Elliptic curve data - 273273.s2

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

  
  {'Ciso': '273273s', 'Clabel': '273273s1', 'Cnumber': 1, 'abc_quality': 1.1307725776312423, 'absD': 18710407763530825204863, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 616, 'ainvs': [1, 0, 0, 5585362, -4182527805], 'analytic_rank': 0, 'bad_primes': [3, 7, 11, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 273273, 'degree': 19353600, 'elladic_images': ['4.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9606618606640860714970569703', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 2], 'jinv': [98931640625, 96059601], 'lmfdb_iso': '273273.s', 'lmfdb_label': '273273.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 675, 5832], 'min_quad_twist_disc': -91, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.f.1', '14.6.0.b.1', '28.24.0.g.1', '88.24.0.?', '616.48.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, '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': '0.21875457014183272464129869193', 'prec': 103}, 'szpiro_ratio': 4.6508650478257705, '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, 0, -1, 0, 3, 1, 0, 1, -1, 0, 0, 0, -1, 4, -1, 8, 0], 'aplist': [-1, 1, 0, 0, 1, 0, 4, 8, -8, 2, 4, -10, -4, 4, 12, 6, 12, -12, -4, 0, 4, -8, 8, 0, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 273273, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '273273.s', 'trace_hash': 2180311686294599036}
• 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': '0.0026816480717265773058297538490', 'prec': 110}, 'conductor': 273273, 'gens': [], 'heights': [], 'lmfdb_label': '273273.s2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.066711581436444474396420569189', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1347706059662231806854582140587420788', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[690, -345, 1]], 'xcoord_integral_points': [690]}
• lmfdb_label 273273.s2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11659520
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '273273.s2', 'torsion': [2, 2]}
  • id: 11659521
    {'degree': 4, 'field': [-248, -88, -2, -2, 1], 'lmfdb_label': '273273.s2', 'torsion': [4]}
  • id: 11659522
    {'degree': 4, 'field': [296, -46, 24, -1, 1], 'lmfdb_label': '273273.s2', 'torsion': [2, 4]}
  • id: 11659524
    {'degree': 8, 'field': [-9194925, -398670, -340122, -29327, 6167, -677, 205, -1, 1], 'lmfdb_label': '273273.s2', 'torsion': [6]}
  • id: 11659523
    {'degree': 8, 'field': [3844, 2728, 968, -80, 125, 46, 2, -2, 1], 'lmfdb_label': '273273.s2', 'torsion': [4, 4]}
  • id: 11659527
    {'degree': 16, 'field': [28708936, -17169300, 13652818, -4494588, 3788730, -1755458, 561851, -247174, 112804, -28428, 6685, -2248, 539, -46, 12, -6, 1], 'lmfdb_label': '273273.s2', 'torsion': [2, 8]}
  • id: 11659526
    {'degree': 16, 'field': [416132648, 205365304, -153515420, -94606188, 25657282, 23010320, -2971672, -3553578, 322261, 337826, -29294, -19206, 1836, 602, -66, -8, 1], 'lmfdb_label': '273273.s2', 'torsion': [2, 8]}
  • id: 11659525
    {'degree': 16, 'field': [547981281, 0, 0, 0, -263044828, 0, 0, 0, 1229990, 0, 0, 0, -2972, 0, 0, 0, 1], 'lmfdb_label': '273273.s2', 'torsion': [8]}
  • id: 11659528
    {'degree': 16, 'field': [135274633209, 0, 208578131181, 0, 70372077885, 0, -1052476229, 0, 23385953, 0, -906332, 0, 5755, 0, 14, 0, 1], 'lmfdb_label': '273273.s2', '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: 6768402
    {'conductor': 273273, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '273273.s2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 6768403
    {'conductor': 273273, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '273273.s2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6768404
    {'conductor': 273273, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '273273.s2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6768405
    {'conductor': 273273, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '273273.s2', '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: 3390321
    {'adelic_gens': [[609, 8, 608, 9], [313, 156, 156, 309], [313, 156, 176, 471], [360, 3, 221, 600], [1, 0, 8, 1], [5, 8, 48, 77], [57, 8, 228, 33], [3, 8, 608, 595], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '616.48.1.?', 'conductor': 273273, 'lmfdb_label': '273273.s2', 'prime': 0}
  • id: 974984
    {'conductor': 273273, 'elladic_image': '4.12.0.11', 'lmfdb_label': '273273.s2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 273273.s does not appear in ec_padic