Elliptic curve data - 25168.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
  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': '25168bj', 'Clabel': '25168bj1', 'Cnumber': 1, 'abc_quality': 0.8444505387279102, 'absD': 1088868352, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 26, 'ainvs': [0, 1, 0, -304, -1388], 'analytic_rank': 2, 'bad_primes': [2, 11, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 25168, 'degree': 9216, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.43550128382403151589759646220', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1], 'jinv': [6289657, 2197], 'lmfdb_iso': '25168.x', 'lmfdb_label': '25168.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -19, 12], 'min_quad_twist_disc': -4, 'modell_images': [], 'modm_images': ['26.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 10, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.55519326769566544700184200017', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 1573], [3, 2, 1936], [11, 32, 208], [13, 14, 1936]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.65729510886897555086329292225', 'prec': 107}, 'szpiro_ratio': 2.8389461027331557, '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, 0, 1, 0, -2, 0, -2, 0, -2, 0, 0, 0, 1, 0, -2, 0, -7, 0, -6, 0], 'aplist': [0, 1, -2, -2, 0, 1, -7, -6, 1, 3, -10, 6, 2, -3, -2, -9, -8, -15, -2, 6, -4, 11, 0, -18, -10], 'class_deg': 1, 'class_size': 1, 'conductor': 25168, 'isogeny_matrix': [[1]], 'lmfdb_iso': '25168.x', 'trace_hash': 1867644015282094025}
• 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': '0.41853173246078633904028444610', 'prec': 103}, 'conductor': 25168, 'gens': [[-12, 26, 1], [66, 520, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.47226218977297580982329111008', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.2298979949534601614983165879', 'prec': 100}], 'lmfdb_label': '25168.x1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '1.1757832610457006541409216246', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.8334434096219380441901141734117667539', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': [-12, -6, 27, 66, 162]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [2, 0], '7': [2, 0], '11': 'a', '13': [3, 0], '17': [2, 0], '19': [4, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '25168.x1'}
• ec_torsion_growth •

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

  
  
  • id: 1265406
    {'degree': 3, 'field': [2, -7, -1, 1], 'lmfdb_label': '25168.x1', 'torsion': [2]}
  • id: 1265407
    {'degree': 6, 'field': [-4, -20, 5, 29, -12, -3, 1], 'lmfdb_label': '25168.x1', 'torsion': [2, 2]}
  • id: 1265408
    {'degree': 8, 'field': [-363, 0, 209, 0, -66, 0, 0, 0, 1], 'lmfdb_label': '25168.x1', 'torsion': [3]}
  • id: 1265409
    {'degree': 12, 'field': [1573, 0, 484, 0, -7260, 0, 110, 0, -220, 0, 0, 0, 1], 'lmfdb_label': '25168.x1', 'torsion': [4]}
• 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: 577574
    {'conductor': 25168, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '25168.x1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 577575
    {'conductor': 25168, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '25168.x1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 577576
    {'conductor': 25168, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '25168.x1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  {'adelic_gens': [[25, 2, 24, 3], [1, 2, 0, 1], [1, 0, 2, 1], [15, 2, 15, 3], [1, 1, 25, 0]], 'adelic_image': '26.2.0.?', 'conductor': 25168, 'lmfdb_label': '25168.x1', 'prime': 0}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 1197480
    {'lmfdb_iso': '25168.x', 'p': 5, 'prec': 20, 'unit': 8630581496787, 'val': 2}
  • id: 1197481
    {'lmfdb_iso': '25168.x', 'p': 7, 'prec': 20, 'unit': 2471155998594452, 'val': 2}
  • id: 1197487
    {'lmfdb_iso': '25168.x', 'p': 17, 'prec': 20, 'unit': 128299287833854278192215, 'val': 2}
  • id: 1197488
    {'lmfdb_iso': '25168.x', 'p': 19, 'prec': 20, 'unit': 92450601129924166594956, 'val': 3}
  • id: 1197492
    {'lmfdb_iso': '25168.x', 'p': 23, 'prec': 20, 'unit': 2536176785701613608229218, 'val': 0}
  • id: 1197485
    {'lmfdb_iso': '25168.x', 'p': 29, 'prec': 20, 'unit': 1085695003057257680936183456, 'val': 2}
  • id: 1197482
    {'lmfdb_iso': '25168.x', 'p': 31, 'prec': 20, 'unit': 2798639955204246287143801506, 'val': 2}
  • id: 1197497
    {'lmfdb_iso': '25168.x', 'p': 37, 'prec': 20, 'unit': 29490483910429226805920312437, 'val': 2}
  • id: 1197483
    {'lmfdb_iso': '25168.x', 'p': 41, 'prec': 20, 'unit': 3577026877444494257381312110696, 'val': 2}
  • id: 1197484
    {'lmfdb_iso': '25168.x', 'p': 43, 'prec': 20, 'unit': 10148956758436504817367482846721, 'val': 2}
  • id: 1197495
    {'lmfdb_iso': '25168.x', 'p': 47, 'prec': 20, 'unit': 36732457456102194759582829260796, 'val': 2}
  • id: 1197489
    {'lmfdb_iso': '25168.x', 'p': 53, 'prec': 20, 'unit': 348580573131588191346344992494645, 'val': 2}
  • id: 1197490
    {'lmfdb_iso': '25168.x', 'p': 59, 'prec': 20, 'unit': 3231868267173329272285069877686607, 'val': 2}
  • id: 1197496
    {'lmfdb_iso': '25168.x', 'p': 61, 'prec': 20, 'unit': 7679992700227401475428345121125070, 'val': 2}
  • id: 1197479
    {'lmfdb_iso': '25168.x', 'p': 67, 'prec': 20, 'unit': 45023244446524515007123260335319260, 'val': 2}
  • id: 1197494
    {'lmfdb_iso': '25168.x', 'p': 71, 'prec': 20, 'unit': 70857473378859857594861922925108117, 'val': 2}
  • id: 1197491
    {'lmfdb_iso': '25168.x', 'p': 73, 'prec': 20, 'unit': 137200928879817652857313459816416862, 'val': 2}
  • id: 1197486
    {'lmfdb_iso': '25168.x', 'p': 79, 'prec': 20, 'unit': 653967922071520217483886811833307035, 'val': 2}
  • id: 1197493
    {'lmfdb_iso': '25168.x', 'p': 89, 'prec': 20, 'unit': 3163645785948603725317770984693046707, 'val': 2}
  • id: 1197478
    {'lmfdb_iso': '25168.x', 'p': 97, 'prec': 20, 'unit': 34130906186551327775248807899385421998, 'val': 2}