Elliptic curve data - 17640.u2

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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': '17640by', 'Clabel': '17640by4', 'Cnumber': 4, 'abc_quality': 0.9482276041115532, 'absD': 720435416400000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 0, 0, -289443, 43871758], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 17640, 'degree': 196608, 'elladic_images': ['8.12.0.14'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1347348463084874298471884940', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2, 4], 'jinv': [30534944836, 8203125], 'lmfdb_iso': '17640.u', 'lmfdb_label': '17640.u2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -656, 4956], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.1', '12.12.0-4.c.1.1', '24.24.0-24.z.1.5', '28.12.0-4.c.1.1', '42.6.0.a.1', '56.24.0-56.ba.1.7', '84.24.0.?', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.034850976980154840415862735934', 'prec': 107}, 'szpiro_ratio': 5.0461368247460765, '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, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 0, -1, 0, 0, 2, 6, 4, -4, -6, 0, 6, 6, -4, 8, -14, -4, 2, 12, 12, -10, 8, -4, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 17640, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '17640.u', 'trace_hash': 243142107115433230}
• 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': '0.013989199762539870396526832258', 'prec': 107}, 'conductor': 17640, 'gens': [], 'heights': [], 'lmfdb_label': '17640.u2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.26650696585652384092393262699', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1320557268521907273914610159214754662', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[434, 0, 1]], 'xcoord_integral_points': [434]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '17640.u2'}
• ec_torsion_growth •

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

  
  
  • id: 903316
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [4]}
  • id: 903314
    {'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '17640.u2', 'torsion': [2, 2]}
  • id: 903315
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [4]}
  • id: 903317
    {'degree': 4, 'field': [1, 0, -5, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [2, 4]}
  • id: 903319
    {'degree': 8, 'field': [1, 2, -20, -16, 63, 16, -20, -2, 1], 'lmfdb_label': '17640.u2', 'torsion': [2, 8]}
  • id: 903320
    {'degree': 8, 'field': [81, 0, 108, 0, 39, 0, -12, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [8]}
  • id: 903321
    {'degree': 8, 'field': [2709, 6846, 5790, 2322, 480, 132, 30, -4, 1], 'lmfdb_label': '17640.u2', 'torsion': [6]}
  • id: 903318
    {'degree': 8, 'field': [7056, 0, 0, 0, 84, 0, 0, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [2, 4]}
  • id: 903323
    {'degree': 16, 'field': [81, 0, 0, 0, -135, 0, 0, 0, 216, 0, 0, 0, -15, 0, 0, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [2, 8]}
  • id: 903326
    {'degree': 16, 'field': [35721, 0, -14921172, 0, 575100, 0, 1503948, 0, 258654, 0, 21972, 0, 1360, 0, 52, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [12]}
  • id: 903322
    {'degree': 16, 'field': [234256, 0, 120032, 0, 38272, 0, 15776, 0, 2812, 0, -688, 0, -32, 0, -4, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [4, 4]}
  • id: 903325
    {'degree': 16, 'field': [14607684, 0, 126138936, 0, 622300, 0, 2237928, 0, -82320, 0, -4312, 0, -588, 0, 0, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [12]}
  • id: 903324
    {'degree': 16, 'field': [18249984, 0, 8014080, 0, 439168, 0, -439680, 0, -67920, 0, 800, 0, 312, 0, 0, 0, 1], 'lmfdb_label': '17640.u2', 'torsion': [2, 6]}
• 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: 394886
    {'conductor': 17640, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '17640.u2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 394887
    {'conductor': 17640, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '17640.u2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 394888
    {'conductor': 17640, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '17640.u2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 394889
    {'conductor': 17640, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '17640.u2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 1781701
    {'adelic_gens': [[52, 167, 89, 162], [88, 165, 139, 166], [67, 66, 34, 115], [1, 0, 8, 1], [161, 8, 160, 9], [7, 6, 162, 163], [1, 4, 4, 17], [67, 64, 2, 69], [1, 8, 0, 1]], 'adelic_image': '168.48.0.?', 'conductor': 17640, 'lmfdb_label': '17640.u2', 'prime': 0}
  • id: 82699
    {'conductor': 17640, 'elladic_image': '8.12.0.14', 'lmfdb_label': '17640.u2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 17640.u does not appear in ec_padic