Elliptic curve data - 12342.e1

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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': '12342b', 'Clabel': '12342b2', 'Cnumber': 2, 'abc_quality': 1.0432060444484623, 'absD': 75880986611028977069531136, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4488, 'ainvs': [1, 1, 0, -134080949, -426032184915], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 12342, 'degree': 3893760, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6726086518813567602325813564', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [150476552140919246594353, 42832838728685592576], 'lmfdb_iso': '12342.e', 'lmfdb_label': '12342.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1108107, 319580601], 'min_quad_twist_disc': -11, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '132.6.0.?', '136.6.0.?', '4488.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2057], [3, 4, 4114], [11, 72, 102], [13, 2, 2057], [17, 18, 726]], 'sha': 16, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4736610154821714882016095674', 'prec': 100}, 'szpiro_ratio': 7.192141791579391, '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, 2, 1, 2, -1, 1, -2, 0, -1, -4, -2, -2, 1, -1, -1, 2, 2], 'aplist': [-1, -1, 2, 2, 0, -4, -1, 2, 2, -6, 8, 2, 2, 2, 4, 12, -10, -6, -12, 6, -8, 2, 4, -2, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 12342, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '12342.e', 'trace_hash': 598532793109912498}
• 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': '0.00064567304553790996126320552709', 'prec': 113}, 'conductor': 12342, 'gens': [], 'heights': [], 'lmfdb_label': '12342.e1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.045326945665685142731666982116', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '16.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4504622613019245674133434276991161047', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-37717, 37717, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 1], '3': [0, 0], '11': 'a', '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '12342.e1'}
• ec_torsion_growth •

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

  
  
  • id: 635964
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '12342.e1', 'torsion': [2, 2]}
  • id: 635965
    {'degree': 4, 'field': [136, 0, 29, 0, 1], 'lmfdb_label': '12342.e1', 'torsion': [4]}
  • id: 635968
    {'degree': 8, 'field': [-238, 277, -322, 89, -41, -7, 7, -4, 1], 'lmfdb_label': '12342.e1', 'torsion': [6]}
  • id: 635966
    {'degree': 8, 'field': [72526, -28220, -10914, 5440, 191, -340, 34, 0, 1], 'lmfdb_label': '12342.e1', 'torsion': [2, 4]}
  • id: 635967
    {'degree': 8, 'field': [11120367, 343004, -355494, 25008, -12573, 80, -22, -4, 1], 'lmfdb_label': '12342.e1', 'torsion': [2, 4]}
  • id: 635969
    {'degree': 16, 'field': [561595204, 0, -505252920, 0, 135279166, 0, -9665316, 0, 276777, 0, -16626, 0, 616, 0, -6, 0, 1], 'lmfdb_label': '12342.e1', 'torsion': [8]}
  • id: 635970
    {'degree': 16, 'field': [1519091425074, 415698183372, -372058409371, -84736676824, 36103534736, 7261276102, -1999391981, -348091184, 71252985, 10167822, -1692021, -181424, 26203, 1834, -242, -8, 1], 'lmfdb_label': '12342.e1', '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: 266406
    {'conductor': 12342, 'conductor_valuation': 1, 'discriminant_valuation': 13, 'j_denominator_valuation': 13, 'kodaira_symbol': 17, 'lmfdb_label': '12342.e1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 266407
    {'conductor': 12342, 'conductor_valuation': 1, 'discriminant_valuation': 26, 'j_denominator_valuation': 26, 'kodaira_symbol': 30, 'lmfdb_label': '12342.e1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 266408
    {'conductor': 12342, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '12342.e1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 266409
    {'conductor': 12342, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '12342.e1', 'prime': 17, '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: 1745803
    {'adelic_gens': [[1, 0, 4, 1], [409, 4, 818, 9], [2993, 4, 1498, 9], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [2, 1, 2243, 0], [2114, 1, 3431, 0], [3929, 562, 560, 3927], [4485, 4, 4484, 5]], 'adelic_image': '4488.12.0.?', 'conductor': 12342, 'lmfdb_label': '12342.e1', 'prime': 0}
  • id: 58756
    {'conductor': 12342, 'elladic_image': '2.3.0.1', 'lmfdb_label': '12342.e1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 12342.e does not appear in ec_padic