Elliptic curve data - 4800.k1

Formats: - HTML - YAML - JSON - 2026-01-26T23:58:16.097487

• 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': '4800k', 'Clabel': '4800k2', 'Cnumber': 2, 'abc_quality': 1.013438728972183, 'absD': 186624000000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 120, 'ainvs': [0, -1, 0, -16833, -518463], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4800, 'degree': 15360, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4394932191654710087514200880', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [2060602, 729], 'lmfdb_iso': '4800.k', 'lmfdb_label': '4800.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -168, -468], 'min_quad_twist_disc': 40, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.j.1', '40.6.0.b.1', '60.6.0.c.1', '120.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 5], [3, 4, 1600], [5, 14, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.74954372095336012720689491732', 'prec': 107}, 'szpiro_ratio': 4.8142006838319045, '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, -1, 0, 0, 0, -2, 0, 1, 0, -2, 0, -2, 0, 0, 0, 6, 0, -8, 0], 'aplist': [0, -1, 0, -2, -2, -2, 6, -8, -4, -8, 0, 10, 2, 12, 0, -10, 6, -2, 8, -4, 4, -8, -4, 6, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 4800, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4800.k', 'trace_hash': 1297095739294374855}
• 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': '0.056191687721612763064444565522', 'prec': 107}, 'conductor': 4800, 'gens': [], 'heights': [], 'lmfdb_label': '4800.k1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.43136779851149748397050714779', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.86273559702299496794101429557938664023', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-33, 0, 1]], 'xcoord_integral_points': [-33]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': 'a'}, 'iwp0': 3, 'lmfdb_label': '4800.k1'}
• ec_torsion_growth •

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

  
  
  • id: 249081
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '4800.k1', 'torsion': [2, 2]}
  • id: 249082
    {'degree': 4, 'field': [40, 0, -10, 0, 1], 'lmfdb_label': '4800.k1', 'torsion': [4]}
  • id: 249085
    {'degree': 8, 'field': [-675, 0, -450, 0, -90, 0, 0, 0, 1], 'lmfdb_label': '4800.k1', 'torsion': [6]}
  • id: 249083
    {'degree': 8, 'field': [1, 0, -6, 0, 26, 0, -6, 0, 1], 'lmfdb_label': '4800.k1', 'torsion': [2, 4]}
  • id: 249084
    {'degree': 8, 'field': [36, 0, -112, 0, 44, 0, -8, 0, 1], 'lmfdb_label': '4800.k1', 'torsion': [2, 4]}
  • id: 249087
    {'degree': 16, 'field': [196, 0, -1280, 0, 148, 0, 720, 0, 444, 0, 180, 0, 52, 0, 10, 0, 1], 'lmfdb_label': '4800.k1', 'torsion': [2, 6]}
  • id: 249086
    {'degree': 16, 'field': [11236, 0, 20556, 0, 9805, 0, -4026, 0, 1089, 0, 444, 0, 25, 0, 6, 0, 1], 'lmfdb_label': '4800.k1', 'torsion': [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: 91903
    {'conductor': 4800, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '4800.k1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 91904
    {'conductor': 4800, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '4800.k1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 91905
    {'conductor': 4800, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4800.k1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1695255
    {'adelic_gens': [[41, 4, 82, 9], [2, 1, 59, 0], [1, 2, 2, 5], [117, 4, 116, 5], [3, 4, 8, 11], [28, 1, 23, 0], [17, 106, 104, 15], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '120.12.0.?', 'conductor': 4800, 'lmfdb_label': '4800.k1', 'prime': 0}
  • id: 23787
    {'conductor': 4800, 'elladic_image': '2.3.0.1', 'lmfdb_label': '4800.k1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4800.k does not appear in ec_padic