Elliptic curve data - 4200.n5

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• 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': '4200d1', 'Cnumber': 1, 'abc_quality': 0.9612989106730464, 'absD': 57408750000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, -1, 0, -383, 12012], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4200, 'degree': 3072, 'elladic_images': ['8.24.0.93'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.74690780008158428394074944507', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-24918016, 229635], 'lmfdb_iso': '4200.n', 'lmfdb_label': '4200.n5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -15, 90], '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.1.5', '20.12.0-4.c.1.2', '28.12.0-4.c.1.2', '40.48.0-40.ca.1.12', '48.48.0-48.h.1.4', '56.48.0-56.bu.2.9', '70.6.0.a.1', '140.24.0.?', '240.96.0.?', '280.96.0.?', '336.96.0.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 175], [3, 4, 1400], [5, 18, 168], [7, 8, 600]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.28886021632211433983204092870', 'prec': 107}, 'szpiro_ratio': 3.8702751580360695, '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': '0.22451436209180841932827456571', 'prec': 103}, 'conductor': 4200, 'gens': [], 'heights': [], 'lmfdb_label': '4200.n5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.95208841091021732022307094644', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9041768218204346404461418928691876756', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-28, 0, 1]], 'xcoord_integral_points': [-28]}
• 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.n5'}
• ec_torsion_growth •

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

  
  
  • id: 219060
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '4200.n5', 'torsion': [4]}
  • id: 219061
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '4200.n5', 'torsion': [4]}
  • id: 219059
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '4200.n5', 'torsion': [2, 2]}
  • id: 219064
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '4200.n5', 'torsion': [8]}
  • id: 219062
    {'degree': 4, 'field': [4, 2, 5, -1, 1], 'lmfdb_label': '4200.n5', 'torsion': [2, 4]}
  • id: 219063
    {'degree': 4, 'field': [29, 16, -15, -2, 1], 'lmfdb_label': '4200.n5', 'torsion': [8]}
  • id: 219068
    {'degree': 8, 'field': [-1875, 0, 2920, 0, -150, 0, 0, 0, 1], 'lmfdb_label': '4200.n5', 'torsion': [6]}
  • id: 219067
    {'degree': 8, 'field': [16, 0, -36, 0, 37, 0, -9, 0, 1], 'lmfdb_label': '4200.n5', 'torsion': [2, 8]}
  • id: 219065
    {'degree': 8, 'field': [81, 0, 122, 0, 299, 0, -2, 0, 1], 'lmfdb_label': '4200.n5', 'torsion': [2, 4]}
  • id: 219066
    {'degree': 8, 'field': [86, -136, 132, 2, 15, -22, 12, -4, 1], 'lmfdb_label': '4200.n5', 'torsion': [8]}
  • id: 219070
    {'degree': 16, 'field': [-311, 14532, -86616, -109872, 89824, 170772, 25116, -78624, -42483, 8148, 10920, 1512, -938, -168, -12, 0, 1], 'lmfdb_label': '4200.n5', 'torsion': [16]}
  • id: 219069
    {'degree': 16, 'field': [7396, 0, -4208, 0, 20548, 0, -36, 0, 2565, 0, -156, 0, -2, 0, -8, 0, 1], 'lmfdb_label': '4200.n5', 'torsion': [4, 8]}
  • id: 219071
    {'degree': 16, 'field': [27556, -88976, 143648, -219952, 336296, -344656, 237600, -105216, 12304, 11208, -4800, 1832, -244, -64, 32, -8, 1], 'lmfdb_label': '4200.n5', 'torsion': [16]}
  • id: 219072
    {'degree': 16, 'field': [59049, 0, -138456, 0, 62190, 0, 26352, 0, 2535, 0, 352, 0, 102, 0, 0, 0, 1], 'lmfdb_label': '4200.n5', 'torsion': [2, 6]}
  • id: 219073
    {'degree': 16, 'field': [327725, 673000, -311600, -734520, 377050, 44120, -111524, 90352, -31725, 6040, -1252, 128, -82, 0, 20, -8, 1], 'lmfdb_label': '4200.n5', 'torsion': [12]}
  • id: 219074
    {'degree': 16, 'field': [60104576, -21117824, 28180096, -13291936, 4475408, 2847096, -1332596, 288392, -22867, -31024, 4656, 512, 218, -168, 44, -8, 1], 'lmfdb_label': '4200.n5', '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: 79004
    {'conductor': 4200, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '4200.n5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 79005
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '4200.n5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 79006
    {'conductor': 4200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '4200.n5', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 79007
    {'conductor': 4200, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4200.n5', 'prime': 7, 'reduction_type': 1, '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: 1691344
    {'adelic_gens': [[5, 4, 1676, 1677], [1, 16, 0, 1], [1665, 16, 1664, 17], [1, 16, 420, 421], [15, 2, 1582, 1667], [496, 5, 915, 1666], [664, 1679, 257, 1670], [1, 0, 16, 1], [1121, 16, 568, 129], [1485, 16, 1274, 1499]], 'adelic_image': '1680.192.1.?', 'conductor': 4200, 'lmfdb_label': '4200.n5', 'prime': 0}
  • id: 20915
    {'conductor': 4200, 'elladic_image': '8.24.0.93', 'lmfdb_label': '4200.n5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4200.n does not appear in ec_padic