912142717', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': 'a', '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '1600.j3'}
• ec_torsion_growth •

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

  
  
  • id: 79811
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [3]}
  • id: 79812
    {'degree': 3, 'field': [2, 2, -1, 1], 'lmfdb_label': '1600.j3', 'torsion': [2]}
  • id: 79813
    {'degree': 4, 'field': [20, 0, 10, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [5]}
  • id: 79816
    {'degree': 6, 'field': [-2, 0, -3, 0, -4, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [6]}
  • id: 79814
    {'degree': 6, 'field': [2, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [2, 2]}
  • id: 79815
    {'degree': 6, 'field': [24, 0, 28, 0, 2, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [3]}
  • id: 79817
    {'degree': 8, 'field': [16, 0, 8, 0, 4, 0, 2, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [15]}
  • id: 79818
    {'degree': 10, 'field': [-10, 0, -20, 0, -10, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [5]}
  • id: 79819
    {'degree': 12, 'field': [1, -1, 0, -1, -3, -4, 0, -4, -3, -1, 0, -1, 1], 'lmfdb_label': '1600.j3', 'torsion': [4]}
  • id: 79820
    {'degree': 12, 'field': [4, 0, 24, 0, 156, 0, -76, 0, 24, 0, -6, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [3, 3]}
  • id: 79822
    {'degree': 12, 'field': [16, 0, 0, 0, 88, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [2, 6]}
  • id: 79821
    {'degree': 12, 'field': [20, 0, 60, 0, 85, 0, 70, 0, 35, 0, 10, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [10]}
  • id: 79823
    {'degree': 18, 'field': [-32, 0, -48, 0, -336, 0, -284, 0, -360, 0, 204, 0, -166, 0, 96, 0, -18, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [9]}
  • id: 79824
    {'degree': 18, 'field': [54, 0, 180, 0, 186, 0, 73, 0, 28, 0, -17, 0, -10, 0, 7, 0, 6, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [6]}
  • id: 79825
    {'degree': 20, 'field': [4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -246, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1600.j3', 'torsion': [15]}
• 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: 24957
    {'conductor': 1600, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '1600.j3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 24958
    {'conductor': 1600, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '1600.j3', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1674492
    {'adelic_gens': [[46, 105, 45, 1], [1, 42, 90, 61], [1, 0, 60, 1], [81, 10, 40, 81], [31, 90, 15, 91], [1, 72, 0, 1], [59, 30, 75, 29], [41, 80, 40, 81], [1, 0, 30, 1], [73, 90, 0, 49], [1, 36, 60, 1]], 'adelic_image': '120.384.9.?', 'conductor': 1600, 'lmfdb_label': '1600.j3', 'prime': 0}
  • id: 7730
    {'conductor': 1600, 'elladic_image': '8.2.0.1', 'lmfdb_label': '1600.j3', 'modell_image': '2G', 'prime': 2}
  • id: 7731
    {'conductor': 1600, 'elladic_image': '3.4.0.1', 'lmfdb_label': '1600.j3', 'modell_image': '3B', 'prime': 3}
  • id: 7732
    {'conductor': 1600, 'elladic_image': '5.12.0.2', 'lmfdb_label': '1600.j3', 'modell_image': '5B.4.2', 'prime': 5}
• lmfdb_iso 1600.j does not appear in ec_padic