Elliptic curve data - 23520.z4

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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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '23520bs', 'Clabel': '23520bs2', 'Cnumber': 2, 'abc_quality': 1.2585717066877196, 'absD': 21346234560000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 1, 0, -16, 222284], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 23520, 'degree': 73728, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2365407151917727615394983167', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 4], 'jinv': [-8, 354375], 'lmfdb_iso': '23520.z', 'lmfdb_label': '23520.z4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 0, -648], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '28.12.0-4.c.1.1', '56.24.0-56.v.1.2', '120.24.0.?', '840.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 49], [3, 4, 7840], [5, 6, 4704], [7, 32, 480]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.25627474475584287307610214612', 'prec': 107}, 'szpiro_ratio': 3.789798141484704, '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, -1, 0, 0, 0, 1, 0, -4, 0, -6, 0, -1, 0, 6, 0, 4, 0], 'aplist': [0, 1, -1, 0, -4, -6, 6, 4, 8, 10, 4, -6, -6, -4, -12, 6, 4, 2, -4, 0, 2, 8, -12, -14, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 23520, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '23520.z', 'trace_hash': 206730920707085368}
• 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': '0.084324617810526361317457392959', 'prec': 107}, 'conductor': 23520, 'gens': [], 'heights': [], 'lmfdb_label': '23520.z4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.54071777692853137455086258664', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1628711077141254982034503465712781696', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-61, 0, 1]], 'xcoord_integral_points': [-61]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [0, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '23520.z4'}
• ec_torsion_growth •

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

  
  
  • id: 1190466
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [4]}
  • id: 1190467
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [4]}
  • id: 1190465
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [2, 2]}
  • id: 1190468
    {'degree': 4, 'field': [9, 0, 8, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [2, 4]}
  • id: 1190472
    {'degree': 8, 'field': [-9408, 0, -5824, 0, 336, 0, 0, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [6]}
  • id: 1190470
    {'degree': 8, 'field': [-1134, 0, 606, 360, 127, -60, -26, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [8]}
  • id: 1190469
    {'degree': 8, 'field': [226, 248, -196, -112, 77, -28, 14, -4, 1], 'lmfdb_label': '23520.z4', 'torsion': [2, 4]}
  • id: 1190471
    {'degree': 8, 'field': [4356, 0, 2496, 0, 892, 0, 64, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [8]}
  • id: 1190476
    {'degree': 16, 'field': [900, 0, 175536, 0, 94320, 0, 23048, 0, 8492, 0, 2480, 0, 340, 0, 28, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [2, 6]}
  • id: 1190473
    {'degree': 16, 'field': [2401, 0, 0, 0, 0, 0, 0, 0, 1666, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [4, 4]}
  • id: 1190474
    {'degree': 16, 'field': [7074, -15552, 22572, -13032, 6210, -5592, 11092, -6548, 27, 956, -112, -12, 2, -28, 24, -8, 1], 'lmfdb_label': '23520.z4', 'torsion': [2, 8]}
  • id: 1190478
    {'degree': 16, 'field': [44100, 0, 705600, 0, 846720, 0, 148232, 0, 5852, 0, -112, 0, 4, 0, 4, 0, 1], 'lmfdb_label': '23520.z4', 'torsion': [12]}
  • id: 1190477
    {'degree': 16, 'field': [1476225, 1968300, -1312200, -1632960, 228420, -98820, 165024, 145512, 6474, -23892, -7752, 64, -188, 28, 16, -8, 1], 'lmfdb_label': '23520.z4', 'torsion': [12]}
  • id: 1190475
    {'degree': 16, 'field': [499254336, 0, 261843456, 0, 49018816, 0, 3687936, 0, 154644, 0, 12544, 0, 588, 0, 0, 0, 1], 'lmfdb_label': '23520.z4', '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: 538387
    {'conductor': 23520, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '23520.z4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 538388
    {'conductor': 23520, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '23520.z4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 538389
    {'conductor': 23520, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '23520.z4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 538390
    {'conductor': 23520, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '23520.z4', 'prime': 7, '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: 1821202
    {'adelic_gens': [[833, 8, 832, 9], [1, 0, 8, 1], [736, 323, 529, 558], [1, 8, 0, 1], [1, 4, 4, 17], [592, 837, 475, 838], [337, 8, 508, 33], [281, 8, 284, 33], [7, 6, 834, 835], [727, 732, 730, 313]], 'adelic_image': '840.48.0.?', 'conductor': 23520, 'lmfdb_label': '23520.z4', 'prime': 0}
  • id: 108159
    {'conductor': 23520, 'elladic_image': '8.12.0.7', 'lmfdb_label': '23520.z4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 23520.z does not appear in ec_padic