Elliptic curve data - 80275.s2

Formats: - HTML - YAML - JSON - 2025-01-20T08:07:41.293593

• 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': '80275o', 'Clabel': '80275o1', 'Cnumber': 1, 'abc_quality': 1.119402634915339, 'absD': 11463671375, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 380, 'ainvs': [1, -1, 0, 53, 5136], 'analytic_rank': 0, 'bad_primes': [5, 13, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 80275, 'degree': 36864, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.60924283378360225019931261058', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2], 'jinv': [27, 19], 'lmfdb_iso': '80275.s', 'lmfdb_label': '80275.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, 0, 2], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.c.1', '76.6.0.?', '190.6.0.?', '380.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 16055], [5, 10, 3211], [13, 86, 475], [19, 20, 4225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0755913230556912114776209435', 'prec': 103}, 'szpiro_ratio': 2.7110393381348357, '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, 0, -1, 0, 0, -2, -3, -3, 0, 4, 0, 0, -2, 0, -1, 4, -3, -1, 0], 'aplist': [1, 0, 0, -2, 4, 0, 4, -1, -6, -6, 4, 10, 10, 2, 6, 10, 0, 2, -8, -4, -4, 4, 18, 2, -6], 'class_deg': 2, 'class_size': 2, 'conductor': 80275, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '80275.s', 'trace_hash': 389746993719883982}
• 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': '0.29567758222317493530785291939', 'prec': 103}, 'conductor': 80275, 'gens': [], 'heights': [], 'lmfdb_label': '80275.s2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.99384967830985973786374744516', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9876993566197194757274948903295949156', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-16, 8, 1]], 'xcoord_integral_points': [-16]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '5': 'a', '13': 'a', '19': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '80275.s2'}
• ec_torsion_growth •

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

  
  
  • id: 3779138
    {'degree': 2, 'field': [24, -1, 1], 'lmfdb_label': '80275.s2', 'torsion': [2, 2]}
  • id: 3779139
    {'degree': 4, 'field': [-979, -81, 16, -1, 1], 'lmfdb_label': '80275.s2', 'torsion': [4]}
  • id: 3779142
    {'degree': 8, 'field': [-2482769, 1123556, -160085, 4649, -926, -226, -5, -4, 1], 'lmfdb_label': '80275.s2', 'torsion': [6]}
  • id: 3779140
    {'degree': 8, 'field': [108020, -39970, -4365, -115, 681, 14, -9, -1, 1], 'lmfdb_label': '80275.s2', 'torsion': [2, 4]}
  • id: 3779141
    {'degree': 8, 'field': [4968441, 0, 306457, 0, 9384, 0, 153, 0, 1], 'lmfdb_label': '80275.s2', 'torsion': [2, 4]}
  • id: 3779144
    {'degree': 16, 'field': [3217191, 45416544, 247560117, 453378231, 485934423, 348979731, 158699373, 50746926, 18722929, 819485, 689980, -26158, 3502, -175, 55, -4, 1], 'lmfdb_label': '80275.s2', 'torsion': [2, 6]}
  • id: 3779143
    {'degree': 16, 'field': [24314761, 0, -10297796, 0, -913690, 0, 328236, 0, -22241, 0, -1644, 0, 150, 0, -16, 0, 1], 'lmfdb_label': '80275.s2', '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: 1953251
    {'conductor': 80275, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '80275.s2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1953252
    {'conductor': 80275, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '80275.s2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1953253
    {'conductor': 80275, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '80275.s2', 'prime': 19, '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: 2193354
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [377, 4, 376, 5], [42, 1, 359, 0], [1, 4, 0, 1], [97, 286, 284, 95], [308, 1, 303, 0]], 'adelic_image': '380.12.0.?', 'conductor': 80275, 'lmfdb_label': '80275.s2', 'prime': 0}
  • id: 329743
    {'conductor': 80275, 'elladic_image': '2.3.0.1', 'lmfdb_label': '80275.s2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 80275.s does not appear in ec_padic