Elliptic curve data - 162624.e1

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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': '162624cd', 'Clabel': '162624cd1', 'Cnumber': 1, 'abc_quality': 0.7629203194196691, 'absD': 41631744, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 42, 'ainvs': [0, -1, 0, -117, -339], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 162624, 'degree': 36864, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.17398495128750695454258832047', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1], 'jinv': [90112, 21], 'lmfdb_iso': '162624.e', 'lmfdb_label': '162624.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -29, 57], 'min_quad_twist_disc': -8, 'modell_images': [], 'modm_images': ['42.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.1982613462980264001553341362', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0343359714988243304545064176', 'prec': 103}, 'szpiro_ratio': 2.1591996288366784, '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, -3, 0, -1, 0, 1, 0, 0, 0, -2, 0, 3, 0, 1, 0, 0, 0], 'aplist': [0, -1, -3, -1, 0, -2, 1, 0, -2, -4, -6, 6, 6, -1, 7, 0, 1, -6, 11, 6, -6, -12, -11, 13, -8], 'class_deg': 1, 'class_size': 1, 'conductor': 162624, 'isogeny_matrix': [[1]], 'lmfdb_iso': '162624.e', 'trace_hash': 900767047570462235}
• 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': '0.70612012829215882787575272413', 'prec': 103}, 'conductor': 162624, 'gens': [[-4, 7, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.1982613462980264001553341362', 'prec': 100}], 'lmfdb_label': '162624.e1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.4749776547196676915452602393', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2423863650235622330346565447801256294', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': [-4]}
• lmfdb_label 162624.e1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7266862
    {'degree': 3, 'field': [57, -29, -1, 1], 'lmfdb_label': '162624.e1', 'torsion': [2]}
  • id: 7266863
    {'degree': 6, 'field': [-27, -9, 114, -3, -38, -1, 1], 'lmfdb_label': '162624.e1', 'torsion': [2, 2]}
  • id: 7266864
    {'degree': 8, 'field': [-1452, 0, -638, 0, -132, 0, 0, 0, 1], 'lmfdb_label': '162624.e1', 'torsion': [3]}
  • id: 7266865
    {'degree': 12, 'field': [-1163382, -3023416, -3065304, -1607100, -484066, -67364, 10574, 6276, 1160, -32, -52, -4, 1], 'lmfdb_label': '162624.e1', '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: 4024768
    {'conductor': 162624, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '162624.e1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4024769
    {'conductor': 162624, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '162624.e1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4024770
    {'conductor': 162624, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '162624.e1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4024771
    {'conductor': 162624, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '162624.e1', 'prime': 11, 'reduction_type': 0, '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

  
  {'adelic_gens': [[1, 1, 41, 0], [1, 2, 0, 1], [31, 2, 31, 3], [1, 0, 2, 1], [41, 2, 40, 3], [29, 2, 29, 3]], 'adelic_image': '42.2.0.?', 'conductor': 162624, 'lmfdb_label': '162624.e1', 'prime': 0}
• lmfdb_iso 162624.e does not appear in ec_padic