Elliptic curve data - 243360.u1

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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': '243360u', 'Clabel': '243360u2', 'Cnumber': 2, 'abc_quality': 0.8083120047644469, 'absD': 1644137244819763200, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, 0, 0, -529308, 134772768], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 243360, 'degree': 3096576, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2315835119381527245571492263', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2], 'jinv': [42144192, 4225], 'lmfdb_iso': '243360.u', 'lmfdb_label': '243360.u1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -348, 2272], 'min_quad_twist_disc': 156, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '52.6.0.e.1', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.2155382811364945480060064112', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 507], [3, 2, 27040], [5, 6, 48672], [13, 98, 1440]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56799756385364322143326054363', 'prec': 107}, 'szpiro_ratio': 4.124363406672512, '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, 0, 0, 0, -1, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, -2, 0], 'aplist': [0, 0, -1, -2, 4, 0, 4, -2, -8, 0, 2, 10, -10, 0, 0, 8, -4, 2, -2, 0, -2, 0, 12, -6, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 243360, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '243360.u', 'trace_hash': 843600289276793186}
• 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': '0.011525802931189717901851598760', 'prec': 107}, 'conductor': 243360, 'gens': [[204, 5940, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.2155382811364945480060064112', 'prec': 100}], 'lmfdb_label': '243360.u1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25879912156048850774683787449', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.6574278600179833827381810368692867222', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[312, 0, 1]], 'xcoord_integral_points': [204, 312, 2509]}
• lmfdb_label 243360.u1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10498761
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '243360.u1', 'torsion': [2, 2]}
  • id: 10498762
    {'degree': 4, 'field': [12, 0, -3, 0, 1], 'lmfdb_label': '243360.u1', 'torsion': [4]}
  • id: 10498764
    {'degree': 8, 'field': [1, 0, 1, 0, 12, 0, 1, 0, 1], 'lmfdb_label': '243360.u1', 'torsion': [2, 4]}
  • id: 10498765
    {'degree': 8, 'field': [5721, 6060, 3982, 1368, 192, -184, -42, 0, 1], 'lmfdb_label': '243360.u1', 'torsion': [6]}
  • id: 10498763
    {'degree': 8, 'field': [140254, 23908, -21958, -3824, 1723, 224, -70, -4, 1], 'lmfdb_label': '243360.u1', 'torsion': [2, 4]}
  • id: 10498767
    {'degree': 16, 'field': [-144719948, 219706544, -131584752, -11395424, 52860752, -12725064, -3284744, 2607416, 120636, 10856, 3328, -13032, 164, 532, -36, -4, 1], 'lmfdb_label': '243360.u1', 'torsion': [2, 6]}
  • id: 10498766
    {'degree': 16, 'field': [41757444, 0, 22985856, 0, 49030380, 0, 3476520, 0, 372501, 0, 22212, 0, 750, 0, 36, 0, 1], 'lmfdb_label': '243360.u1', 'torsion': [8]}
• 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: 6032490
    {'conductor': 243360, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '243360.u1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6032491
    {'conductor': 243360, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '243360.u1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6032492
    {'conductor': 243360, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '243360.u1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6032493
    {'conductor': 243360, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '243360.u1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 3210745
    {'adelic_gens': [[145, 4, 134, 9], [1, 2, 2, 5], [40, 121, 117, 40], [3, 4, 8, 11], [153, 4, 152, 5], [56, 1, 103, 0], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 243360, 'lmfdb_label': '243360.u1', 'prime': 0}
  • id: 881248
    {'conductor': 243360, 'elladic_image': '2.3.0.1', 'lmfdb_label': '243360.u1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 243360.u does not appear in ec_padic