Elliptic curve data - 340704.ct1

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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': '340704ct', 'Clabel': '340704ct2', 'Cnumber': 2, 'abc_quality': 1.276651235761742, 'absD': 3573156367872, 'adelic_genus': 3, 'adelic_index': 72, 'adelic_level': 2184, 'ainvs': [0, 0, 0, -4875, 94302], 'analytic_rank': 2, 'bad_primes': [2, 3, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 340704, 'degree': 387072, 'elladic_images': ['2.3.0.1', '3.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1159129009011666195194985251', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 71, 'isogeny_degrees': [1, 2], 'jinv': [421875000, 117649], 'lmfdb_iso': '340704.ct', 'lmfdb_label': '340704.ct1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -43875, 2546154], 'min_quad_twist_disc': 12, 'modell_images': ['2B', '3Nn'], 'modm_images': ['2.3.0.a.1', '3.3.0.a.1', '6.9.0.a.1', '24.18.0.g.1', '56.6.0.e.1', '84.18.0.?', '156.18.0.?', '168.36.0.?', '312.36.1.?', '1092.36.1.?', '2184.72.3.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 15, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.7635685473971171464805623206', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 39], [3, 6, 5408], [7, 8, 48672], [13, 50, 2016]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.31983789605120396940560873562', 'prec': 107}, 'szpiro_ratio': 2.911523725810749, '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, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, 0, 1, -4, 0, -2, 0, 0, -2, 0, -6, -6, 12, -10, 2, 8, 0, -14, -4, -6, 0, -4, -6, -6], 'class_deg': 2, 'class_size': 2, 'conductor': 340704, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '340704.ct', 'trace_hash': 1059233976117342927}
• 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': '0.10733228365104235351173997362', 'prec': 103}, 'conductor': 340704, 'gens': [[69, 294, 1], [-3, 330, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.57568635419824518010536638219', 'prec': 103}, {'__RealLiteral__': 0, 'data': '3.0749878955281874938739879142', 'prec': 100}], 'lmfdb_label': '340704.ct1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.73591561321528649538848626804', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '15.574051548059298134778512396552665446', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-78, 0, 1]], 'xcoord_integral_points': [-78, -3, 13, 69, 118, 597, 1014, 10933]}
• lmfdb_label 340704.ct1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 14245300
    {'degree': 2, 'field': [-78, 0, 1], 'lmfdb_label': '340704.ct1', 'torsion': [2, 2]}
  • id: 14245301
    {'degree': 4, 'field': [1108, 368, 15, -1, 1], 'lmfdb_label': '340704.ct1', 'torsion': [4]}
  • id: 14245304
    {'degree': 8, 'field': [-350, -940, -1316, -952, -332, -16, 10, -4, 1], 'lmfdb_label': '340704.ct1', 'torsion': [6]}
  • id: 14245302
    {'degree': 8, 'field': [1849, 0, 1540, 0, 180, 0, -44, 0, 1], 'lmfdb_label': '340704.ct1', 'torsion': [2, 4]}
  • id: 14245303
    {'degree': 8, 'field': [1136083, -109772, 114608, -9776, 5149, -316, 110, -4, 1], 'lmfdb_label': '340704.ct1', 'torsion': [2, 4]}
  • id: 14245306
    {'degree': 16, 'field': [122500, 329000, 423000, 570640, 720776, 634272, 447352, 265952, 116022, 28676, -2864, -3768, 368, -8, 6, -4, 1], 'lmfdb_label': '340704.ct1', 'torsion': [3, 6]}
  • id: 14245307
    {'degree': 16, 'field': [2941225, -6434680, 6131468, -5536608, 5001878, -2783252, 850888, -206904, 56488, 3480, -13196, 6296, -1354, 12, 44, -8, 1], 'lmfdb_label': '340704.ct1', 'torsion': [2, 6]}
  • id: 14245305
    {'degree': 16, 'field': [25800069376, 0, -949333888, 0, -385429384, 0, -24002152, 0, 7154920, 0, -142448, 0, -2788, 0, 22, 0, 1], 'lmfdb_label': '340704.ct1', '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: 8429650
    {'conductor': 340704, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '340704.ct1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8429651
    {'conductor': 340704, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '340704.ct1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8429652
    {'conductor': 340704, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '340704.ct1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 8429653
    {'conductor': 340704, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '340704.ct1', 'prime': 13, 'reduction_type': 0, '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: 3792785
    {'adelic_gens': [[1916, 641, 1745, 832], [7, 12, 144, 247], [1249, 12, 942, 73], [10, 3, 1065, 2176], [1, 0, 12, 1], [1, 6, 6, 37], [848, 7, 1657, 2164], [1, 12, 0, 1], [9, 8, 2140, 2145], [2173, 12, 2172, 13], [736, 7, 1433, 2164]], 'adelic_image': '2184.72.3.?', 'conductor': 340704, 'lmfdb_label': '340704.ct1', 'prime': 0}
  • id: 1181570
    {'conductor': 340704, 'elladic_image': '2.3.0.1', 'lmfdb_label': '340704.ct1', 'modell_image': '2B', 'prime': 2}
  • id: 1181571
    {'conductor': 340704, 'elladic_image': '3.3.0.1', 'lmfdb_label': '340704.ct1', 'modell_image': '3Nn', 'prime': 3}
• lmfdb_iso 340704.ct does not appear in ec_padic