Elliptic curve data - 74529.r2

Formats: - HTML - YAML - JSON - 2024-05-23T12:25:28.201835

• 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': '74529h', 'Clabel': '74529h2', 'Cnumber': 2, 'absD': 1888975612458987507, 'ainvs': [0, 0, 1, 0, 66125855], 'analytic_rank': 0, 'bad_primes': [3, 7, 13], 'class_deg': 3, 'class_size': 2, 'cm': -3, 'conductor': 74529, 'degree': 707616, 'elladic_images': ['13.273.11.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1857631009083921634782327313', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 17, 'isogeny_degrees': [1, 3], 'jinv': [0, 1], 'lmfdb_iso': '74529.r', 'lmfdb_label': '74529.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 3], 'min_quad_twist_disc': 273, 'modell_images': ['13Ns.5.1.4'], 'nonmax_primes': [13], 'nonmax_rad': 13, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691958', 'prec': 103}, 'szpiro_ratio': 4.415503643669518, '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, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -8, 0], 'aplist': [0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 7, -10, 0, -13, 0, 0, 0, 13, 11, 0, -17, -13, 0, 0, -5], 'class_deg': 3, 'class_size': 2, 'conductor': 74529, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '74529.r', 'trace_hash': 743988779416539374}
• 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': '0.012631946948389535366933937501', 'prec': 107}, 'conductor': 74529, 'gens': [], 'heights': [], 'lmfdb_label': '74529.r2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20918496080323417874804440244', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.41836992160646835749608880487644394822', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 's?', '3': 'a', '5': [0, 0, 0], '7': 'a', '11': [0, 0, 0], '13': 'a', '17': [0, 0, 0], '19': [0, 0], '23': [0, 0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '74529.r2'}
• ec_torsion_growth •

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

  
  
  • id: 3527500
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '74529.r2', 'torsion': [3]}
  • id: 3527501
    {'degree': 3, 'field': [-26, 0, 0, 1], 'lmfdb_label': '74529.r2', 'torsion': [2]}
  • id: 3527504
    {'degree': 6, 'field': [-27, -9, -44, -51, 2, -3, 1], 'lmfdb_label': '74529.r2', 'torsion': [6]}
  • id: 3527502
    {'degree': 6, 'field': [27, 0, -17, 0, 1, 0, 1], 'lmfdb_label': '74529.r2', 'torsion': [2, 2]}
  • id: 3527503
    {'degree': 6, 'field': [242, -129, -21, 13, 9, -3, 1], 'lmfdb_label': '74529.r2', 'torsion': [3]}
  • id: 3527505
    {'degree': 12, 'field': [-71336, -48160, 112848, -67400, 16732, -5160, 1840, -192, -162, -4, 16, -6, 1], 'lmfdb_label': '74529.r2', 'torsion': [4]}
  • id: 3527508
    {'degree': 12, 'field': [25, 435, 2513, -174, 807, -39, 328, -195, -9, 12, -1, -3, 1], 'lmfdb_label': '74529.r2', 'torsion': [2, 6]}
  • id: 3527506
    {'degree': 12, 'field': [12544, 11760, 4641, 14721, 6336, -4449, 1547, 96, -93, 51, 0, -3, 1], 'lmfdb_label': '74529.r2', 'torsion': [3, 3]}
  • id: 3527507
    {'degree': 12, 'field': [113659, 37037, 29445, -3966, 7783, -27, 836, -330, 66, -29, -4, 0, 1], 'lmfdb_label': '74529.r2', 'torsion': [7]}
  • id: 3527509
    {'degree': 18, 'field': [21952, 131712, 77616, -376320, -301224, -5544, 239703, -64677, -114372, -17345, 16338, 2304, -4857, -195, 360, -42, -33, 0, 1], 'lmfdb_label': '74529.r2', 'torsion': [9]}
  • id: 3527510
    {'degree': 18, 'field': [56200, -12180, -72798, -101343, 228825, -102360, -8658, 45327, -21735, 11361, -1353, -465, 1149, -327, 213, -30, 24, -3, 1], 'lmfdb_label': '74529.r2', '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: 1809962
    {'conductor': 74529, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '74529.r2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1809963
    {'conductor': 74529, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '74529.r2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1809964
    {'conductor': 74529, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '74529.r2', 'prime': 13, '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

  
  {'conductor': 74529, 'elladic_image': '13.273.11.1', 'lmfdb_label': '74529.r2', 'modell_image': '13Ns.5.1.4', 'prime': 13}
• lmfdb_iso 74529.r does not appear in ec_padic