Elliptic curve data - 75810.l8

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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': '75810l', 'Clabel': '75810l7', 'Cnumber': 7, 'abc_quality': 1.0876511700840974, 'absD': 638220562413574218750, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 15960, 'ainvs': [1, 1, 0, 263162, 1214466442], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 19], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 75810, 'degree': 3981312, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6712455026191449888304563166', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 12, 'iso_nlabel': 11, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [42841933504271, 13565917968750], 'lmfdb_iso': '75810.l', 'lmfdb_label': '75810.l8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 729, -176985], 'min_quad_twist_disc': -19, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.48.0.bu.2', '56.12.0.v.1', '57.8.0-3.a.1.2', '84.48.0.?', '114.24.0.?', '120.96.1.?', '152.12.0.?', '168.96.1.?', '228.48.0.?', '456.96.0.?', '532.12.0.?', '840.192.5.?', '1064.24.0.?', '1596.96.0.?', '2280.192.1.?', '3192.192.1.?', '15960.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0922103264089371800285035347', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2527], [3, 4, 722], [5, 6, 15162], [7, 8, 10830], [19, 182, 210]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1990260130359247588259426007', 'prec': 100}, 'szpiro_ratio': 4.926858116624157, '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, 1, -1, 1, 1, 0, -1, -2, -1, 1, 1, -6, -1, 0, -1], 'aplist': [-1, -1, -1, 1, 0, -2, -6, 0, 0, 6, 4, -2, -6, 8, -12, -6, 12, 2, -8, 0, 14, 16, 12, -6, -14], 'class_deg': 12, 'class_size': 8, 'conductor': 75810, 'isogeny_matrix': [[1, 3, 2, 4, 6, 12, 12, 4], [3, 1, 6, 12, 2, 4, 4, 12], [2, 6, 1, 2, 3, 6, 6, 2], [4, 12, 2, 1, 6, 12, 3, 4], [6, 2, 3, 6, 1, 2, 2, 6], [12, 4, 6, 12, 2, 1, 4, 3], [12, 4, 6, 3, 2, 4, 1, 12], [4, 12, 2, 4, 6, 3, 12, 1]], 'lmfdb_iso': '75810.l', 'trace_hash': 1914018885338562391}
• 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': '0.0047839390383333659262738784437', 'prec': 110}, 'conductor': 75810, 'gens': [[-173, 34201, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0922103264089371800285035347', 'prec': 100}], 'lmfdb_label': '75810.l8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12571812522335185683102407982', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1563451177088235216054000764846923709', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-3941, 3941, 2]], 'xcoord_integral_points': [-173, 2921]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 2], '3': [1, 0], '5': [1, 0], '7': [2, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': 'a', '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '75810.l8'}
• ec_torsion_growth •

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

  
  
  • id: 3583601
    {'degree': 2, 'field': [-38, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [4]}
  • id: 3583603
    {'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '75810.l8', 'torsion': [6]}
  • id: 3583600
    {'degree': 2, 'field': [14, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [2, 2]}
  • id: 3583602
    {'degree': 2, 'field': [133, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [4]}
  • id: 3583606
    {'degree': 4, 'field': [64, 0, -22, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [12]}
  • id: 3583604
    {'degree': 4, 'field': [169, 0, -12, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [2, 4]}
  • id: 3583605
    {'degree': 4, 'field': [798, 0, 1, -2, 1], 'lmfdb_label': '75810.l8', 'torsion': [2, 6]}
  • id: 3583607
    {'degree': 4, 'field': [1246, -14, 15, -2, 1], 'lmfdb_label': '75810.l8', 'torsion': [12]}
  • id: 3583608
    {'degree': 6, 'field': [245, -237, 72, -19, 18, -3, 1], 'lmfdb_label': '75810.l8', 'torsion': [6]}
  • id: 3583610
    {'degree': 8, 'field': [-884, 7920, -8472, 10080, 3248, -360, -132, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [8]}
  • id: 3583609
    {'degree': 8, 'field': [9948, 9968, 1256, 672, 776, -56, 52, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [2, 4]}
  • id: 3583612
    {'degree': 8, 'field': [17689, 0, 6384, 0, 842, 0, -48, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [2, 12]}
  • id: 3583611
    {'degree': 8, 'field': [8172004, -189924, 173806, 79800, 1686, -798, 325, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [8]}
  • id: 3583613
    {'degree': 12, 'field': [60025, -58065, 38529, -7754, -3729, 6429, -1156, -147, 195, -16, -9, -3, 1], 'lmfdb_label': '75810.l8', 'torsion': [3, 6]}
  • id: 3583615
    {'degree': 12, 'field': [116267, -80646, 4389, 17554, 3840, -9606, 7569, -2694, 948, -206, 57, -6, 1], 'lmfdb_label': '75810.l8', 'torsion': [12]}
  • id: 3583616
    {'degree': 12, 'field': [3323117, -1259160, 76407, -117554, -41934, 46428, -189, -1938, 462, 16, 3, -6, 1], 'lmfdb_label': '75810.l8', 'torsion': [12]}
  • id: 3583614
    {'degree': 12, 'field': [4375175, -4983342, 1403781, -693374, 596436, -222654, 104769, -19398, 5664, -566, 129, -6, 1], 'lmfdb_label': '75810.l8', 'torsion': [2, 6]}
  • id: 3583617
    {'degree': 16, 'field': [3374569, 6378064, 6027392, 2499056, 877930, 472808, 250880, -6496, -6577, 14168, 1568, -1792, 358, -56, 0, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [4, 4]}
  • id: 3583620
    {'degree': 16, 'field': [86044176, 0, -38220864, 0, 4843072, 0, 3178912, 0, 615480, 0, 58256, 0, 3216, 0, 88, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [2, 12]}
  • id: 3583621
    {'degree': 16, 'field': [148937616, 0, -390235968, 0, 71932032, 0, -4339488, 0, 336088, 0, -37424, 0, 1728, 0, -56, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [24]}
  • id: 3583619
    {'degree': 16, 'field': [3857905636, -467900160, 1336926656, -422236640, 103371736, 23087120, 27801296, -4014080, -1398776, 161840, 18224, -560, 2068, -280, -40, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [2, 8]}
  • id: 3583618
    {'degree': 16, 'field': [10585528996, 0, 857359272, 0, 206039848, 0, -103740, 0, 794301, 0, -11280, 0, 1258, 0, -12, 0, 1], 'lmfdb_label': '75810.l8', 'torsion': [2, 8]}
  • id: 3583622
    {'degree': 16, 'field': [41190932736, 7134378624, -6314176224, -1571387904, 616705576, 192935488, -48192592, -13227252, 2586997, 454196, -65768, -12916, 1546, 252, -16, -8, 1], 'lmfdb_label': '75810.l8', 'torsion': [24]}
  • id: 3583623
    {'degree': 18, 'field': [14835984876, -50006074680, 71494676820, -54389326938, 20431794114, -69264084, -3214716719, 1043486157, 72364680, -101649566, 9101619, 4636161, -658128, -122571, 16881, 1666, -204, -9, 1], 'lmfdb_label': '75810.l8', 'torsion': [18]}
• 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: 1842321
    {'conductor': 75810, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '75810.l8', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1842322
    {'conductor': 75810, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '75810.l8', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1842323
    {'conductor': 75810, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '75810.l8', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1842324
    {'conductor': 75810, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '75810.l8', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1842325
    {'conductor': 75810, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '75810.l8', 'prime': 19, '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: 2164924
    {'adelic_gens': [[1, 24, 0, 1], [1, 0, 24, 1], [12256, 7581, 11115, 10546], [1, 12, 12, 145], [3991, 10944, 1482, 3649], [8646, 6289, 12635, 15296], [15, 106, 14654, 6731], [9577, 10944, 684, 3649], [2661, 4484, 14288, 1293], [11759, 0, 0, 15959], [15937, 24, 15936, 25]], 'adelic_image': '15960.384.5.?', 'conductor': 75810, 'lmfdb_label': '75810.l8', 'prime': 0}
  • id: 313142
    {'conductor': 75810, 'elladic_image': '4.6.0.1', 'lmfdb_label': '75810.l8', 'modell_image': '2B', 'prime': 2}
  • id: 313143
    {'conductor': 75810, 'elladic_image': '3.4.0.1', 'lmfdb_label': '75810.l8', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 3901265
    {'lmfdb_iso': '75810.l', 'p': 13, 'prec': 20, 'unit': 349926741449955259517, 'val': 1}
  • id: 3901267
    {'lmfdb_iso': '75810.l', 'p': 17, 'prec': 20, 'unit': 124160537716710898424462, 'val': 1}
  • id: 3901264
    {'lmfdb_iso': '75810.l', 'p': 29, 'prec': 20, 'unit': 4954780731188143650737586929, 'val': 1}
  • id: 3901275
    {'lmfdb_iso': '75810.l', 'p': 31, 'prec': 20, 'unit': 13461116334369711284525214957, 'val': 1}
  • id: 3901261
    {'lmfdb_iso': '75810.l', 'p': 37, 'prec': 20, 'unit': 232365534034127921642189015269, 'val': 1}
  • id: 3901262
    {'lmfdb_iso': '75810.l', 'p': 41, 'prec': 20, 'unit': 2476151314923909026633587985864, 'val': 1}
  • id: 3901263
    {'lmfdb_iso': '75810.l', 'p': 43, 'prec': 20, 'unit': 6227195095894501165488606261801, 'val': 1}
  • id: 3901273
    {'lmfdb_iso': '75810.l', 'p': 47, 'prec': 20, 'unit': 20109875672130546180490249400679, 'val': 1}
  • id: 3901269
    {'lmfdb_iso': '75810.l', 'p': 53, 'prec': 20, 'unit': 58851921046675663672244420758592, 'val': 1}
  • id: 3901270
    {'lmfdb_iso': '75810.l', 'p': 59, 'prec': 20, 'unit': 1200546431137766207924500346141906, 'val': 1}
  • id: 3901274
    {'lmfdb_iso': '75810.l', 'p': 61, 'prec': 20, 'unit': 2549552388537156308000848875066152, 'val': 1}
  • id: 3901260
    {'lmfdb_iso': '75810.l', 'p': 67, 'prec': 20, 'unit': 5507265116293193736667588167630263, 'val': 1}
  • id: 3901271
    {'lmfdb_iso': '75810.l', 'p': 73, 'prec': 20, 'unit': 232613860380246895974479421653144001, 'val': 1}
  • id: 3901266
    {'lmfdb_iso': '75810.l', 'p': 79, 'prec': 20, 'unit': 1005016806356889723291950063812113985, 'val': 1}
  • id: 3901268
    {'lmfdb_iso': '75810.l', 'p': 83, 'prec': 20, 'unit': 58803560262406182041415088251131571, 'val': 1}
  • id: 3901272
    {'lmfdb_iso': '75810.l', 'p': 89, 'prec': 20, 'unit': 5735648774601874846216668311851559744, 'val': 1}
  • id: 3901259
    {'lmfdb_iso': '75810.l', 'p': 97, 'prec': 20, 'unit': 50463483304231517612900264600617177040, 'val': 1}