Elliptic curve data - 336.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': '336e', 'Clabel': '336e5', 'Cnumber': 5, 'abc_quality': 1.0508747826837916, 'absD': 602112, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [0, -1, 0, -12544, 544960], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 336, 'degree': 256, 'elladic_images': ['16.48.0.32'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.76735256395088508017549797613', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [53297461115137, 147], 'lmfdb_iso': '336.a', 'lmfdb_label': '336.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -784, -8515], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.n.1.2', '12.24.0-12.h.1.2', '16.48.0-16.e.2.7', '24.48.0-24.bl.1.5', '48.96.0-48.y.1.6', '56.48.0-56.bu.1.3', '112.96.0.?', '168.96.0.?', '336.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.9851968347780548356377504145', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 4, 112], [7, 8, 48]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.074205383390939770758265854672', 'prec': 107}, 'szpiro_ratio': 6.863316667147092, '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, -1, 0, -2, 0, 1, 0, 1, 0, -4, 0, -2, 0, 2, 0, -6, 0, -4, 0], 'aplist': [0, -1, -2, 1, -4, -2, -6, -4, 0, -2, 0, 6, 2, 4, 0, 6, -12, -2, -4, 0, -6, 16, 12, -14, 18], 'class_deg': 8, 'class_size': 6, 'conductor': 336, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '336.a', 'trace_hash': 2299192538271944600}
• 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': '0.21551923240928174515903931677', 'prec': 103}, 'conductor': 336, 'gens': [[90, 370, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9851968347780548356377504145', 'prec': 100}], 'lmfdb_label': '336.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.9109897807518291965531482188', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4261701611983923742568767354193679913', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[66, 14, 1]], 'xcoord_integral_points': [65, 66, 90, 101]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '336.a1'}
• ec_torsion_growth •

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

  
  
  • id: 14571
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [8]}
  • id: 14570
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [8]}
  • id: 14569
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [2, 4]}
  • id: 14572
    {'degree': 4, 'field': [49, 0, -28, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [2, 8]}
  • id: 14577
    {'degree': 8, 'field': [-3, 0, 1, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [12]}
  • id: 14574
    {'degree': 8, 'field': [1, -4, 8, -10, 7, -2, 2, -2, 1], 'lmfdb_label': '336.a1', 'torsion': [2, 8]}
  • id: 14575
    {'degree': 8, 'field': [21609, 0, -8232, 0, 1064, 0, -56, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [16]}
  • id: 14573
    {'degree': 8, 'field': [21609, 0, 0, 0, 147, 0, 0, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [4, 4]}
  • id: 14576
    {'degree': 8, 'field': [345744, 0, 49392, 0, 2898, 0, 84, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [16]}
  • id: 14582
    {'degree': 16, 'field': [81, 0, -327, 0, 292, 0, 177, 0, -207, 0, -49, 0, 15, 0, -6, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [2, 12]}
  • id: 14581
    {'degree': 16, 'field': [2257, 12232, 27290, 31524, 17132, -2068, -9188, -4836, 223, 1188, 328, -104, -40, 24, 2, -4, 1], 'lmfdb_label': '336.a1', 'torsion': [2, 16]}
  • id: 14579
    {'degree': 16, 'field': [2401, 0, -38416, 0, 122108, 0, -120736, 0, 52087, 0, -10976, 0, 1148, 0, -56, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [2, 16]}
  • id: 14578
    {'degree': 16, 'field': [133921, -1090268, 2836206, -1439824, 1486194, -403368, 335254, -61048, 53319, -7844, 6022, -672, 504, -68, 36, -4, 1], 'lmfdb_label': '336.a1', 'torsion': [4, 8]}
  • id: 14583
    {'degree': 16, 'field': [2152089, 0, -2217942, 0, 123741, 0, -176888, 0, 26126, 0, -6578, 0, 520, 0, -28, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [24]}
  • id: 14584
    {'degree': 16, 'field': [4108729, 0, -15984310, 0, -4546127, 0, -497152, 0, 41806, 0, 13190, 0, 1024, 0, 56, 0, 1], 'lmfdb_label': '336.a1', 'torsion': [24]}
  • id: 14580
    {'degree': 16, 'field': [94128804, 0, 43563744, 0, 12113388, 0, 889056, 0, 55125, 0, 3528, 0, 504, 0, 0, 0, 1], 'lmfdb_label': '336.a1', '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: 3272
    {'conductor': 336, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '336.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3273
    {'conductor': 336, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '336.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3274
    {'conductor': 336, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '336.a1', '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: 1667180
    {'adelic_gens': [[15, 2, 238, 323], [1, 16, 0, 1], [109, 16, 128, 21], [128, 5, 291, 322], [5, 4, 332, 333], [321, 16, 320, 17], [1, 0, 16, 1], [202, 247, 123, 166], [13, 16, 164, 105]], 'adelic_image': '336.192.1.?', 'conductor': 336, 'lmfdb_label': '336.a1', 'prime': 0}
  • id: 1388
    {'conductor': 336, 'elladic_image': '16.48.0.32', 'lmfdb_label': '336.a1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 3891
    {'lmfdb_iso': '336.a', 'p': 5, 'prec': 20, 'unit': 10125968997116, 'val': 1}
  • id: 3897
    {'lmfdb_iso': '336.a', 'p': 11, 'prec': 20, 'unit': 21226206564202725350, 'val': 1}
  • id: 3895
    {'lmfdb_iso': '336.a', 'p': 13, 'prec': 20, 'unit': 1236198034160611558019, 'val': 1}
  • id: 3898
    {'lmfdb_iso': '336.a', 'p': 17, 'prec': 20, 'unit': 212962455240718112371409, 'val': 1}
  • id: 3899
    {'lmfdb_iso': '336.a', 'p': 19, 'prec': 20, 'unit': 777992468787872713692079, 'val': 1}
  • id: 3894
    {'lmfdb_iso': '336.a', 'p': 29, 'prec': 20, 'unit': 254026197314387120199688955, 'val': 1}
  • id: 3905
    {'lmfdb_iso': '336.a', 'p': 37, 'prec': 20, 'unit': 331324926510039729197284999768, 'val': 1}
  • id: 3892
    {'lmfdb_iso': '336.a', 'p': 41, 'prec': 20, 'unit': 3767987605840882752543080851563, 'val': 1}
  • id: 3893
    {'lmfdb_iso': '336.a', 'p': 43, 'prec': 20, 'unit': 8955429227610706923098306876097, 'val': 1}
  • id: 3900
    {'lmfdb_iso': '336.a', 'p': 53, 'prec': 20, 'unit': 20974431377762072907596944827398, 'val': 1}
  • id: 3903
    {'lmfdb_iso': '336.a', 'p': 59, 'prec': 20, 'unit': 3247791728432655415918868997077267, 'val': 1}
  • id: 3904
    {'lmfdb_iso': '336.a', 'p': 61, 'prec': 20, 'unit': 3847424090267720492571203796545707, 'val': 1}
  • id: 3890
    {'lmfdb_iso': '336.a', 'p': 67, 'prec': 20, 'unit': 48135579582249312010850125103182339, 'val': 1}
  • id: 3901
    {'lmfdb_iso': '336.a', 'p': 73, 'prec': 20, 'unit': 195663707343103204803485600536963077, 'val': 1}
  • id: 3896
    {'lmfdb_iso': '336.a', 'p': 79, 'prec': 20, 'unit': 437502367262140672791516721101593857, 'val': 1}
  • id: 3889
    {'lmfdb_iso': '336.a', 'p': 83, 'prec': 20, 'unit': 1396232222471688582944534871736624357, 'val': 1}
  • id: 3902
    {'lmfdb_iso': '336.a', 'p': 89, 'prec': 20, 'unit': 7376982730014980543952031092396948175, 'val': 1}
  • id: 3888
    {'lmfdb_iso': '336.a', 'p': 97, 'prec': 20, 'unit': 30881964577877913033495220423471655243, 'val': 1}