Elliptic curve data - 495.a4

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '495a', 'Clabel': '495a1', 'Cnumber': 1, 'abc_quality': 0.7920712085843463, 'absD': 40095, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1320, 'ainvs': [1, -1, 1, 7, -8], 'analytic_rank': 1, 'bad_primes': [3, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 495, 'degree': 32, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.42950651620064936438259691264', 'prec': 97}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [59319, 55], 'lmfdb_iso': '495.a', 'lmfdb_label': '495.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 1, 0], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.3', '40.12.0.z.1', '60.12.0-4.c.1.2', '88.12.0.?', '110.6.0.?', '120.24.0.?', '132.12.0.?', '220.12.0.?', '264.24.0.?', '440.24.0.?', '660.24.0.?', '1320.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3186317800226628430785586238', 'prec': 97}, 'semistable': False, 'serre_invariants': [[3, 6, 55], [5, 6, 99], [11, 12, 45]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.97881266053470421008021953110', 'prec': 97}, 'szpiro_ratio': 2.8337811240101165, '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, -1, 0, 0, 3, 0, 1, 1, 0, 2, 0, 0, -1, -6, 0, -4, 1], 'aplist': [-1, 0, -1, 0, 1, 2, -6, -4, -4, -6, -8, -2, -2, 4, 12, 2, -4, -10, -16, -8, 14, 8, 4, -10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 495, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '495.a', 'trace_hash': 91216303966333709}
• 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': '2.3608294812753873057354581524', 'prec': 97}, 'conductor': 495, 'gens': [[2, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3186317800226628430785586238', 'prec': 97}], 'lmfdb_label': '495.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.9875553779555521990938230806', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3104268429635731064072771357487571982', 'prec': 127}, 'tamagawa_product': 2, 'torsion_generators': [[1, -1, 1]], 'xcoord_integral_points': [1, 2, 10]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': [2, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '495.a4'}
• ec_torsion_growth •

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

  
  
  • id: 22302
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '495.a4', 'torsion': [4]}
  • id: 22303
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '495.a4', 'torsion': [4]}
  • id: 22301
    {'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '495.a4', 'torsion': [2, 2]}
  • id: 22304
    {'degree': 4, 'field': [34, -23, 5, -1, 1], 'lmfdb_label': '495.a4', 'torsion': [2, 4]}
  • id: 22308
    {'degree': 8, 'field': [-3, -12, -21, -21, -18, -15, -6, 0, 1], 'lmfdb_label': '495.a4', 'torsion': [6]}
  • id: 22307
    {'degree': 8, 'field': [16, -16, 20, -4, 9, -9, 0, -1, 1], 'lmfdb_label': '495.a4', 'torsion': [8]}
  • id: 22306
    {'degree': 8, 'field': [49, 0, -34, 0, 35, 0, -14, 0, 1], 'lmfdb_label': '495.a4', 'torsion': [8]}
  • id: 22305
    {'degree': 8, 'field': [4096, 0, -1472, 0, 384, 0, -23, 0, 1], 'lmfdb_label': '495.a4', 'torsion': [2, 4]}
  • id: 22310
    {'degree': 16, 'field': [1, 0, 1, 0, -15, 0, 14, 0, 254, 0, 14, 0, -15, 0, 1, 0, 1], 'lmfdb_label': '495.a4', 'torsion': [2, 8]}
  • id: 22313
    {'degree': 16, 'field': [1, 4, -99, 626, -2194, 4908, -7457, 8098, -6603, 4156, -1973, 654, -109, -28, 24, -8, 1], 'lmfdb_label': '495.a4', 'torsion': [12]}
  • id: 22312
    {'degree': 16, 'field': [169, 0, 2090, 0, 2683, 0, 6647, 0, 4765, 0, 1442, 0, 295, 0, 29, 0, 1], 'lmfdb_label': '495.a4', 'torsion': [2, 6]}
  • id: 22314
    {'degree': 16, 'field': [256, 0, 256, -288, 688, -408, 112, 432, -311, 216, 28, -51, 43, -9, 4, 0, 1], 'lmfdb_label': '495.a4', 'torsion': [12]}
  • id: 22311
    {'degree': 16, 'field': [1156, 0, -768, 0, 209, 0, -692, 0, 744, 0, -362, 0, 132, 0, -20, 0, 1], 'lmfdb_label': '495.a4', 'torsion': [2, 8]}
  • id: 22309
    {'degree': 16, 'field': [207936, -700416, 1179648, -1409856, 1167472, -630560, 280352, -119808, 35580, -1168, -3568, 1820, -403, 14, 18, -6, 1], 'lmfdb_label': '495.a4', 'torsion': [4, 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: 5475
    {'conductor': 495, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '495.a4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5476
    {'conductor': 495, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '495.a4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5477
    {'conductor': 495, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '495.a4', 'prime': 11, '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: 1668018
    {'adelic_gens': [[169, 168, 1278, 175], [808, 3, 285, 442], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [499, 498, 618, 835], [1313, 8, 1312, 9], [439, 0, 0, 1319], [268, 441, 111, 886], [7, 6, 1314, 1315]], 'adelic_image': '1320.48.0.?', 'conductor': 495, 'lmfdb_label': '495.a4', 'prime': 0}
  • id: 2218
    {'conductor': 495, 'elladic_image': '4.6.0.1', 'lmfdb_label': '495.a4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 7606
    {'lmfdb_iso': '495.a', 'p': 13, 'prec': 20, 'unit': 68673702297886553638, 'val': 2}
  • id: 7608
    {'lmfdb_iso': '495.a', 'p': 17, 'prec': 20, 'unit': 54768245293043587501371, 'val': 1}
  • id: 7609
    {'lmfdb_iso': '495.a', 'p': 19, 'prec': 20, 'unit': 749826309682637209024763, 'val': 1}
  • id: 7613
    {'lmfdb_iso': '495.a', 'p': 23, 'prec': 20, 'unit': 44716277298051597809380776, 'val': 1}
  • id: 7605
    {'lmfdb_iso': '495.a', 'p': 29, 'prec': 20, 'unit': 5346828069996644997365741420, 'val': 1}
  • id: 7617
    {'lmfdb_iso': '495.a', 'p': 31, 'prec': 20, 'unit': 8574796192999942819461844974, 'val': 1}
  • id: 7601
    {'lmfdb_iso': '495.a', 'p': 37, 'prec': 20, 'unit': 187397252322702975114073102669, 'val': 1}
  • id: 7603
    {'lmfdb_iso': '495.a', 'p': 41, 'prec': 20, 'unit': 2014852069761477169812703009560, 'val': 1}
  • id: 7604
    {'lmfdb_iso': '495.a', 'p': 43, 'prec': 20, 'unit': 9872797671136281335496024701535, 'val': 1}
  • id: 7615
    {'lmfdb_iso': '495.a', 'p': 47, 'prec': 20, 'unit': 16617134706163323985370139000688, 'val': 1}
  • id: 7610
    {'lmfdb_iso': '495.a', 'p': 53, 'prec': 20, 'unit': 436202646659668068909528047561578, 'val': 1}
  • id: 7611
    {'lmfdb_iso': '495.a', 'p': 59, 'prec': 20, 'unit': 545521419970160167854383977646721, 'val': 1}
  • id: 7616
    {'lmfdb_iso': '495.a', 'p': 61, 'prec': 20, 'unit': 3298084002508714388650150462155088, 'val': 1}
  • id: 7600
    {'lmfdb_iso': '495.a', 'p': 67, 'prec': 20, 'unit': 35500270315518656420449739118430552, 'val': 1}
  • id: 7602
    {'lmfdb_iso': '495.a', 'p': 71, 'prec': 20, 'unit': 80937299401459884745275101409393763, 'val': 1}
  • id: 7612
    {'lmfdb_iso': '495.a', 'p': 73, 'prec': 20, 'unit': 62013580246777389863234375273173470, 'val': 1}
  • id: 7607
    {'lmfdb_iso': '495.a', 'p': 79, 'prec': 20, 'unit': 542589791789418837739433238360144941, 'val': 1}
  • id: 7599
    {'lmfdb_iso': '495.a', 'p': 83, 'prec': 20, 'unit': 1723866979688825506868167638555852430, 'val': 1}
  • id: 7614
    {'lmfdb_iso': '495.a', 'p': 89, 'prec': 20, 'unit': 3363387975405420406007796396910791127, 'val': 1}
  • id: 7598
    {'lmfdb_iso': '495.a', 'p': 97, 'prec': 20, 'unit': 23244356651196206127831020878151587294, 'val': 1}