Elliptic curve data - 1050.c8

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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
  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': '1050c', 'Clabel': '1050c6', 'Cnumber': 6, 'abc_quality': 1.1083142308531486, 'absD': 4205703735351562500, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 3360, 'ainvs': [1, 1, 0, 31750, -98631000], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 1050, 'degree': 24576, 'elladic_images': ['32.96.0.24'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2525747828326405795448018533', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [226523624554079, 269165039062500], 'lmfdb_iso': '1050.c', 'lmfdb_label': '1050.c8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1270, -789048], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.24.0.q.1', '16.48.0.j.1', '20.24.0-4.d.1.1', '24.48.0.be.1', '32.96.0-16.j.1.4', '40.48.0-8.q.1.2', '48.96.1.bf.2', '56.48.0.bd.1', '80.96.0.?', '84.24.0.?', '96.192.1.?', '112.96.1.?', '120.96.0.?', '160.192.2.?', '168.96.1.?', '224.192.1.?', '240.192.1.?', '280.96.0.?', '336.192.5.?', '420.48.0.?', '480.384.5.?', '560.192.1.?', '672.384.5.?', '840.192.1.?', '1120.384.5.?', '1680.384.5.?', '3360.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 25], [3, 4, 350], [5, 18, 42], [7, 8, 150]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4478558266155903922444221867', 'prec': 100}, 'szpiro_ratio': 7.235948723020153, '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, -1, -1, 1, 0, 1, 1, -1, 1, 0, -4, -1, 2, -1, 0, 1, -2, -1, 4, 0], 'aplist': [-1, -1, 0, 1, -4, 2, -2, 4, 8, -2, 0, -6, -6, 4, 0, 10, 12, 14, 12, -8, -10, 16, 12, 10, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 1050, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '1050.c', 'trace_hash': 1840108885404238702}
• 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': '0.011051937072916984879378442679', 'prec': 107}, 'conductor': 1050, 'gens': [], 'heights': [], 'lmfdb_label': '1050.c8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.11470279753823246109347246493', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.91762238030585968874777971940783629772', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[1755, -1755, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 2], '3': [0, 0], '5': 'a', '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1050.c8'}
• ec_torsion_growth •

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

  
  
  • id: 51187
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '1050.c8', 'torsion': [4]}
  • id: 51186
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [2, 2]}
  • id: 51188
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [4]}
  • id: 51189
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [2, 4]}
  • id: 51190
    {'degree': 4, 'field': [19, 14, -13, -2, 1], 'lmfdb_label': '1050.c8', 'torsion': [8]}
  • id: 51191
    {'degree': 4, 'field': [55, -10, 11, -2, 1], 'lmfdb_label': '1050.c8', 'torsion': [8]}
  • id: 51192
    {'degree': 4, 'field': [81, 0, 38, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [8]}
  • id: 51193
    {'degree': 4, 'field': [361, 0, -18, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [8]}
  • id: 51199
    {'degree': 8, 'field': [-75, 0, -20, 0, 30, 0, 0, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [6]}
  • id: 51196
    {'degree': 8, 'field': [145, -140, 164, -44, 13, 8, 2, -4, 1], 'lmfdb_label': '1050.c8', 'torsion': [2, 8]}
  • id: 51198
    {'degree': 8, 'field': [745, -380, 434, -104, 43, 8, 2, -4, 1], 'lmfdb_label': '1050.c8', 'torsion': [16]}
  • id: 51194
    {'degree': 8, 'field': [1780, 700, -566, -254, 93, 38, -8, -4, 1], 'lmfdb_label': '1050.c8', 'torsion': [4, 4]}
  • id: 51195
    {'degree': 8, 'field': [2745, -1260, -484, 56, 109, -28, 6, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [2, 8]}
  • id: 51197
    {'degree': 8, 'field': [1374745, 18820, -21166, 4696, -2357, 8, 2, -4, 1], 'lmfdb_label': '1050.c8', 'torsion': [16]}
  • id: 51200
    {'degree': 16, 'field': [1, 0, 0, 0, 161, 0, 0, 0, 576, 0, 0, 0, 161, 0, 0, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [4, 8]}
  • id: 51203
    {'degree': 16, 'field': [25, 0, 8940, 0, 8206, 0, -1728, 0, 399, 0, 216, 0, 34, 0, 12, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [2, 16]}
  • id: 51206
    {'degree': 16, 'field': [320, 440, -1095, 1200, -150, -990, 931, -128, -645, 730, -377, 48, 83, -70, 30, -8, 1], 'lmfdb_label': '1050.c8', 'torsion': [12]}
  • id: 51205
    {'degree': 16, 'field': [576, 0, 39168, 0, -11952, 0, 5536, 0, 320, 0, -104, 0, 88, 0, 8, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [2, 6]}
  • id: 51207
    {'degree': 16, 'field': [529984, 0, 570997, 0, 223930, 0, -37181, 0, -13205, 0, 1231, 0, -17, 0, 10, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [12]}
  • id: 51202
    {'degree': 16, 'field': [5764801, 0, 0, 0, 584472, 0, 0, 0, 11858, 0, 0, 0, -168, 0, 0, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [16]}
  • id: 51201
    {'degree': 16, 'field': [271712961, 363714624, -192042576, -167493312, 111259116, -33264000, 9924912, -2395008, 268582, 76608, -5360, -4032, 1644, 0, 16, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [16]}
  • id: 51204
    {'degree': 16, 'field': [7831365025, 0, -914895060, 0, 120082006, 0, -5200128, 0, 519399, 0, -3384, 0, 1234, 0, 12, 0, 1], 'lmfdb_label': '1050.c8', 'torsion': [2, 16]}
• 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: 14744
    {'conductor': 1050, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1050.c8', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 14745
    {'conductor': 1050, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1050.c8', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 14746
    {'conductor': 1050, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '1050.c8', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 14747
    {'conductor': 1050, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1050.c8', 'prime': 7, 'reduction_type': 1, '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: 1671163
    {'adelic_gens': [[1, 8, 0, 421], [1, 0, 32, 1], [25, 16, 1624, 2249], [2269, 24, 126, 2885], [1, 32, 0, 1], [7, 16, 2775, 793], [1343, 3344, 0, 3359], [985, 16, 1974, 2473], [3329, 32, 3328, 33], [1, 32, 4, 129]], 'adelic_image': '3360.768.13.?', 'conductor': 1050, 'lmfdb_label': '1050.c8', 'prime': 0}
  • id: 4944
    {'conductor': 1050, 'elladic_image': '32.96.0.24', 'lmfdb_label': '1050.c8', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1050.c does not appear in ec_padic