Elliptic curve data - 159120.q2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '159120cr', 'Clabel': '159120cr1', 'Cnumber': 1, 'abc_quality': 1.016987102247835, 'absD': 31028400, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 13260, 'ainvs': [0, 0, 0, -48, -297], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 159120, 'degree': 30720, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.12532965762889238511652620941', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2], 'jinv': [-28311552, 71825], 'lmfdb_iso': '159120.q', 'lmfdb_label': '159120.q2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -48, 297], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '102.6.0.?', '780.6.0.?', '4420.6.0.?', '13260.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.9469957185536463078658864163', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 51], [3, 6, 17680], [5, 6, 31824], [13, 14, 12240], [17, 18, 9360]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.38037247472478347420469580697', 'prec': 107}, 'szpiro_ratio': 2.079798694030128, '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, -1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 4, 0], 'aplist': [0, 0, -1, -2, 0, 1, -1, 4, -8, -2, -4, -10, -2, 4, -8, -2, 6, 14, 4, 0, -2, -10, 16, 6, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 159120, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '159120.q', 'trace_hash': 975655017965168500}
• 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': '0.77828747706618610552159434562', 'prec': 103}, 'conductor': 159120, 'gens': [[69, 570, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.9469957185536463078658864163', 'prec': 100}], 'lmfdb_label': '159120.q2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.84422700853994101075334561099', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9758667593091175138830039426508833778', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[9, 0, 1]], 'xcoord_integral_points': [9, 69]}
• lmfdb_label 159120.q2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7120978
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '159120.q2', 'torsion': [2, 2]}
  • id: 7120979
    {'degree': 4, 'field': [-51, 0, -54, 0, 1], 'lmfdb_label': '159120.q2', 'torsion': [4]}
  • id: 7120982
    {'degree': 8, 'field': [-12675, 0, 0, 0, 390, 0, 36, 0, 1], 'lmfdb_label': '159120.q2', 'torsion': [6]}
  • id: 7120980
    {'degree': 8, 'field': [38025, 0, 5022, 0, 1527, 0, 54, 0, 1], 'lmfdb_label': '159120.q2', 'torsion': [2, 4]}
  • id: 7120981
    {'degree': 8, 'field': [668629, -114712, 117082, -4684, 2203, 164, -50, -4, 1], 'lmfdb_label': '159120.q2', 'torsion': [2, 4]}
  • id: 7120984
    {'degree': 16, 'field': [10989225, 0, 0, 0, 338130, 0, -150552, 0, 45543, 0, -3672, 0, 426, 0, -36, 0, 1], 'lmfdb_label': '159120.q2', 'torsion': [2, 6]}
  • id: 7120983
    {'degree': 16, 'field': [26936687376, 0, 31764851136, 0, -3235336128, 0, 73273248, 0, -2999160, 0, 371952, 0, 912, 0, -216, 0, 1], 'lmfdb_label': '159120.q2', 'torsion': [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: 3936167
    {'conductor': 159120, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '159120.q2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3936168
    {'conductor': 159120, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '159120.q2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3936169
    {'conductor': 159120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '159120.q2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3936170
    {'conductor': 159120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '159120.q2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3936171
    {'conductor': 159120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '159120.q2', 'prime': 17, '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: 2693632
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [4424, 1, 8839, 0], [9949, 3316, 9944, 3315], [7957, 4, 2654, 9], [11702, 1, 779, 0], [13257, 4, 13256, 5], [11221, 4, 9182, 9]], 'adelic_image': '13260.12.0.?', 'conductor': 159120, 'lmfdb_label': '159120.q2', 'prime': 0}
  • id: 606641
    {'conductor': 159120, 'elladic_image': '2.3.0.1', 'lmfdb_label': '159120.q2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 159120.q does not appear in ec_padic