Elliptic curve data - 169338.x1

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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': '169338c', 'Clabel': '169338c2', 'Cnumber': 2, 'abc_quality': 0.9314568742371903, 'absD': 205158725155124442, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 4008, 'ainvs': [1, 0, 0, -3041243, -2041521561], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 167], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 169338, 'degree': 2830464, 'elladic_images': ['3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3780827429034623314554819130', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 23, 'isogeny_degrees': [1, 3], 'jinv': [3813557241924625, 251503002], 'lmfdb_iso': '169338.x', 'lmfdb_label': '169338.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -17996, -930616], 'min_quad_twist_disc': 13, 'modell_images': ['3B.1.2'], 'modm_images': ['3.8.0-3.a.1.1', '4008.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '13.030697910596045063741762937', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.66811650459577117408649028529', 'prec': 103}, 'szpiro_ratio': 4.6842660970207115, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 1, 1, 1, 0, 1, -1, 1, 1, 0, -3, 1, 0, -1, 0, 1, 3, 1, 2, 0], 'aplist': [1, 1, 0, -1, -3, 0, 3, 2, 0, -3, -1, 2, 6, -7, 0, 6, 6, 8, 5, -3, 2, -10, 0, 0, -19], 'class_deg': 3, 'class_size': 2, 'conductor': 169338, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '169338.x', 'trace_hash': 2159178091472741623}
• 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': '0.0085985174010866272582106601305', 'prec': 110}, 'conductor': 169338, 'gens': [[-4940309, 58494001, 70]], 'heights': [{'__RealLiteral__': 0, 'data': '13.030697910596045063741762937', 'prec': 100}], 'lmfdb_label': '169338.x1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.11432428447266629408388045424', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '13.407526933275245002848073977697422873', 'prec': 130}, 'tamagawa_product': 9, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 169338.x1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7533007
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '169338.x1', 'torsion': [3]}
  • id: 7533008
    {'degree': 3, 'field': [-404, -160, -1, 1], 'lmfdb_label': '169338.x1', 'torsion': [2]}
  • id: 7533009
    {'degree': 3, 'field': [-52, 0, 0, 1], 'lmfdb_label': '169338.x1', 'torsion': [3]}
  • id: 7533010
    {'degree': 6, 'field': [-144288, 0, 65664, 0, -594, 0, 1], 'lmfdb_label': '169338.x1', 'torsion': [2, 2]}
  • id: 7533011
    {'degree': 6, 'field': [2809, -159, -150, 97, 6, -3, 1], 'lmfdb_label': '169338.x1', 'torsion': [3, 3]}
  • id: 7533012
    {'degree': 6, 'field': [292032, 0, 16900, 0, 260, 0, 1], 'lmfdb_label': '169338.x1', 'torsion': [6]}
  • id: 7533013
    {'degree': 9, 'field': [13824, 0, 0, -39872, 0, 0, -890, 0, 0, 1], 'lmfdb_label': '169338.x1', 'torsion': [6]}
  • id: 7533014
    {'degree': 12, 'field': [-1293743907, -1138307256, -315675954, -133576128, -25747065, -8935920, -1627020, -258048, -30981, -1944, -162, 0, 1], 'lmfdb_label': '169338.x1', 'torsion': [4]}
  • id: 7533015
    {'degree': 12, 'field': [28558336, 0, -38989824, 0, 52173504, 0, -1433920, 0, 31908, 0, -198, 0, 1], 'lmfdb_label': '169338.x1', 'torsion': [2, 6]}
  • id: 7533017
    {'degree': 18, 'field': [330225942528, 0, 0, 0, 0, 0, 690783232, 0, 0, 0, 0, 0, 124736, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '169338.x1', 'torsion': [3, 6]}
  • id: 7533018
    {'degree': 18, 'field': [52995814421568, -83594779031808, -311700021239040, -115869145281504, 17086375834080, 8552248554240, 333193706404, -262149813240, -7940906508, 4780336632, 118441176, -77660448, -3888824, 611316, 43998, -2412, -240, 0, 1], 'lmfdb_label': '169338.x1', 'torsion': [2, 6]}
  • id: 7533016
    {'degree': 18, 'field': [1115906277282951168, 0, 0, 1909114515399168, 0, 0, 1714960825408, 0, 0, -1599296208, 0, 0, 337492, 0, 0, -1002, 0, 0, 1], 'lmfdb_label': '169338.x1', 'torsion': [9]}
• 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: 4190047
    {'conductor': 169338, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '169338.x1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4190048
    {'conductor': 169338, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '169338.x1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 4190049
    {'conductor': 169338, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '169338.x1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
  • id: 4190050
    {'conductor': 169338, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '169338.x1', 'prime': 167, '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: 2756854
    {'adelic_gens': [[2005, 6, 2007, 19], [4003, 6, 4002, 7], [4, 3, 9, 7], [3007, 6, 0, 1], [170, 3843, 1, 2506], [673, 6, 2019, 19], [4005, 4006, 3998, 4001], [1, 6, 0, 1], [3, 4, 8, 11], [1, 0, 6, 1]], 'adelic_image': '4008.16.0.?', 'conductor': 169338, 'lmfdb_label': '169338.x1', 'prime': 0}
  • id: 639998
    {'conductor': 169338, 'elladic_image': '3.8.0.2', 'lmfdb_label': '169338.x1', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 169338.x does not appear in ec_padic