Elliptic curve data - 42.a5

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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': '42a', 'Clabel': '42a1', 'Cnumber': 1, 'abc_quality': 0.9822408596528094, 'absD': 16128, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 112, 'ainvs': [1, 1, 1, -4, 5], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 4, 'elladic_images': ['16.96.0.98'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.50404598714222480057576106699', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-7189057, 16128], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -4, 5], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.48.0-8.bb.1.1', '14.6.0.b.1', '16.96.0-16.z.1.2', '28.24.0-28.g.1.2', '56.96.0-56.bh.2.1', '112.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 7], [3, 4, 14], [7, 8, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.50404598714222480057576106699', 'prec': 107}, 'szpiro_ratio': 4.647955287455925, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [8]}
• 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, -2, -1, -1, 1, 1, -2, -4, -1, 6, -1, 2, 1, 2, 1, -4, -2], 'aplist': [1, -1, -2, -1, -4, 6, 2, -4, 8, -2, 0, -10, -6, -4, 0, 6, 4, 6, 4, 8, 10, 0, -4, -6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 42, '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': '42.a', 'trace_hash': 1611795495172191507}
• 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': '2.7403673322640581903689791821', 'prec': 100}, 'conductor': 42, 'gens': [], 'heights': [], 'lmfdb_label': '42.a5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.4754474574968195117771866301', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.86886186437420487794429665753039351028', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[5, 9, 1]], 'xcoord_integral_points': [-3, -1, 1, 5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [0, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '42.a5'}
• ec_torsion_growth •

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

  
  
  • id: 1253
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '42.a5', 'torsion': [2, 8]}
  • id: 1254
    {'degree': 4, 'field': [-2, -4, -1, -2, 1], 'lmfdb_label': '42.a5', 'torsion': [16]}
  • id: 1258
    {'degree': 8, 'field': [-4, 16, -16, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '42.a5', 'torsion': [24]}
  • id: 1257
    {'degree': 8, 'field': [2, -12, 23, -2, 1, 8, -3, -2, 1], 'lmfdb_label': '42.a5', 'torsion': [2, 16]}
  • id: 1256
    {'degree': 8, 'field': [18, 0, 15, -18, 1, -4, 5, -2, 1], 'lmfdb_label': '42.a5', 'torsion': [2, 16]}
  • id: 1255
    {'degree': 8, 'field': [36, -72, 72, -24, 13, -10, 2, -2, 1], 'lmfdb_label': '42.a5', 'torsion': [4, 8]}
  • id: 1260
    {'degree': 16, 'field': [-6368, 18752, -32272, 38832, -17758, 280, 1276, -3096, 4045, -2280, 880, -496, 224, -48, 20, -8, 1], 'lmfdb_label': '42.a5', 'torsion': [32]}
  • id: 1261
    {'degree': 16, 'field': [8, -52, 154, 141, 34, -113, 103, 2, -63, 2, 92, -83, 44, -21, 11, -4, 1], 'lmfdb_label': '42.a5', 'torsion': [2, 24]}
  • id: 1259
    {'degree': 16, 'field': [256, 0, -320, 0, 112, 0, 196, 0, 280, 0, 49, 0, 7, 0, -5, 0, 1], 'lmfdb_label': '42.a5', 'torsion': [4, 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: 172
    {'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '42.a5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 173
    {'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42.a5', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 174
    {'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42.a5', '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: 1665973
    {'adelic_gens': [[24, 1, 111, 10], [15, 2, 14, 99], [81, 16, 34, 47], [97, 16, 96, 17], [1, 0, 16, 1], [5, 4, 108, 109], [1, 16, 84, 85], [1, 16, 0, 1]], 'adelic_image': '112.192.1.?', 'conductor': 42, 'lmfdb_label': '42.a5', 'prime': 0}
  • id: 112
    {'conductor': 42, 'elladic_image': '16.96.0.98', 'lmfdb_label': '42.a5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 42.a does not appear in ec_padic