Elliptic curve data - 51744.cl4

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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': '51744bn', 'Clabel': '51744bn2', 'Cnumber': 2, 'abc_quality': 0.894198818057269, 'absD': 38181614456832, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [0, 1, 0, 5423, -252673], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 51744, 'degree': 122880, 'elladic_images': ['8.12.0.12'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2903424272071465227579256021', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 63, 'isogeny_degrees': [1, 2, 4], 'jinv': [36594368, 79233], 'lmfdb_iso': '51744.cl', 'lmfdb_label': '51744.cl4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 111, 705], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.2', '84.12.0.?', '132.12.0.?', '168.24.0.?', '264.24.0.?', '308.12.0.?', '616.24.0.?', '924.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '13.712614796062519215296869557', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1617], [3, 4, 17248], [7, 32, 1056], [11, 12, 4704]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37575982788045543921198289108', 'prec': 107}, 'szpiro_ratio': 3.5394213714586074, '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, 1, 0, 2, 0, 0, 0, 1, 0, -1, 0, 2, 0, 2, 0, 2, 0, -4, 0], 'aplist': [0, 1, 2, 0, -1, 2, 2, -4, 8, 2, 4, -2, -6, -12, 0, 2, -4, -14, -8, -8, -14, 16, 0, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 51744, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '51744.cl', 'trace_hash': 900318346163257019}
• 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': '0.075722127627618524423555646818', 'prec': 107}, 'conductor': 51744, 'gens': [[744493, 535943400, 133]], 'heights': [{'__RealLiteral__': 0, 'data': '13.712614796062519215296869557', 'prec': 100}], 'lmfdb_label': '51744.cl4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.33676439020245934314167858231', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.2358407197544313395368187930126539306', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[37, 0, 1]], 'xcoord_integral_points': [37]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': 'a', '11': [5, 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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '51744.cl4'}
• ec_torsion_growth •

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

  
  
  • id: 2506031
    {'degree': 2, 'field': [-19, -1, 1], 'lmfdb_label': '51744.cl4', 'torsion': [4]}
  • id: 2506032
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '51744.cl4', 'torsion': [4]}
  • id: 2506030
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '51744.cl4', 'torsion': [2, 2]}
  • id: 2506033
    {'degree': 4, 'field': [9, 0, 27, 0, 1], 'lmfdb_label': '51744.cl4', 'torsion': [2, 4]}
  • id: 2506034
    {'degree': 8, 'field': [1089, 0, 0, 0, 759, 0, 0, 0, 1], 'lmfdb_label': '51744.cl4', 'torsion': [2, 4]}
  • id: 2506035
    {'degree': 8, 'field': [1089, 0, 39930, 0, -3179, 0, 22, 0, 1], 'lmfdb_label': '51744.cl4', 'torsion': [8]}
  • id: 2506036
    {'degree': 8, 'field': [66049, 0, 19292, 0, -318, 0, -28, 0, 1], 'lmfdb_label': '51744.cl4', 'torsion': [8]}
  • id: 2506037
    {'degree': 8, 'field': [3645441, 335520, -173628, 18060, 9282, -336, -140, -4, 1], 'lmfdb_label': '51744.cl4', 'torsion': [6]}
  • id: 2506038
    {'degree': 16, 'field': [3418801, 0, -7678300, 0, 5236270, 0, 2200892, 0, 552523, 0, -2980, 0, 1546, 0, 8, 0, 1], 'lmfdb_label': '51744.cl4', 'torsion': [4, 4]}
  • id: 2506040
    {'degree': 16, 'field': [914467401, 328380156, -281083824, -90603900, 35532000, 11167416, -2821092, -722604, 123385, 29920, 2464, -4868, 1054, -140, 40, -8, 1], 'lmfdb_label': '51744.cl4', 'torsion': [2, 8]}
  • id: 2506039
    {'degree': 16, 'field': [2523726913, -1528504228, 1913564432, -830416548, 573317840, -210786968, 106631884, -33766044, 11767681, -2352600, 608152, -78244, 15710, -1260, 200, -8, 1], 'lmfdb_label': '51744.cl4', 'torsion': [2, 8]}
  • id: 2506042
    {'degree': 16, 'field': [7501811769, 0, 6638826912, 0, 1557928738, 0, 114636288, 0, -1616649, 0, -319520, 0, 2202, 0, 0, 0, 1], 'lmfdb_label': '51744.cl4', 'torsion': [12]}
  • id: 2506043
    {'degree': 16, 'field': [26097680574, 2885876028, -2089760840, -1664884016, 1016299492, -226921508, 86331658, -9578876, 2931387, -386364, 107250, -18140, 4540, -728, 124, -8, 1], 'lmfdb_label': '51744.cl4', 'torsion': [12]}
  • id: 2506041
    {'degree': 16, 'field': [858124135801, -30706017808, 36432321972, -18556066448, -152337502, -987585612, 180865408, -13024612, 10326807, -789724, 233320, -38148, 3338, -836, 60, -4, 1], 'lmfdb_label': '51744.cl4', '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: 1238458
    {'conductor': 51744, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '51744.cl4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1238459
    {'conductor': 51744, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '51744.cl4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1238460
    {'conductor': 51744, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '51744.cl4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1238461
    {'conductor': 51744, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '51744.cl4', '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: 2007904
    {'adelic_gens': [[1163, 1158, 698, 1619], [1, 0, 8, 1], [1688, 3, 1517, 2], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [7, 6, 1842, 1843], [263, 1840, 1052, 1815], [620, 1, 1255, 6], [1616, 685, 1613, 1584]], 'adelic_image': '1848.48.0.?', 'conductor': 51744, 'lmfdb_label': '51744.cl4', 'prime': 0}
  • id: 221412
    {'conductor': 51744, 'elladic_image': '8.12.0.12', 'lmfdb_label': '51744.cl4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2604385
    {'lmfdb_iso': '51744.cl', 'p': 5, 'prec': 20, 'unit': 7641585177621, 'val': 1}
  • id: 2604391
    {'lmfdb_iso': '51744.cl', 'p': 13, 'prec': 20, 'unit': 47190686352458445995, 'val': 2}
  • id: 2604393
    {'lmfdb_iso': '51744.cl', 'p': 17, 'prec': 20, 'unit': 101113785947258838631954, 'val': 1}
  • id: 2604394
    {'lmfdb_iso': '51744.cl', 'p': 19, 'prec': 20, 'unit': 1490644414703395044551667, 'val': 1}
  • id: 2604397
    {'lmfdb_iso': '51744.cl', 'p': 23, 'prec': 20, 'unit': 51333776808065184116630409, 'val': 1}
  • id: 2604390
    {'lmfdb_iso': '51744.cl', 'p': 29, 'prec': 20, 'unit': 4276223659563350802078806005, 'val': 1}
  • id: 2604387
    {'lmfdb_iso': '51744.cl', 'p': 31, 'prec': 20, 'unit': 10825687129837802144115025274, 'val': 1}
  • id: 2604401
    {'lmfdb_iso': '51744.cl', 'p': 37, 'prec': 20, 'unit': 300255437681474643763980829540, 'val': 1}
  • id: 2604388
    {'lmfdb_iso': '51744.cl', 'p': 41, 'prec': 20, 'unit': 3533536651155009780871993792103, 'val': 1}
  • id: 2604389
    {'lmfdb_iso': '51744.cl', 'p': 43, 'prec': 20, 'unit': 3502103109795163089439075648444, 'val': 1}
  • id: 2604395
    {'lmfdb_iso': '51744.cl', 'p': 53, 'prec': 20, 'unit': 4445879616551381204395868294538, 'val': 2}
  • id: 2604399
    {'lmfdb_iso': '51744.cl', 'p': 59, 'prec': 20, 'unit': 2861096664479990706450353022242399, 'val': 1}
  • id: 2604400
    {'lmfdb_iso': '51744.cl', 'p': 61, 'prec': 20, 'unit': 1786440585013473902225712764368595, 'val': 1}
  • id: 2604384
    {'lmfdb_iso': '51744.cl', 'p': 67, 'prec': 20, 'unit': 35308468355844501004571990393888697, 'val': 1}
  • id: 2604386
    {'lmfdb_iso': '51744.cl', 'p': 71, 'prec': 20, 'unit': 54452333645766919335280716907483206, 'val': 1}
  • id: 2604396
    {'lmfdb_iso': '51744.cl', 'p': 73, 'prec': 20, 'unit': 56942737461755583157529875896704990, 'val': 1}
  • id: 2604392
    {'lmfdb_iso': '51744.cl', 'p': 79, 'prec': 20, 'unit': 161025301152320639444499891808905296, 'val': 1}
  • id: 2604398
    {'lmfdb_iso': '51744.cl', 'p': 89, 'prec': 20, 'unit': 4013410050050799112395507416898905444, 'val': 1}
  • id: 2604383
    {'lmfdb_iso': '51744.cl', 'p': 97, 'prec': 20, 'unit': 8820552961178482434360768570035412750, 'val': 1}