Elliptic curve data - 392784.h2

Formats: - HTML - YAML - JSON - 2024-05-20T12:35:03.432716

• 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': '392784h', 'Clabel': '392784h1', 'Cnumber': 1, 'abc_quality': 0.8862376285433565, 'absD': 145366119295746048, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 14028, 'ainvs': [0, -1, 0, -348504, -81168912], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 167], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 392784, 'degree': 5308416, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0700202105468039159358434328', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2], 'jinv': [-9714044119753, 301658112], 'lmfdb_iso': '392784.h', 'lmfdb_label': '392784.h2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -444, -3888], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '84.6.0.?', '334.6.0.?', '14028.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.0243608158624384898089823939', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.40391795545920195396593493962', 'prec': 103}, 'szpiro_ratio': 3.877807078728728, '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, 0, -1, 0, -2, 0, 0, 0, 1, 0, -4, 0, 4, 0, 2, 0, -2, 0, -8, 0], 'aplist': [0, -1, -2, 0, -4, 4, -2, -8, -6, 6, -4, -10, -6, -4, 0, -4, 0, 10, -12, 10, 0, 8, -16, -10, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 392784, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '392784.h', 'trace_hash': 1364418056087175223}
• 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': '0.015922207898448242369418165973', 'prec': 107}, 'conductor': 392784, 'gens': [[978, 22638, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.0243608158624384898089823939', 'prec': 100}], 'lmfdb_label': '392784.h2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.098067199997031536731284114715', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3727247759389377909965134593044690226', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[684, 0, 1]], 'xcoord_integral_points': [684, 978, 4268]}
• lmfdb_label 392784.h2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16227255
    {'degree': 2, 'field': [42, -1, 1], 'lmfdb_label': '392784.h2', 'torsion': [2, 2]}
  • id: 16227256
    {'degree': 4, 'field': [-167, 0, 26, 0, 1], 'lmfdb_label': '392784.h2', 'torsion': [4]}
  • id: 16227259
    {'degree': 8, 'field': [-1714608, 0, -166131, 0, -4536, 0, 0, 0, 1], 'lmfdb_label': '392784.h2', 'torsion': [6]}
  • id: 16227257
    {'degree': 8, 'field': [33457, -4590, 4960, -746, 389, -22, 12, -4, 1], 'lmfdb_label': '392784.h2', 'torsion': [2, 4]}
  • id: 16227258
    {'degree': 8, 'field': [55605384, 1906956, -1874030, -65596, 32159, 764, -250, -4, 1], 'lmfdb_label': '392784.h2', 'torsion': [2, 4]}
  • id: 16227260
    {'degree': 16, 'field': [50376904704, 0, -12594226176, 0, 184271808, 0, 106332240, 0, -6108143, 0, -75842, 0, 11955, 0, -242, 0, 1], 'lmfdb_label': '392784.h2', 'torsion': [8]}
  • id: 16227261
    {'degree': 16, 'field': [205258867128, -372987441792, 586421000802, -470197980378, 344110791213, -132735728160, 47461576302, -2784428472, 730857982, -23616314, 5177158, -253736, 47446, -2408, 364, -8, 1], 'lmfdb_label': '392784.h2', '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: 9717866
    {'conductor': 392784, 'conductor_valuation': 4, 'discriminant_valuation': 24, 'j_denominator_valuation': 12, 'kodaira_symbol': -20, 'lmfdb_label': '392784.h2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9717867
    {'conductor': 392784, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '392784.h2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9717868
    {'conductor': 392784, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '392784.h2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9717869
    {'conductor': 392784, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '392784.h2', 'prime': 167, '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: 4102486
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [3509, 10522, 10520, 3507], [1, 2, 2, 5], [2005, 4, 4010, 9], [1, 4, 0, 1], [9353, 4, 4678, 9], [14025, 4, 14024, 5], [1346, 1, 13355, 0]], 'adelic_image': '14028.12.0.?', 'conductor': 392784, 'lmfdb_label': '392784.h2', 'prime': 0}
  • id: 1338882
    {'conductor': 392784, 'elladic_image': '2.3.0.1', 'lmfdb_label': '392784.h2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 392784.h does not appear in ec_padic