Elliptic curve data - 4200.n6

Formats: - HTML - YAML - JSON - 2026-05-03T06:20:18.621773

• 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': '4200d', 'Clabel': '4200d6', 'Cnumber': 6, 'abc_quality': 1.1006655403587287, 'absD': 13835522400000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, -1, 0, 59992, 180012], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4200, 'degree': 24576, 'elladic_images': ['8.24.0.94'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7866285709215022480665976273', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [746185003198, 432360075], 'lmfdb_iso': '4200.n', 'lmfdb_label': '4200.n6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 2400, 2400], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.3', '20.12.0-4.c.1.1', '24.48.0-24.bn.1.9', '40.48.0-40.ca.2.8', '112.48.0.?', '120.96.0.?', '336.96.0.?', '560.96.0.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 75], [3, 4, 1400], [5, 18, 168], [7, 8, 600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.34652469919116886046708851602', 'prec': 103}, 'szpiro_ratio': 5.348237159952068, '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, 1, 0, 1, 0, 4, 0, 2, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, -1, 0, 1, 4, 2, -2, 4, 0, -2, 8, 2, 2, -4, 0, 10, -12, 6, -12, 0, 6, -8, -4, 2, 14], 'class_deg': 8, 'class_size': 6, 'conductor': 4200, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '4200.n', 'trace_hash': 1389101446378439024}
• 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': '0.028064295261476052416034320714', 'prec': 107}, 'conductor': 4200, 'gens': [], 'heights': [], 'lmfdb_label': '4200.n6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.23802210272755433005576773661', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9041768218204346404461418928691876756', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-3, 0, 1]], 'xcoord_integral_points': [-3]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': 'a', '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '4200.n6'}
• ec_torsion_growth •

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

  
  
  • id: 219131
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [4]}
  • id: 219132
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [4]}
  • id: 219130
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [2, 2]}
  • id: 219134
    {'degree': 4, 'field': [9, 0, 4, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [8]}
  • id: 219135
    {'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [8]}
  • id: 219133
    {'degree': 4, 'field': [81, 0, -12, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [2, 4]}
  • id: 219139
    {'degree': 8, 'field': [-1875, 0, 2920, 0, -150, 0, 0, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [6]}
  • id: 219138
    {'degree': 8, 'field': [81, 0, -36, 0, 7, 0, -4, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [2, 8]}
  • id: 219137
    {'degree': 8, 'field': [409, 388, -430, 88, -53, 8, 2, -4, 1], 'lmfdb_label': '4200.n6', 'torsion': [8]}
  • id: 219136
    {'degree': 8, 'field': [745, -380, 434, -104, 43, 8, 2, -4, 1], 'lmfdb_label': '4200.n6', 'torsion': [2, 4]}
  • id: 219140
    {'degree': 16, 'field': [25, 0, 8940, 0, 8206, 0, -1728, 0, 399, 0, 216, 0, 34, 0, 12, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [4, 4]}
  • id: 219141
    {'degree': 16, 'field': [6241, 0, -8916, 0, 7318, 0, -2304, 0, 423, 0, 72, 0, 82, 0, 12, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [2, 8]}
  • id: 219144
    {'degree': 16, 'field': [285750, 1738200, 4694380, 1002220, 3355450, 631880, 900410, 238820, 150326, 27992, 17138, 364, 760, -56, -2, -8, 1], 'lmfdb_label': '4200.n6', 'torsion': [2, 6]}
  • id: 219146
    {'degree': 16, 'field': [8307600, -11616000, 15572800, -8225120, 4004800, 227440, -421184, 268192, -83800, -1120, 4088, -752, 388, -140, 40, -8, 1], 'lmfdb_label': '4200.n6', 'torsion': [12]}
  • id: 219142
    {'degree': 16, 'field': [65610000, 0, 38880000, 0, 16974000, 0, 3012000, 0, 503500, 0, 35600, 0, 1940, 0, 40, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [16]}
  • id: 219143
    {'degree': 16, 'field': [1049760000, 0, 699840000, 0, 198288000, 0, 30132000, 0, 2592900, 0, 128700, 0, 4230, 0, 90, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [16]}
  • id: 219145
    {'degree': 16, 'field': [1199375424, 0, -157223808, 0, 8490240, 0, -2081376, 0, 259200, 0, -27864, 0, 1548, 0, -60, 0, 1], 'lmfdb_label': '4200.n6', 'torsion': [12]}
• 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: 79024
    {'conductor': 4200, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '4200.n6', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 79025
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4200.n6', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 79026
    {'conductor': 4200, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '4200.n6', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 79027
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '4200.n6', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
• ec_galrep •

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

  
  
  • id: 1691345
    {'adelic_gens': [[5, 4, 1676, 1677], [436, 421, 999, 850], [1, 16, 0, 1], [1665, 16, 1664, 17], [1136, 5, 1635, 1666], [15, 2, 1582, 1667], [211, 16, 630, 421], [241, 16, 248, 129], [1, 0, 16, 1], [659, 1664, 592, 315]], 'adelic_image': '1680.192.1.?', 'conductor': 4200, 'lmfdb_label': '4200.n6', 'prime': 0}
  • id: 20916
    {'conductor': 4200, 'elladic_image': '8.24.0.94', 'lmfdb_label': '4200.n6', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4200.n does not appear in ec_padic