Elliptic curve data - 105.a3

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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': '105a', 'Clabel': '105a1', 'Cnumber': 1, 'abc_quality': 0.9665903421508077, 'absD': 105, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [1, 0, 1, -3, 1], 'analytic_rank': 0, 'bad_primes': [3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 105, 'degree': 4, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.85910933998716858719228147827', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [1771561, 105], 'lmfdb_iso': '105.a', 'lmfdb_label': '105.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -3, 1], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '20.12.0-4.c.1.2', '40.24.0-40.ba.1.10', '84.12.0.?', '168.24.0.?', '210.6.0.?', '420.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[3, 4, 35], [5, 6, 21], [7, 8, 15]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.85910933998716858719228147827', 'prec': 107}, 'szpiro_ratio': 3.091425485888218, '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, 1, 1, 1, -3, 1, 1, 0, -1, -6, 1, 1, -1, 2, 1, -8, -1], 'aplist': [1, 1, 1, 1, 0, -6, 2, -8, 8, -2, 4, -2, -6, 4, 8, 10, 4, -2, 4, -12, -2, 8, -4, -6, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 105, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '105.a', 'trace_hash': 734083615354671920}
• 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': '5.5745894867667058593303153140', 'prec': 100}, 'conductor': 105, 'gens': [], 'heights': [], 'lmfdb_label': '105.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '5.8634534536772028437765003520', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4658633634193007109441250880108268142', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [[1, -1, 1]], 'xcoord_integral_points': [1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 0], '3': [3, 0], '5': [1, 0], '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '105.a3'}
• ec_torsion_growth •

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

  
  
  • id: 3910
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '105.a3', 'torsion': [2, 2]}
  • id: 3912
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '105.a3', 'torsion': [4]}
  • id: 3911
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '105.a3', 'torsion': [4]}
  • id: 3914
    {'degree': 4, 'field': [4, 10, -9, -2, 1], 'lmfdb_label': '105.a3', 'torsion': [8]}
  • id: 3913
    {'degree': 4, 'field': [16, 0, -13, 0, 1], 'lmfdb_label': '105.a3', 'torsion': [2, 4]}
  • id: 3918
    {'degree': 8, 'field': [-3, 0, -13, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '105.a3', 'torsion': [6]}
  • id: 3917
    {'degree': 8, 'field': [1, 0, -17, 0, 48, 0, -17, 0, 1], 'lmfdb_label': '105.a3', 'torsion': [2, 8]}
  • id: 3916
    {'degree': 8, 'field': [36, 0, 16, 0, 21, 0, 6, 0, 1], 'lmfdb_label': '105.a3', 'torsion': [8]}
  • id: 3915
    {'degree': 8, 'field': [3126, -1986, -1107, 900, 256, -50, -18, -2, 1], 'lmfdb_label': '105.a3', 'torsion': [2, 4]}
  • id: 3921
    {'degree': 16, 'field': [-269, 5500, 5070, -15904, -3703, 10584, 574, -1220, -804, -1688, 2212, -336, -490, 224, -12, -8, 1], 'lmfdb_label': '105.a3', 'torsion': [16]}
  • id: 3923
    {'degree': 16, 'field': [9, 0, 117, 0, 295, 0, 234, 0, -105, 0, -234, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '105.a3', 'torsion': [12]}
  • id: 3919
    {'degree': 16, 'field': [256, 0, 0, 0, -3104, 0, 0, 0, 16161, 0, 0, 0, -194, 0, 0, 0, 1], 'lmfdb_label': '105.a3', 'torsion': [4, 4]}
  • id: 3920
    {'degree': 16, 'field': [256, 0, 3440, 0, 5921, 0, 4920, 0, 2576, 0, 870, 0, 176, 0, 20, 0, 1], 'lmfdb_label': '105.a3', 'torsion': [2, 8]}
  • id: 3924
    {'degree': 16, 'field': [441, 0, -42, 0, -1889, 0, -789, 0, 2601, 0, -986, 0, 51, 0, -3, 0, 1], 'lmfdb_label': '105.a3', 'torsion': [12]}
  • id: 3922
    {'degree': 16, 'field': [71289, 0, -156693, 0, 100480, 0, -26781, 0, 4575, 0, -1244, 0, 78, 0, 0, 0, 1], 'lmfdb_label': '105.a3', 'torsion': [2, 6]}
• 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: 666
    {'conductor': 105, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '105.a3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 667
    {'conductor': 105, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '105.a3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 668
    {'conductor': 105, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '105.a3', '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: 1666190
    {'adelic_gens': [[568, 3, 565, 2], [1, 0, 8, 1], [113, 108, 110, 527], [833, 8, 832, 9], [1, 8, 0, 1], [1, 4, 4, 17], [508, 1, 191, 6], [248, 3, 365, 2], [7, 6, 834, 835], [739, 738, 538, 115]], 'adelic_image': '840.48.0.?', 'conductor': 105, 'lmfdb_label': '105.a3', 'prime': 0}
  • id: 376
    {'conductor': 105, 'elladic_image': '8.12.0.6', 'lmfdb_label': '105.a3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 105.a does not appear in ec_padic