Elliptic curve data - 159600.gv1

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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': '159600bn', 'Clabel': '159600bn4', 'Cnumber': 4, 'abc_quality': 1.0038346664696574, 'absD': 28374530688000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 15960, 'ainvs': [0, 1, 0, -7260608, -7532635212], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 159600, 'degree': 3932160, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4731678991442576076067712521', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 177, 'isogeny_degrees': [1, 2, 4], 'jinv': [661397832743623417, 443352042], 'lmfdb_iso': '159600.gv', 'lmfdb_label': '159600.gv1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -18152, 939764], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '60.12.0-4.c.1.2', '168.12.0.?', '280.12.0.?', '456.12.0.?', '760.12.0.?', '840.24.0.?', '1064.12.0.?', '2280.24.0.?', '3192.24.0.?', '5320.24.0.?', '15960.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.9817327552293494532978919490', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 525], [3, 4, 53200], [5, 14, 2128], [7, 8, 22800], [19, 20, 8400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.97530176236726211088915946403', 'prec': 103}, 'szpiro_ratio': 4.925327842042371, '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, 0, 0, 1, 0, 1, 0, 4, 0, 2, 0, 0, 0, 2, 0, 1, 0], 'aplist': [0, 1, 0, 1, 4, 2, 2, 1, -4, 2, -4, 6, -10, -4, -8, -10, -12, -2, -8, 16, -10, 8, 0, -10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 159600, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '159600.gv', 'trace_hash': 86020896288509307}
• 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': '0.0071094115785560718656623505432', 'prec': 110}, 'conductor': 159600, 'gens': [[-1556, 66, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9817327552293494532978919490', 'prec': 100}], 'lmfdb_label': '159600.gv1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.091972145923266304617805668992', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.969454402725464738114159528031112440', 'prec': 130}, 'tamagawa_product': 160, 'torsion_generators': [[-1557, 0, 1]], 'xcoord_integral_points': [-1557, -1556, 7468]}
• lmfdb_label 159600.gv1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7140356
    {'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '159600.gv1', 'torsion': [2, 2]}
  • id: 7140358
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '159600.gv1', 'torsion': [4]}
  • id: 7140357
    {'degree': 2, 'field': [70, 0, 1], 'lmfdb_label': '159600.gv1', 'torsion': [4]}
  • id: 7140359
    {'degree': 4, 'field': [784, 0, 14, 0, 1], 'lmfdb_label': '159600.gv1', 'torsion': [2, 4]}
  • id: 7140363
    {'degree': 8, 'field': [-3466875, 0, 282500, 0, -6450, 0, 0, 0, 1], 'lmfdb_label': '159600.gv1', 'torsion': [6]}
  • id: 7140362
    {'degree': 8, 'field': [12424, 692, -422, -526, 229, 38, -8, -4, 1], 'lmfdb_label': '159600.gv1', 'torsion': [8]}
  • id: 7140360
    {'degree': 8, 'field': [23409, 0, -81540, 0, 594, 0, -60, 0, 1], 'lmfdb_label': '159600.gv1', 'torsion': [2, 4]}
  • id: 7140361
    {'degree': 8, 'field': [48902049, 0, -248724, 0, 47152, 0, 252, 0, 1], 'lmfdb_label': '159600.gv1', 'torsion': [8]}
  • id: 7140364
    {'degree': 16, 'field': [813333361, 0, -100810240, 0, 21055720, 0, -1251208, 0, 132958, 0, -1120, 0, 616, 0, 8, 0, 1], 'lmfdb_label': '159600.gv1', 'torsion': [4, 4]}
  • id: 7140369
    {'degree': 16, 'field': [1945286704, 231527968, -212520144, -40424992, 26223776, -7198968, 2432620, -141128, 172845, -86480, 12544, 1968, 218, -280, 60, -8, 1], 'lmfdb_label': '159600.gv1', 'torsion': [12]}
  • id: 7140365
    {'degree': 16, 'field': [10798598871, 8594763696, 4713309126, 666889452, 37484286, -30114864, -5260026, 2171904, 443479, -49816, -25010, 1184, 3328, 272, -80, -4, 1], 'lmfdb_label': '159600.gv1', 'torsion': [2, 8]}
  • id: 7140368
    {'degree': 16, 'field': [20795658849, 0, 86042506284, 0, 14606401572, 0, 5796847588, 0, 123232550, 0, 287812, 0, 868, 0, 140, 0, 1], 'lmfdb_label': '159600.gv1', 'torsion': [12]}
  • id: 7140367
    {'degree': 16, 'field': [611467236801, 2913120911772, 2215861847046, -793252982988, -352763287794, 15919625412, 29886238140, -1658498424, -369622620, 65713104, -1002726, -812232, 50272, 3776, -360, -4, 1], 'lmfdb_label': '159600.gv1', 'torsion': [2, 6]}
  • id: 7140366
    {'degree': 16, 'field': [74129517022500, 0, 654472062000, 0, 180352314900, 0, -1485292320, 0, 127446301, 0, -570308, 0, 15054, 0, 148, 0, 1], 'lmfdb_label': '159600.gv1', '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: 3947732
    {'conductor': 159600, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '159600.gv1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3947733
    {'conductor': 159600, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '159600.gv1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 3947734
    {'conductor': 159600, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '159600.gv1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3947735
    {'conductor': 159600, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '159600.gv1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3947736
    {'conductor': 159600, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '159600.gv1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2696557
    {'adelic_gens': [[7456, 3195, 10645, 6386], [7, 6, 15954, 15955], [10036, 6385, 14615, 6], [1, 0, 8, 1], [1189, 7580, 1150, 5979], [1, 8, 0, 1], [15953, 8, 15952, 9], [1, 4, 4, 17], [4201, 3200, 10420, 12801], [10776, 9185, 14755, 5166], [6383, 0, 0, 15959]], 'adelic_image': '15960.48.0.?', 'conductor': 159600, 'lmfdb_label': '159600.gv1', 'prime': 0}
  • id: 608408
    {'conductor': 159600, 'elladic_image': '4.6.0.1', 'lmfdb_label': '159600.gv1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 159600.gv does not appear in ec_padic