Elliptic curve data - 3168.a1

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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': '3168i', 'Clabel': '3168i3', 'Cnumber': 3, 'abc_quality': 1.0696710617503884, 'absD': 10974610944, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 24, 'ainvs': [0, 0, 0, -2822691, 1825337270], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3168, 'degree': 30720, 'elladic_images': ['8.24.0.54'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0130853450709727410788665995', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [6663712298552914184, 29403], 'lmfdb_iso': '3168.a', 'lmfdb_label': '3168.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -313632, -67500540], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.m.1.8', '24.48.0-24.bi.1.7'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 9], [3, 8, 352], [11, 12, 288]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.94391881531695891331831988995', 'prec': 103}, 'szpiro_ratio': 6.9686406113816535, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 0, 0, -2, 0, -4, 0, 0, 0, -1, 0, -2, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, -2, -4, -1, -2, -2, -4, 0, 6, -4, -2, 6, 4, -8, 6, 12, -10, -4, 0, 10, -12, 12, -10, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 3168, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '3168.a', 'trace_hash': 2207858509991484325}
• 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': '0.017842523855029963991200535757', 'prec': 107}, 'conductor': 3168, 'gens': [], 'heights': [], 'lmfdb_label': '3168.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.61274892408216422598294278905', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.61274892408216422598294278904477922655', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[973, 162, 1]], 'xcoord_integral_points': [970, 973]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '11': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '3168.a1'}
• ec_torsion_growth •

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

  
  
  • id: 165213
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '3168.a1', 'torsion': [2, 4]}
  • id: 165214
    {'degree': 4, 'field': [6, 0, -6, 0, 1], 'lmfdb_label': '3168.a1', 'torsion': [8]}
  • id: 165218
    {'degree': 8, 'field': [-108, 0, 0, 0, -36, 0, -20, 0, 1], 'lmfdb_label': '3168.a1', 'torsion': [12]}
  • id: 165216
    {'degree': 8, 'field': [1, 4, -4, -20, 4, 20, -4, -4, 1], 'lmfdb_label': '3168.a1', 'torsion': [2, 8]}
  • id: 165217
    {'degree': 8, 'field': [527076, 0, 31944, 0, 1210, 0, 44, 0, 1], 'lmfdb_label': '3168.a1', 'torsion': [2, 8]}
  • id: 165215
    {'degree': 8, 'field': [528529, 0, -8708, 0, 1458, 0, 4, 0, 1], 'lmfdb_label': '3168.a1', 'torsion': [4, 4]}
  • id: 165220
    {'degree': 16, 'field': [527076, 0, -772848, 0, 279424, 0, 31272, 0, -18444, 0, -1168, 0, 60, 0, -12, 0, 1], 'lmfdb_label': '3168.a1', 'torsion': [2, 12]}
  • id: 165219
    {'degree': 16, 'field': [1185921, 0, -4312440, 0, 3933468, 0, -1355904, 0, 203586, 0, -17544, 0, 1092, 0, -48, 0, 1], 'lmfdb_label': '3168.a1', 'torsion': [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: 57175
    {'conductor': 3168, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '3168.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 57176
    {'conductor': 3168, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '3168.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 57177
    {'conductor': 3168, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '3168.a1', 'prime': 11, '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: 1684555
    {'adelic_gens': [[16, 11, 1, 6], [16, 11, 3, 4], [1, 0, 8, 1], [7, 6, 18, 19], [4, 23, 17, 18], [1, 4, 4, 17], [1, 8, 0, 1], [17, 8, 16, 9]], 'adelic_image': '24.48.0.?', 'conductor': 3168, 'lmfdb_label': '3168.a1', 'prime': 0}
  • id: 15859
    {'conductor': 3168, 'elladic_image': '8.24.0.54', 'lmfdb_label': '3168.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 3168.a does not appear in ec_padic