Elliptic curve data - 208080.em2

Formats: - HTML - YAML - JSON - 2025-11-02T08:38:52.043605

• 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': '208080i', 'Clabel': '208080i1', 'Cnumber': 1, 'abc_quality': 1.2368891427142117, 'absD': 16567166290825728000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 60, 'ainvs': [0, 0, 0, -638112, 11980784], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 208080, 'degree': 3981312, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3773810359797144284864670928', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 116, 'isogeny_degrees': [1, 3], 'jinv': [115220905984, 66430125], 'lmfdb_iso': '208080.em', 'lmfdb_label': '208080.em2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -4431, 5456], 'min_quad_twist_disc': 12, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '10.2.0.a.1', '12.8.0-3.a.1.2', '30.8.0.a.1', '60.16.0-30.a.1.4'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.6696512461419358155236420045', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 13005], [3, 2, 4624], [5, 6, 41616], [17, 114, 720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.19052326306697557995510081359', 'prec': 103}, 'szpiro_ratio': 4.2229111969974715, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -3, 0, -4, 0, 0, 0, 0, 0, -5, 0], 'aplist': [0, 0, 1, -2, -3, -4, 0, -5, 0, 3, -8, 2, 3, 10, -6, 6, 15, 5, -2, -15, 2, 1, -6, -9, -10], 'class_deg': 3, 'class_size': 2, 'conductor': 208080, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '208080.em', 'trace_hash': 1823682138210868405}
• 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': '0.0086105931511306579422814234926', 'prec': 110}, 'conductor': 208080, 'gens': [[-287, 13095, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.6696512461419358155236420045', 'prec': 100}], 'lmfdb_label': '208080.em2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.18708915294497679681062561422', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2418465771349007210001963782800742155', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [-287]}
• lmfdb_label 208080.em2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9099371
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [3]}
  • id: 9099372
    {'degree': 3, 'field': [5, -11, -1, 1], 'lmfdb_label': '208080.em2', 'torsion': [2]}
  • id: 9099375
    {'degree': 6, 'field': [-188, -104, 132, 44, -30, -2, 1], 'lmfdb_label': '208080.em2', 'torsion': [6]}
  • id: 9099373
    {'degree': 6, 'field': [-125, -25, 130, 15, -26, -1, 1], 'lmfdb_label': '208080.em2', 'torsion': [2, 2]}
  • id: 9099374
    {'degree': 6, 'field': [144, 0, 12, 0, -11, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [3]}
  • id: 9099376
    {'degree': 12, 'field': [-408735, 1242036, -1104822, 186624, 130783, -30624, -8208, 1824, 443, -84, -18, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [4]}
  • id: 9099377
    {'degree': 12, 'field': [144, 0, -132, 0, 109, 0, -35, 0, 12, 0, 1, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [3, 3]}
  • id: 9099378
    {'degree': 12, 'field': [3001, 7408, -20325, -25406, 41646, 12068, -12933, -1894, 1494, 112, -69, -2, 1], 'lmfdb_label': '208080.em2', 'torsion': [2, 6]}
  • id: 9099379
    {'degree': 18, 'field': [-26343, 79488, -158112, -517728, 1017864, -242460, -568106, 374016, 132834, -169106, -5472, 39132, -3579, -4752, 630, 274, -42, -6, 1], 'lmfdb_label': '208080.em2', 'torsion': [9]}
  • id: 9099380
    {'degree': 18, 'field': [36, 0, 232, 0, 376, 0, 249, 0, 221, 0, 58, 0, -31, 0, -18, 0, 1, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [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: 5154987
    {'conductor': 208080, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '208080.em2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5154988
    {'conductor': 208080, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '208080.em2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5154989
    {'conductor': 208080, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '208080.em2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 5154990
    {'conductor': 208080, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '208080.em2', 'prime': 17, 'reduction_type': 0, '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: 2995731
    {'adelic_gens': [[1, 0, 6, 1], [4, 3, 9, 7], [53, 54, 39, 41], [3, 4, 8, 11], [54, 59, 35, 39], [55, 6, 54, 7], [35, 54, 36, 53], [29, 0, 0, 59], [1, 6, 0, 1]], 'adelic_image': '60.16.0.?', 'conductor': 208080, 'lmfdb_label': '208080.em2', 'prime': 0}
  • id: 768569
    {'conductor': 208080, 'elladic_image': '3.4.0.1', 'lmfdb_label': '208080.em2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 208080.em does not appear in ec_padic