Elliptic curve data - 42.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': '42a', 'Clabel': '42a4', 'Cnumber': 4, 'abc_quality': 1.0572692378622217, 'absD': 252, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 112, 'ainvs': [1, 1, 1, -1344, 18405], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 42, 'degree': 16, 'elladic_images': ['16.96.0.103'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.18910119341772050884147105447', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [268498407453697, 252], 'lmfdb_iso': '42.a', 'lmfdb_label': '42.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1344, 18405], '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.2.4', '16.96.0-16.z.2.3', '28.24.0-28.h.1.2', '56.96.0-56.bl.1.5', '112.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, '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': '0.18910119341772050884147105447', 'prec': 103}, 'szpiro_ratio': 8.888925317547928, '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, 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': '0.68509183306601454759224479552', 'prec': 103}, 'conductor': 42, 'gens': [], 'heights': [], 'lmfdb_label': '42.a1', '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': 4, 'torsion_generators': [[21, -9, 1]], 'xcoord_integral_points': [21]}
• 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.a1'}
• ec_torsion_growth •

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

  
  
  • id: 1290
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [8]}
  • id: 1288
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [2, 4]}
  • id: 1289
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [8]}
  • id: 1291
    {'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [2, 8]}
  • id: 1292
    {'degree': 4, 'field': [126, 0, -24, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [16]}
  • id: 1297
    {'degree': 8, 'field': [-4, 16, -16, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '42.a1', 'torsion': [12]}
  • id: 1293
    {'degree': 8, 'field': [36, -72, 72, -24, 13, -10, 2, -2, 1], 'lmfdb_label': '42.a1', 'torsion': [4, 4]}
  • id: 1296
    {'degree': 8, 'field': [81, 0, -324, 0, 216, 0, -36, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [2, 16]}
  • id: 1295
    {'degree': 8, 'field': [784, 0, 0, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [16]}
  • id: 1294
    {'degree': 8, 'field': [3844, 0, 760, 0, -120, 0, 4, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [2, 8]}
  • id: 1303
    {'degree': 16, 'field': [-1528, 5872, -164, -11320, 5258, 1272, -2663, 3512, -2344, 266, 477, -76, -139, 42, 14, -8, 1], 'lmfdb_label': '42.a1', 'torsion': [24]}
  • id: 1298
    {'degree': 16, 'field': [256, 0, 1088, 0, 1892, 0, 2004, 0, 1601, 0, 144, 0, -34, 0, -4, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [4, 8]}
  • id: 1302
    {'degree': 16, 'field': [8836, 0, -39320, 0, 7156, 0, -5616, 0, 912, 0, -72, 0, 121, 0, -14, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [2, 12]}
  • id: 1304
    {'degree': 16, 'field': [34022, 411136, 317428, -1030120, -476074, 980664, 5683, -255448, 28790, 20558, -1641, -916, -181, 126, 2, -8, 1], 'lmfdb_label': '42.a1', 'torsion': [24]}
  • id: 1300
    {'degree': 16, 'field': [38416, 0, -76832, 0, 76832, 0, -46648, 0, 17297, 0, -3332, 0, 392, 0, -28, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [2, 16]}
  • id: 1299
    {'degree': 16, 'field': [63001, 0, 14120, 0, -35252, 0, 14168, 0, -434, 0, 56, 0, 28, 0, 8, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [4, 8]}
  • id: 1301
    {'degree': 16, 'field': [4032758016, 0, -1536288768, 0, 257572224, 0, -26163648, 0, 1893150, 0, -103824, 0, 4056, 0, -96, 0, 1], 'lmfdb_label': '42.a1', 'torsion': [32]}
• 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: 181
    {'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42.a1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 182
    {'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '42.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 183
    {'conductor': 42, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '42.a1', '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: 1665969
    {'adelic_gens': [[1, 0, 16, 1], [1, 16, 0, 1], [15, 2, 14, 99], [13, 16, 12, 73], [5, 4, 108, 109], [97, 16, 96, 17], [24, 1, 111, 10], [106, 39, 43, 54]], 'adelic_image': '112.192.1.?', 'conductor': 42, 'lmfdb_label': '42.a1', 'prime': 0}
  • id: 102
    {'conductor': 42, 'elladic_image': '16.96.0.103', 'lmfdb_label': '42.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 42.a does not appear in ec_padic