Elliptic curve data - 1600.s1

Formats: - HTML - YAML - JSON - 2026-02-13T13:21:22.890960

• 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': '1600i', 'Clabel': '1600i1', 'Cnumber': 1, 'abc_quality': 0.9949912704917342, 'absD': 12800000000, 'adelic_genus': 3, 'adelic_index': 60, 'adelic_level': 40, 'ainvs': [0, 1, 0, -833, 10463], 'analytic_rank': 0, 'bad_primes': [2, 5], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 1600, 'degree': 960, 'elladic_images': ['8.2.0.1', '5.15.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.66215769036217024529229831376', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1], 'jinv': [-5000, 1], 'lmfdb_iso': '1600.s', 'lmfdb_label': '1600.s1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -8, -8], 'min_quad_twist_disc': -40, 'modell_images': ['5Ns'], 'modm_images': ['5.15.0.a.1', '8.2.0.a.1', '20.30.0.b.1', '40.60.3.u.1'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 25], [5, 10, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2772348936271616412130813935', 'prec': 103}, 'szpiro_ratio': 4.349118019259314, '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, 5, 0, 0, 0, 0, 0, 5, 0, 5, 0], 'aplist': [0, 1, 0, 2, 5, 0, 5, 5, -6, -4, -10, 10, 5, 4, 8, 10, 0, 10, 3, 0, -5, -10, -1, -9, 10], 'class_deg': 1, 'class_size': 1, 'conductor': 1600, 'isogeny_matrix': [[1]], 'lmfdb_iso': '1600.s', 'trace_hash': 2180088398821517094}
• 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': '0.26598499522385955203728467001', 'prec': 103}, 'conductor': 1600, 'gens': [], 'heights': [], 'lmfdb_label': '1600.s1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2102547858860431478166305318', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4205095717720862956332610635396154870', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  conductor	integer
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'conductor': 1600, 'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': [0, 0], '11': [0, 0], '13': [0, 0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '1600.s1'}
• ec_torsion_growth •

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

  
  
  • id: 79805
    {'conductor': 1600, 'degree': 3, 'field': [2, 2, -1, 1], 'lmfdb_label': '1600.s1', 'torsion': [2]}
  • id: 79806
    {'conductor': 1600, 'degree': 6, 'field': [2, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '1600.s1', 'torsion': [2, 2]}
  • id: 79807
    {'conductor': 1600, 'degree': 8, 'field': [-108, 0, 72, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '1600.s1', 'torsion': [3]}
  • id: 79808
    {'conductor': 1600, 'degree': 8, 'field': [20, 0, -40, 0, 20, 0, 0, 0, 1], 'lmfdb_label': '1600.s1', 'torsion': [5]}
  • id: 79809
    {'conductor': 1600, 'degree': 12, 'field': [2, 2, -15, 0, 27, 0, 4, 8, 6, -2, -1, 0, 1], 'lmfdb_label': '1600.s1', 'torsion': [4]}
  • id: 79810
    {'conductor': 1600, 'degree': 16, 'field': [25, 0, 0, 0, 100, 0, 0, 0, -210, 0, 0, 0, 20, 0, 0, 0, 1], 'lmfdb_label': '1600.s1', 'torsion': [5]}
• 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: 24955
    {'conductor': 1600, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '1600.s1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 24956
    {'conductor': 1600, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '1600.s1', '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: 1674511
    {'adelic_gens': [[21, 0, 0, 21], [31, 32, 8, 39], [1, 16, 0, 9], [31, 10, 20, 31], [31, 30, 30, 11], [21, 20, 20, 21], [31, 0, 0, 31], [9, 0, 0, 9], [1, 20, 0, 1], [31, 25, 25, 6], [9, 18, 37, 31], [9, 8, 15, 23], [33, 0, 0, 33]], 'adelic_image': '40.60.3.?', 'conductor': 1600, 'lmfdb_label': '1600.s1', 'prime': 0}
  • id: 7770
    {'conductor': 1600, 'elladic_image': '8.2.0.1', 'lmfdb_label': '1600.s1', 'modell_image': '2G', 'prime': 2}
  • id: 7771
    {'conductor': 1600, 'elladic_image': '5.15.0.1', 'lmfdb_label': '1600.s1', 'modell_image': '5Ns', 'prime': 5}
• lmfdb_iso 1600.s does not appear in ec_padic