Elliptic curve data - 489762.r4

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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': '489762r', 'Clabel': '489762r3', 'Cnumber': 3, 'abc_quality': 1.0093203953110568, 'absD': 206290002542740150104697536, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 7176, 'ainvs': [1, -1, 0, 99767682, -574833722540], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 489762, 'degree': 222953472, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7339319873070572326294179704', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [31210858401683537303, 58626037175299776], 'lmfdb_iso': '489762.r', 'lmfdb_label': '489762.r4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 65594, 9717460], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.ba.1', '104.12.0.?', '156.12.0.?', '184.12.0.?', '276.12.0.?', '312.24.0.?', '552.24.0.?', '598.6.0.?', '1196.12.0.?', '2392.24.0.?', '3588.24.0.?', '7176.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7404893595492376756549154936', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.9021511642422340189050516312', 'prec': 100}, 'szpiro_ratio': 5.1655801956183, '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, -1, 0, 1, -2, 0, 1, -1, 0, 2, -4, 0, 0, -1, 0, 1, -6, 0, 4, -2], 'aplist': [-1, 0, -2, 1, -4, 0, -6, 4, -1, 10, -4, -6, -10, 8, 0, -10, -4, 6, -12, -16, 6, -4, 12, 10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 489762, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '489762.r', 'trace_hash': 362296140243250932}
• 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': '0.00057114697929284976151704185256', 'prec': 113}, 'conductor': 489762, 'gens': [[26036, 4422218, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7404893595492376756549154936', 'prec': 100}], 'lmfdb_label': '489762.r4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.029460318853936864917592071254', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2816237756291139646898162860799630346', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[18851, -18851, 2]], 'xcoord_integral_points': [5769, 12516, 26036]}
• lmfdb_label 489762.r4 does not appear in ec_iwasawa
• lmfdb_label 489762.r4 does not appear in ec_torsion_growth
• 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: 12075013
    {'conductor': 489762, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '489762.r4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 12075014
    {'conductor': 489762, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '489762.r4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 12075015
    {'conductor': 489762, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '489762.r4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 12075016
    {'conductor': 489762, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '489762.r4', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 12075017
    {'conductor': 489762, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '489762.r4', 'prime': 23, '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: 4665675
    {'adelic_gens': [[1, 0, 8, 1], [7169, 8, 7168, 9], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 7170, 7171], [2699, 2692, 2738, 6285], [6283, 6282, 4498, 907], [1648, 7173, 5515, 7174], [1880, 3, 6557, 2], [4783, 7168, 4780, 7143]], 'adelic_image': '7176.48.0.?', 'conductor': 489762, 'lmfdb_label': '489762.r4', 'prime': 0}
  • id: 1620920
    {'conductor': 489762, 'elladic_image': '4.6.0.1', 'lmfdb_label': '489762.r4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 489762.r does not appear in ec_padic