Elliptic curve data - 1568.e2

Formats: - HTML - YAML - JSON - 2024-05-03T13:17:37.791077

• 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': '1568g', 'Clabel': '1568g3', 'Cnumber': 3, 'abc_quality': 1.172456969504371, 'absD': 60236288, 'ainvs': [0, 0, 0, -539, 4802], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 4, 'class_size': 4, 'cm': -16, 'conductor': 1568, 'degree': 384, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.35556932917609244371763340988', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [287496, 1], 'lmfdb_iso': '1568.e', 'lmfdb_label': '1568.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -11, -14], 'min_quad_twist_disc': -7, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4944407538016703049134574706', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1372461307715231908979670529', 'prec': 103}, 'szpiro_ratio': 4.143053605445654, '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, 2, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, 2, 0, 0, -6, -2, 0, 0, -10, 0, -2, -10, 0, 0, 14, 0, 10, 0, 0, 6, 0, 0, -10, -18], 'class_deg': 4, 'class_size': 4, 'conductor': 1568, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '1568.e', 'trace_hash': 1875721864117269597}
• 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': '0.49108470128716948767786398427', 'prec': 103}, 'conductor': 1568, 'gens': [[-14, 98, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4944407538016703049134574706', 'prec': 100}], 'lmfdb_label': '1568.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.9820892034157685460763917976', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9621148832548133741401093523738541723', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[14, 0, 1]], 'xcoord_integral_points': [-14, 14]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [1, 0], '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1568.e2'}
• ec_torsion_growth •

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

  
  
  • id: 77567
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [4]}
  • id: 77568
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [4]}
  • id: 77566
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [2, 2]}
  • id: 77569
    {'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [2, 4]}
  • id: 77573
    {'degree': 8, 'field': [-227, -652, -446, 92, -56, -16, 10, -4, 1], 'lmfdb_label': '1568.e2', 'torsion': [6]}
  • id: 77571
    {'degree': 8, 'field': [1, 0, -128, 0, 80, 0, -16, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [2, 8]}
  • id: 77572
    {'degree': 8, 'field': [64, 0, -48, 0, 18, 0, -6, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [8]}
  • id: 77570
    {'degree': 8, 'field': [64, 0, 0, 0, -2, 0, 0, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [2, 4]}
  • id: 77574
    {'degree': 8, 'field': [802, -892, 264, 72, -16, -12, 2, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [10]}
  • id: 77583
    {'degree': 16, 'field': [-887, 1032, 1354, -1104, -950, 120, -98, 264, 799, -192, -530, 72, 148, -12, -20, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [12]}
  • id: 77575
    {'degree': 16, 'field': [256, 0, -768, 0, 1152, 0, -1392, 0, 1057, 0, -348, 0, 72, 0, -12, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [4, 4]}
  • id: 77576
    {'degree': 16, 'field': [256, 0, 0, 0, 96, 0, 0, 0, 545, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [2, 8]}
  • id: 77582
    {'degree': 16, 'field': [505, 2220, 3060, -1200, -4278, 1160, 2272, -1200, 524, -1100, 1028, -504, 206, -96, 36, -8, 1], 'lmfdb_label': '1568.e2', 'torsion': [20]}
  • id: 77579
    {'degree': 16, 'field': [3742, 8376, 16604, 29472, 19096, 22728, 10868, 10632, 4288, 1404, -400, -264, -206, -48, -4, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [2, 6]}
  • id: 77584
    {'degree': 16, 'field': [6400, 0, 0, 0, -160, 0, 0, 0, -91, 0, 0, 0, -2, 0, 0, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [20]}
  • id: 77578
    {'degree': 16, 'field': [10201, 50500, 106790, 55684, -76314, -126000, -74134, -3372, 1366, 44, -1142, -148, 142, -24, 6, -4, 1], 'lmfdb_label': '1568.e2', 'torsion': [10]}
  • id: 77581
    {'degree': 16, 'field': [14641, 0, -67324, 0, 62548, 0, -32044, 0, 10858, 0, -2428, 0, 340, 0, -28, 0, 1], 'lmfdb_label': '1568.e2', 'torsion': [12]}
  • id: 77580
    {'degree': 16, 'field': [42457, 64268, -27132, -86128, -8198, 54504, 13344, -21744, -5364, 5748, 1236, -1208, -18, 96, 4, -8, 1], 'lmfdb_label': '1568.e2', 'torsion': [2, 10]}
  • id: 77577
    {'degree': 16, 'field': [219529, 294628, 97826, 41652, 140738, -2212, -16454, 21456, 1519, -5052, 1426, 280, -316, 36, 8, -4, 1], 'lmfdb_label': '1568.e2', 'torsion': [3, 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: 24208
    {'conductor': 1568, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1568.e2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 24209
    {'conductor': 1568, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1568.e2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• lmfdb_label 1568.e2 does not appear in ec_galrep
• ec_padic •

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

  
  
  • id: 41678
    {'lmfdb_iso': '1568.e', 'p': 5, 'prec': 20, 'unit': 12173236956899, 'val': 1}
  • id: 41671
    {'lmfdb_iso': '1568.e', 'p': 13, 'prec': 20, 'unit': 751888543927704543694, 'val': 1}
  • id: 41673
    {'lmfdb_iso': '1568.e', 'p': 17, 'prec': 20, 'unit': 33060192009724198811800, 'val': 1}
  • id: 41672
    {'lmfdb_iso': '1568.e', 'p': 29, 'prec': 20, 'unit': 6017321539537443252781175357, 'val': 1}
  • id: 41669
    {'lmfdb_iso': '1568.e', 'p': 37, 'prec': 20, 'unit': 196505131950123184589148590217, 'val': 1}
  • id: 41670
    {'lmfdb_iso': '1568.e', 'p': 41, 'prec': 20, 'unit': 141917612703433820099716536259, 'val': 1}
  • id: 41674
    {'lmfdb_iso': '1568.e', 'p': 53, 'prec': 20, 'unit': 3002080943678095423708762066130, 'val': 1}
  • id: 41677
    {'lmfdb_iso': '1568.e', 'p': 61, 'prec': 20, 'unit': 1541543281343428529301101564505235, 'val': 1}
  • id: 41675
    {'lmfdb_iso': '1568.e', 'p': 73, 'prec': 20, 'unit': 200186292848026068494836054375688139, 'val': 1}
  • id: 41676
    {'lmfdb_iso': '1568.e', 'p': 89, 'prec': 20, 'unit': 10513981729329876188457045508135851705, 'val': 1}
  • id: 41668
    {'lmfdb_iso': '1568.e', 'p': 97, 'prec': 20, 'unit': 40406911783782944209140233880740221079, 'val': 1}