Elliptic curve data - 161700.dg3

Formats: - HTML - YAML - JSON - 2024-05-06T06:39:01.548720

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '161700bt', 'Clabel': '161700bt1', 'Cnumber': 1, 'abc_quality': 1.00810273363178, 'absD': 66196757963778750000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 4620, 'ainvs': [0, 1, 0, -3260133, -2300347512], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 161700, 'degree': 5971968, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6012150256767378014169548319', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 84, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-130287139815424, 2250652635], 'lmfdb_iso': '161700.dg', 'lmfdb_label': '161700.dg3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -2661, 52740], 'min_quad_twist_disc': -35, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.24.0-6.a.1.1', '44.6.0.b.1', '70.6.0.a.1', '105.8.0.?', '132.48.0.?', '210.48.0.?', '1540.12.0.?', '4620.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.59249193474538252509148808641', 'prec': 103}, 'szpiro_ratio': 4.722129636999028, '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, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, 0, 0, 0, -6, 0, -8, 0], 'aplist': [0, 1, 0, 0, -1, 2, -6, -8, 6, 6, -2, -2, 0, -8, -12, -6, -6, -8, -2, 0, -10, 8, 12, -6, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 161700, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '161700.dg', 'trace_hash': 1889115143286216283}
• 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': '0.0055031751608070016149011206559', 'prec': 110}, 'conductor': 161700, 'gens': [], 'heights': [], 'lmfdb_label': '161700.dg3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.056119711084632085237109060400', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3468730660311700456906174496027564754', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[2088, 0, 1]], 'xcoord_integral_points': [2088]}
• lmfdb_label 161700.dg3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7226147
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '161700.dg3', 'torsion': [2, 6]}
  • id: 7226148
    {'degree': 4, 'field': [5, 30, 4, -2, 1], 'lmfdb_label': '161700.dg3', 'torsion': [4]}
  • id: 7226149
    {'degree': 6, 'field': [-3156, 492, -500, 15, -5, -3, 1], 'lmfdb_label': '161700.dg3', 'torsion': [6]}
  • id: 7226151
    {'degree': 8, 'field': [2025, -1350, 9310, -3850, 571, -6, -8, -4, 1], 'lmfdb_label': '161700.dg3', 'torsion': [2, 12]}
  • id: 7226150
    {'degree': 8, 'field': [9801, 0, 1102, 0, 839, 0, 38, 0, 1], 'lmfdb_label': '161700.dg3', 'torsion': [2, 12]}
  • id: 7226152
    {'degree': 12, 'field': [9960336, -1552752, -1335936, -151320, 226840, 6888, -7111, -2583, 570, -15, 14, -3, 1], 'lmfdb_label': '161700.dg3', 'torsion': [6, 6]}
  • id: 7226153
    {'degree': 16, 'field': [3890016900, 0, -7508350080, 0, 3090821976, 0, 485670240, 0, 22067296, 0, 192208, 0, -5196, 0, 64, 0, 1], 'lmfdb_label': '161700.dg3', 'torsion': [8]}
  • id: 7226154
    {'degree': 18, 'field': [1169877804461, 1832787164520, 1375151101515, -9796826307, -43792635681, 20991085587, 3309934611, -156103263, 11599371, -17189508, 3704490, 697653, 84741, -22815, -153, 222, 63, -9, 1], 'lmfdb_label': '161700.dg3', 'torsion': [2, 18]}
• 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: 4000664
    {'conductor': 161700, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '161700.dg3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4000665
    {'conductor': 161700, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '161700.dg3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 4000666
    {'conductor': 161700, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '161700.dg3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4000667
    {'conductor': 161700, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '161700.dg3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4000668
    {'conductor': 161700, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '161700.dg3', 'prime': 11, '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: 2709595
    {'adelic_gens': [[4609, 12, 4608, 13], [2630, 4617, 3987, 8], [4239, 2698, 1946, 401], [1, 0, 12, 1], [1, 6, 6, 37], [1, 12, 0, 1], [11, 2, 4570, 4611], [4610, 4617, 2799, 8], [2521, 12, 1266, 73], [3089, 2, 3138, 13]], 'adelic_image': '4620.96.1.?', 'conductor': 161700, 'lmfdb_label': '161700.dg3', 'prime': 0}
  • id: 615062
    {'conductor': 161700, 'elladic_image': '2.3.0.1', 'lmfdb_label': '161700.dg3', 'modell_image': '2B', 'prime': 2}
  • id: 615063
    {'conductor': 161700, 'elladic_image': '3.4.0.1', 'lmfdb_label': '161700.dg3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 161700.dg does not appear in ec_padic