Elliptic curve data - 162288.dz3

Formats: - HTML - YAML - JSON - 2025-10-17T17:16:53.935315

• 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': '162288bu', 'Clabel': '162288bu3', 'Cnumber': 3, 'abc_quality': 1.052056363650569, 'absD': 82675471669216356834956279808, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 3864, 'ainvs': [0, 0, 0, -295861755, 13971941514538], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 23], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 162288, 'degree': 132710400, 'elladic_images': ['8.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.2291967080950391505224595827', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 103, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-8152944444844179625, 235342826399858688], 'lmfdb_iso': '162288.dz', 'lmfdb_label': '162288.dz3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -41931, -23576714], 'min_quad_twist_disc': -84, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.c.1', '24.24.0.bw.1', '46.6.0.a.1', '84.24.0.?', '138.24.0.?', '168.48.0.?', '184.12.0.?', '552.48.1.?', '1932.48.0.?', '3864.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '36.754047986819338587190273153', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 10143], [3, 8, 18032], [7, 32, 3312], [23, 24, 7056]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.0137883086733823428549284711', 'prec': 100}, 'szpiro_ratio': 6.173085025190437, '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, 0, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, -6, 0, 2, 0], 'aplist': [0, 0, 0, 0, 6, -2, -6, 2, 1, 6, 8, 8, 6, -2, 0, 12, 0, -8, 10, 0, -14, -8, -6, 6, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 162288, 'isogeny_matrix': [[1, 3, 2, 6], [3, 1, 6, 2], [2, 6, 1, 3], [6, 2, 3, 1]], 'lmfdb_iso': '162288.dz', 'trace_hash': 282020715786835016}
• 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': '0.00021211257370385705223917797495', 'prec': 113}, 'conductor': 162288, 'gens': [[51837111545711423, 31168384132350629687716710, 2075471]], 'heights': [{'__RealLiteral__': 0, 'data': '36.754047986819338587190273153', 'prec': 100}], 'lmfdb_label': '162288.dz3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.028569327369370941325375919468', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.4003074326800854114452301901630624725', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-28147, 0, 1]], 'xcoord_integral_points': [-28147]}
• lmfdb_label 162288.dz3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7252508
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '162288.dz3', 'torsion': [6]}
  • id: 7252507
    {'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '162288.dz3', 'torsion': [2, 2]}
  • id: 7252509
    {'degree': 4, 'field': [-2567, -168, -64, 0, 1], 'lmfdb_label': '162288.dz3', 'torsion': [4]}
  • id: 7252510
    {'degree': 4, 'field': [162, 2, -1, -2, 1], 'lmfdb_label': '162288.dz3', 'torsion': [2, 6]}
  • id: 7252511
    {'degree': 6, 'field': [14022, 8694, 1323, -138, 63, 0, 1], 'lmfdb_label': '162288.dz3', 'torsion': [6]}
  • id: 7252514
    {'degree': 8, 'field': [-542, 1260, -338, -260, 83, 44, -18, -4, 1], 'lmfdb_label': '162288.dz3', 'torsion': [12]}
  • id: 7252512
    {'degree': 8, 'field': [29052, 27171, 9987, 2157, 349, 99, 19, -3, 1], 'lmfdb_label': '162288.dz3', 'torsion': [2, 4]}
  • id: 7252513
    {'degree': 8, 'field': [1077444, 0, -75228, 0, 2269, 0, -52, 0, 1], 'lmfdb_label': '162288.dz3', 'torsion': [2, 4]}
  • id: 7252515
    {'degree': 12, 'field': [19518724, 12803364, 7748958, -793362, -285537, 142002, 30967, 0, 294, -276, 21, 0, 1], 'lmfdb_label': '162288.dz3', 'torsion': [3, 6]}
  • id: 7252516
    {'degree': 12, 'field': [54730404, 0, 49152096, 0, 1743525, 0, 188946, 0, 6615, 0, 126, 0, 1], 'lmfdb_label': '162288.dz3', 'torsion': [2, 6]}
  • id: 7252519
    {'degree': 16, 'field': [198216, -240336, 227688, 415248, -14804, -111120, 86904, -50240, 8774, 2908, -574, -1028, 363, 60, -22, -4, 1], 'lmfdb_label': '162288.dz3', 'torsion': [2, 12]}
  • id: 7252518
    {'degree': 16, 'field': [2706048, -1290816, 2391312, -1651152, 1450864, -563464, 359678, -132942, 13093, 6850, -68, -230, 130, -66, 14, -4, 1], 'lmfdb_label': '162288.dz3', 'torsion': [2, 12]}
  • id: 7252517
    {'degree': 16, 'field': [18274473, 35872200, 40473024, 30870576, 14263024, 4248696, -579424, -702624, -409626, -70248, -22784, -1488, -96, -24, 32, 0, 1], 'lmfdb_label': '162288.dz3', 'torsion': [8]}
  • id: 7252520
    {'degree': 18, 'field': [2076374342288, 6197585365872, 7197627976200, 4137739368912, 1089560440476, -19429851528, -88134022167, -17591750424, 1165620726, 813450960, 51275691, -15649128, -2068980, 146232, 32643, -576, -270, 0, 1], 'lmfdb_label': '162288.dz3', 'torsion': [18]}
• 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: 4016039
    {'conductor': 162288, 'conductor_valuation': 4, 'discriminant_valuation': 42, 'j_denominator_valuation': 30, 'kodaira_symbol': -38, 'lmfdb_label': '162288.dz3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4016040
    {'conductor': 162288, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '162288.dz3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4016041
    {'conductor': 162288, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '162288.dz3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4016042
    {'conductor': 162288, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '162288.dz3', 'prime': 23, '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: 2713468
    {'adelic_gens': [[1933, 2772, 3318, 1177], [1103, 0, 0, 3863], [2626, 1659, 693, 2752], [3853, 12, 3852, 13], [1, 12, 0, 1], [1, 6, 6, 37], [1, 0, 12, 1], [11, 2, 3814, 3855], [2589, 1400, 3178, 307], [2575, 1092, 644, 3863]], 'adelic_image': '3864.96.1.?', 'conductor': 162288, 'lmfdb_label': '162288.dz3', 'prime': 0}
  • id: 617335
    {'conductor': 162288, 'elladic_image': '8.6.0.1', 'lmfdb_label': '162288.dz3', 'modell_image': '2B', 'prime': 2}
  • id: 617336
    {'conductor': 162288, 'elladic_image': '3.4.0.1', 'lmfdb_label': '162288.dz3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 162288.dz does not appear in ec_padic