Elliptic curve data - 4032.m1

Formats: - HTML - YAML - JSON - 2024-04-30T14:51:39.913193

• 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': '4032bl', 'Clabel': '4032bl4', 'Cnumber': 4, 'abc_quality': 1.0572692378622217, 'absD': 48157949952, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 336, 'ainvs': [0, 0, 0, -774156, 262174736], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4032, 'degree': 24576, 'elladic_images': ['16.48.0.120'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7781281085916933186649418551', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [268498407453697, 252], 'lmfdb_iso': '4032.m', 'lmfdb_label': '4032.m1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1344, 18405], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '16.48.0.z.2', '24.48.0-8.bb.2.1', '28.12.0.h.1', '48.96.0-16.z.2.1', '56.48.0.bl.1', '112.96.1.?', '168.96.0.?', '336.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.18910119341772050884147105445', 'prec': 103}, 'szpiro_ratio': 6.2987324622763605, '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, 0, 0, -2, 0, 1, 0, 0, 0, 4, 0, -6, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, 0, -2, 1, 4, -6, -2, -4, 8, -2, 0, 10, 6, -4, 0, 6, -4, -6, 4, 8, 10, 0, 4, 6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 4032, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '4032.m', 'trace_hash': 932920968172359527}
• 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': '0.028545493044417272816343533147', 'prec': 107}, 'conductor': 4032, 'gens': [], 'heights': [], 'lmfdb_label': '4032.m1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.70942274156002789348921768519', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4188454831200557869784353703713062510', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[508, 0, 1]], 'xcoord_integral_points': [508]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '4032.m1'}
• ec_torsion_growth •

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

  
  
  • id: 210665
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [4]}
  • id: 210663
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [2, 2]}
  • id: 210664
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [4]}
  • id: 210667
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [8]}
  • id: 210668
    {'degree': 4, 'field': [4, 0, -10, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [8]}
  • id: 210666
    {'degree': 4, 'field': [81, 0, -24, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [2, 4]}
  • id: 210673
    {'degree': 8, 'field': [-192, 0, 42, 0, 36, 0, 4, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [6]}
  • id: 210669
    {'degree': 8, 'field': [4, 0, 108, 0, 61, 0, 12, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [2, 4]}
  • id: 210671
    {'degree': 8, 'field': [9, 0, -120, 0, 79, 0, -16, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [2, 8]}
  • id: 210672
    {'degree': 8, 'field': [49, 0, -196, 0, 116, 0, -20, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [16]}
  • id: 210670
    {'degree': 8, 'field': [324, 0, -270, 0, 45, 0, 6, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [8]}
  • id: 210678
    {'degree': 16, 'field': [81, 0, -756, 0, 2448, 0, -3696, 0, 2911, 0, -1232, 0, 272, 0, -28, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [2, 16]}
  • id: 210674
    {'degree': 16, 'field': [256, 0, 0, 0, -752, 0, 0, 0, 600, 0, 0, 0, -47, 0, 0, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [4, 4]}
  • id: 210680
    {'degree': 16, 'field': [1296, 0, 216, 0, -2124, 0, -648, 0, 612, 0, -132, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [12]}
  • id: 210675
    {'degree': 16, 'field': [2209, -9400, 20000, -8532, 4642, -7172, 4968, -4840, 2163, 68, 24, -80, 46, 12, 8, -4, 1], 'lmfdb_label': '4032.m1', 'torsion': [2, 8]}
  • id: 210676
    {'degree': 16, 'field': [27657, -30744, -40572, 68544, -14448, -34104, 47964, -21000, 5482, -1016, 196, -224, 112, -56, 28, -8, 1], 'lmfdb_label': '4032.m1', 'torsion': [2, 8]}
  • id: 210677
    {'degree': 16, 'field': [614656, 0, 0, 0, -32928, 0, 0, 0, 980, 0, 0, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [16]}
  • id: 210679
    {'degree': 16, 'field': [1774224, 0, -1520928, 0, 104337, 0, 94392, 0, -1329, 0, -2868, 0, -45, 0, 28, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [2, 6]}
  • id: 210681
    {'degree': 16, 'field': [4198401, 0, -1917036, 0, -88200, 0, 59472, 0, -3150, 0, 252, 0, 28, 0, -16, 0, 1], 'lmfdb_label': '4032.m1', 'torsion': [12]}
• 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: 75612
    {'conductor': 4032, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '4032.m1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 75613
    {'conductor': 4032, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '4032.m1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 75614
    {'conductor': 4032, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4032.m1', 'prime': 7, '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: 1690205
    {'adelic_gens': [[5, 4, 332, 333], [1, 16, 0, 1], [15, 2, 238, 323], [230, 297, 69, 170], [321, 16, 320, 17], [223, 0, 0, 335], [1, 0, 16, 1], [323, 96, 324, 263], [136, 225, 111, 10]], 'adelic_image': '336.192.1.?', 'conductor': 4032, 'lmfdb_label': '4032.m1', 'prime': 0}
  • id: 20002
    {'conductor': 4032, 'elladic_image': '16.48.0.120', 'lmfdb_label': '4032.m1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4032.m does not appear in ec_padic