Elliptic curve data - 327795.d8

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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': '327795d', 'Clabel': '327795d5', 'Cnumber': 5, 'abc_quality': 1.0149811194984983, 'absD': 871831340400619746225, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 255840, 'ainvs': [1, 1, 1, 1016970, -1364240700], 'analytic_rank': 2, 'bad_primes': [3, 5, 13, 41], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 327795, 'degree': 13271040, 'elladic_images': ['8.24.0.67'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6996295108668151341989624993', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [24487529386319, 183539412225], 'lmfdb_iso': '327795.d', 'lmfdb_label': '327795.d8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 605, -19750], 'min_quad_twist_disc': 41, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.24.0.q.1', '24.48.0.be.2', '40.48.0.bf.1', '120.96.1.?', '164.24.0.?', '208.48.0.?', '328.48.0.?', '416.96.2.?', '624.96.1.?', '984.96.0.?', '1040.96.1.?', '1248.192.5.?', '1640.96.0.?', '2080.192.5.?', '3120.192.5.?', '4920.192.1.?', '6240.384.13.?', '8528.96.0.?', '17056.192.2.?', '25584.192.1.?', '42640.192.1.?', '51168.384.5.?', '85280.384.5.?', '127920.384.5.?', '255840.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '13.966814736692325651780197793', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1681], [3, 4, 109265], [5, 6, 65559], [13, 14, 25215], [41, 842, 195]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.84284347751466123226558081278', 'prec': 103}, 'szpiro_ratio': 4.377233493549363, '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, -1, -1, 1, 1, 0, 3, 1, -1, -4, 1, -1, 0, -1, -1, -2, -1, 4, -1], 'aplist': [-1, -1, 1, 0, -4, -1, -2, 4, 8, 2, -8, 6, 0, -4, 8, -6, -12, -2, 4, 0, -6, -16, -4, -10, -18], 'class_deg': 16, 'class_size': 8, 'conductor': 327795, 'isogeny_matrix': [[1, 2, 4, 4, 8, 16, 16, 8], [2, 1, 2, 2, 4, 8, 8, 4], [4, 2, 1, 4, 8, 16, 16, 8], [4, 2, 4, 1, 2, 4, 4, 2], [8, 4, 8, 2, 1, 2, 2, 4], [16, 8, 16, 4, 2, 1, 4, 8], [16, 8, 16, 4, 2, 4, 1, 8], [8, 4, 8, 2, 4, 8, 8, 1]], 'lmfdb_iso': '327795.d', 'trace_hash': 1644553512779103084}
• 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': '0.0045199288711474031419692941023', 'prec': 110}, 'conductor': 327795, 'gens': [[1233, 41408, 1], [7351, 648235, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '3.1315085806746622724046347950', 'prec': 100}, {'__RealLiteral__': 0, 'data': '5.0081706128835897204260889263', 'prec': 100}], 'lmfdb_label': '327795.d8', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.078532923775167598566879094010', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.7748383767883673933797352867799764042', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[3251, -3255, 2]], 'xcoord_integral_points': [1233, 7953, 38953]}
• lmfdb_label 327795.d8 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 13764099
    {'degree': 2, 'field': [-10, -1, 1], 'lmfdb_label': '327795.d8', 'torsion': [4]}
  • id: 13764098
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [2, 2]}
  • id: 13764100
    {'degree': 2, 'field': [41, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [4]}
  • id: 13764102
    {'degree': 4, 'field': [46, 26, -25, -2, 1], 'lmfdb_label': '327795.d8', 'torsion': [8]}
  • id: 13764101
    {'degree': 4, 'field': [100, 0, 21, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [2, 4]}
  • id: 13764103
    {'degree': 4, 'field': [100, 10, 11, -1, 1], 'lmfdb_label': '327795.d8', 'torsion': [8]}
  • id: 13764104
    {'degree': 4, 'field': [961, 0, 102, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [8]}
  • id: 13764105
    {'degree': 4, 'field': [2601, 0, 62, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [8]}
  • id: 13764109
    {'degree': 8, 'field': [-25005, -47655, -52595, -16776, -2139, -903, -27, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [6]}
  • id: 13764108
    {'degree': 8, 'field': [10000, 0, -2100, 0, 341, 0, -21, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [2, 8]}
  • id: 13764107
    {'degree': 8, 'field': [16650, 5700, 1250, 400, 691, -20, 42, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [2, 8]}
  • id: 13764106
    {'degree': 8, 'field': [114850, 5100, -22350, 1200, 1091, -60, 42, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [4, 4]}
  • id: 13764116
    {'degree': 16, 'field': [65632103, 102014314, -69697784, -58885410, 15775087, 14493332, -1817870, -2258576, 178668, 227962, -17362, -13984, 1178, 504, -52, -8, 1], 'lmfdb_label': '327795.d8', 'torsion': [12]}
  • id: 13764110
    {'degree': 16, 'field': [66425625, 98280000, 93656250, 19335000, 52521100, 5104700, 7233050, 553800, 855381, 10180, 63494, -440, 2996, -20, 84, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [4, 8]}
  • id: 13764117
    {'degree': 16, 'field': [69472225, 0, 101063800, 0, 41701600, 0, 8415151, 0, 896632, 0, 61441, 0, 2881, 0, 82, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [12]}
  • id: 13764112
    {'degree': 16, 'field': [184483459, 29501735, -101680005, -6833732, 29921064, 1556079, -5590391, -433022, 683199, 63185, -54569, -4416, 2736, 146, -78, -2, 1], 'lmfdb_label': '327795.d8', 'torsion': [16]}
  • id: 13764115
    {'degree': 16, 'field': [625250025, 0, -359276925, 0, 1274284855, 0, 141147426, 0, -22932015, 0, 805093, 0, -3549, 0, 54, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [2, 6]}
  • id: 13764111
    {'degree': 16, 'field': [4045455625, 3224442500, -2438781250, -1494910500, 560720300, 212148100, -51102050, -16264020, 3388741, 440172, -77822, -4156, -460, 504, -52, -8, 1], 'lmfdb_label': '327795.d8', 'torsion': [16]}
  • id: 13764113
    {'degree': 16, 'field': [566611117796, -416865604480, 158872766032, -39671116160, 11924193348, -3456720800, 889948784, -161740800, 31920285, -5434000, 1101964, -122720, 18078, -1040, 212, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [16]}
  • id: 13764114
    {'degree': 16, 'field': [158702524002961, 0, 29050147783768, 0, 1866708406468, 0, 55720930936, 0, 806765590, 0, 5365096, 0, 28708, 0, 328, 0, 1], 'lmfdb_label': '327795.d8', 'torsion': [16]}
• 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: 8116959
    {'conductor': 327795, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '327795.d8', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8116960
    {'conductor': 327795, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '327795.d8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 8116961
    {'conductor': 327795, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '327795.d8', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8116962
    {'conductor': 327795, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '327795.d8', 'prime': 41, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 3717117
    {'adelic_gens': [[237145, 243376, 145878, 180073], [155999, 0, 0, 255839], [1, 0, 32, 1], [1, 32, 0, 1], [255809, 32, 255808, 33], [118573, 243376, 151454, 7545], [53055, 230912, 30217, 160065], [118081, 237144, 0, 1], [1, 32, 4, 129], [191389, 249608, 223614, 93317], [25, 16, 254104, 254729]], 'adelic_image': '255840.768.13.?', 'conductor': 327795, 'lmfdb_label': '327795.d8', 'prime': 0}
  • id: 1143575
    {'conductor': 327795, 'elladic_image': '8.24.0.67', 'lmfdb_label': '327795.d8', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 327795.d does not appear in ec_padic