Elliptic curve data - 143745.z2

Formats: - HTML - YAML - JSON - 2024-06-06T22:08:54.538622

• 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': '143745x', 'Clabel': '143745x1', 'Cnumber': 1, 'abc_quality': 0.9877749277480878, 'absD': 2399158849785932780855859375, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 444, 'ainvs': [1, 0, 1, -496311813, -4864745230469], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 143745, 'degree': 85929984, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9792878323247613966993159762', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2], 'jinv': [-104033217621345013, 18460501171875], 'lmfdb_iso': '143745.z', 'lmfdb_label': '143745.z2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -362536, -96070009], 'min_quad_twist_disc': 37, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.f.1', '148.6.0.?', '222.6.0.?', '444.12.0.?'], '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': '1.2710993978415930634232442229', 'prec': 100}, 'szpiro_ratio': 6.0584737558326704, '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, 1, 1, -1, -3, 1, 1, -4, -1, 4, -1, 1, -1, 2, 1, -2, -1], 'aplist': [1, 1, 1, -1, -4, 4, 2, -2, -4, -10, 2, 0, -10, -10, 4, -6, 8, -8, -4, -8, -14, 6, -4, -10, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 143745, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '143745.z', 'trace_hash': 1298695452778929005}
• 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': '0.00034965078292487526036499334631', 'prec': 113}, 'conductor': 143745, 'gens': [], 'heights': [], 'lmfdb_label': '143745.z2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.015839925257049013361919380715', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1404746185075289620581954114534432828', 'prec': 130}, 'tamagawa_product': 288, 'torsion_generators': [[26125, -13063, 1]], 'xcoord_integral_points': [26125]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [1, 0], '5': [1, 0], '7': [0, 0], '37': 'a'}, 'iwp0': 5, 'lmfdb_label': '143745.z2'}
• ec_torsion_growth •

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

  
  
  • id: 6490721
    {'degree': 2, 'field': [28, -1, 1], 'lmfdb_label': '143745.z2', 'torsion': [2, 2]}
  • id: 6490722
    {'degree': 4, 'field': [12, 30, 5, -1, 1], 'lmfdb_label': '143745.z2', 'torsion': [4]}
  • id: 6490725
    {'degree': 8, 'field': [-42501, -10071, 9336, 1469, -731, -7, 7, -4, 1], 'lmfdb_label': '143745.z2', 'torsion': [6]}
  • id: 6490723
    {'degree': 8, 'field': [144, 360, 840, 174, 43, -65, -4, -1, 1], 'lmfdb_label': '143745.z2', 'torsion': [2, 4]}
  • id: 6490724
    {'degree': 8, 'field': [2217, 240, 885, 1842, 616, 62, 21, -4, 1], 'lmfdb_label': '143745.z2', 'torsion': [2, 4]}
  • id: 6490727
    {'degree': 16, 'field': [227529, 0, 3187809, 0, -542043, 0, 98568, 0, -101700, 0, 26862, 0, -2712, 0, 111, 0, 1], 'lmfdb_label': '143745.z2', 'torsion': [2, 6]}
  • id: 6490726
    {'degree': 16, 'field': [21986721, 0, -2249334, 0, 13471749, 0, 2115174, 0, -415116, 0, 1726, 0, 645, 0, -30, 0, 1], 'lmfdb_label': '143745.z2', '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: 3553720
    {'conductor': 143745, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '143745.z2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 9}
  • id: 3553721
    {'conductor': 143745, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '143745.z2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 3553722
    {'conductor': 143745, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '143745.z2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3553723
    {'conductor': 143745, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '143745.z2', 'prime': 37, '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: 2598084
    {'adelic_gens': [[1, 0, 4, 1], [298, 1, 295, 0], [3, 4, 8, 11], [1, 2, 2, 5], [113, 334, 332, 111], [1, 4, 0, 1], [304, 1, 35, 0], [441, 4, 440, 5]], 'adelic_image': '444.12.0.?', 'conductor': 143745, 'lmfdb_label': '143745.z2', 'prime': 0}
  • id: 554585
    {'conductor': 143745, 'elladic_image': '2.3.0.1', 'lmfdb_label': '143745.z2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 143745.z does not appear in ec_padic