Elliptic curve data - 4032.h2

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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': '4032h', 'Clabel': '4032h4', 'Cnumber': 4, 'abc_quality': 1.0814902740568197, 'absD': 4129544208384, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 168, 'ainvs': [0, 0, 0, -28236, 1823600], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 4032, 'degree': 8192, 'elladic_images': ['8.48.0.129'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3166587082849399258731205946', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 7, 'isogeny_degrees': [1, 2, 4], 'jinv': [13027640977, 21609], 'lmfdb_iso': '4032.h', 'lmfdb_label': '4032.h2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -49, -136], 'min_quad_twist_disc': -24, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.e.1.14', '12.24.0.c.1', '24.96.0-24.j.2.8', '56.96.0-56.u.1.10', '168.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020605', 'prec': 107}, 'szpiro_ratio': 5.102212873901214, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 2, 0, 0, 0, 6, 0, -4, 0], 'aplist': [0, 0, -2, -1, 4, 2, 6, -4, 0, -2, 0, -6, -2, 4, 0, 6, 12, 2, -4, 0, -6, -16, -12, 14, 18], 'class_deg': 8, 'class_size': 6, 'conductor': 4032, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '4032.h', 'trace_hash': 488341209145645414}
• 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': '0.071839744136427248386346438924', 'prec': 107}, 'conductor': 4032, 'gens': [], 'heights': [], 'lmfdb_label': '4032.h2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.78015831108584666780945012842', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5603166221716933356189002568353143856', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[94, 0, 1], [100, 0, 1]], 'xcoord_integral_points': [-194, 94, 100]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '4032.h2'}
• ec_torsion_growth •

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

  
  
  • id: 209558
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [2, 4]}
  • id: 209559
    {'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [2, 4]}
  • id: 209560
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [2, 4]}
  • id: 209565
    {'degree': 8, 'field': [-432, 0, 0, 0, 72, 0, -2, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [2, 6]}
  • id: 209561
    {'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [4, 4]}
  • id: 209562
    {'degree': 8, 'field': [1, 0, 4, 0, 3, 0, -2, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [2, 8]}
  • id: 209563
    {'degree': 8, 'field': [9, 0, -120, 0, 79, 0, -16, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [2, 8]}
  • id: 209564
    {'degree': 8, 'field': [106, 148, -106, -92, 67, -28, 14, -4, 1], 'lmfdb_label': '4032.h2', 'torsion': [2, 8]}
  • id: 209568
    {'degree': 16, 'field': [1, -12, 68, -232, 488, -564, 194, 396, -665, 444, -62, -152, 162, -92, 34, -8, 1], 'lmfdb_label': '4032.h2', 'torsion': [4, 8]}
  • id: 209567
    {'degree': 16, 'field': [256, 0, 0, 0, -16, 0, 0, 0, -15, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [4, 8]}
  • id: 209569
    {'degree': 16, 'field': [441, 0, -1764, 0, -1260, 0, 1572, 0, 570, 0, -336, 0, 169, 0, 8, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [2, 12]}
  • id: 209566
    {'degree': 16, 'field': [2241, 2808, -3654, -5796, 3642, 4812, -978, -2256, 319, 528, -142, -24, 36, -12, -4, 0, 1], 'lmfdb_label': '4032.h2', 'torsion': [2, 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: 75324
    {'conductor': 4032, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '4032.h2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 75325
    {'conductor': 4032, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '4032.h2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 75326
    {'conductor': 4032, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '4032.h2', 'prime': 7, 'reduction_type': -1, '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: 1690188
    {'adelic_gens': [[73, 8, 124, 33], [79, 124, 104, 75], [5, 4, 164, 165], [7, 48, 162, 121], [161, 8, 160, 9], [1, 0, 8, 1], [49, 166, 18, 5], [1, 8, 0, 1]], 'adelic_image': '168.192.1.?', 'conductor': 4032, 'lmfdb_label': '4032.h2', 'prime': 0}
  • id: 19985
    {'conductor': 4032, 'elladic_image': '8.48.0.129', 'lmfdb_label': '4032.h2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 4032.h does not appear in ec_padic