Elliptic curve data - 48510.j1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '48510r', 'Clabel': '48510r4', 'Cnumber': 4, 'abc_quality': 1.0393554700052399, 'absD': 407730423911580000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [1, -1, 0, -4656960450, -122320093527500], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 48510, 'degree': 23592960, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7974652305867148654906884662', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4], 'jinv': [130231365028993807856757649, 4753980000], 'lmfdb_iso': '48510.j', 'lmfdb_label': '48510.j1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -10560001, -13209092695], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.3', '56.12.0.z.1', '84.12.0.?', '88.12.0.?', '168.24.0.?', '264.24.0.?', '616.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '27.018743713935041227061560448', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2752040117250033672403894760', 'prec': 100}, 'szpiro_ratio': 7.266166740882118, '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, -1, 0, 1, -1, 0, 2, 0, 0, 1, 6, 0, -8, -1], 'aplist': [-1, 0, -1, 0, -1, 2, 6, -8, 0, 2, 4, -2, -2, 4, -4, -14, 4, -14, 12, 8, 2, -8, 16, 2, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 48510, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '48510.j', 'trace_hash': 1720640906169211637}
• 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': '0.00050299493315114590851446137575', 'prec': 113}, 'conductor': 48510, 'gens': [[21080465924379, 84354834636687370265, 11797]], 'heights': [{'__RealLiteral__': 0, 'data': '27.018743713935041227061560448', 'prec': 100}], 'lmfdb_label': '48510.j1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.018275695660231755579438070991', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9502906979014132726435343081017717144', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-157597, 157597, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 1], '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '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': '48510.j1'}
• ec_torsion_growth •

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

  
  
  • id: 2360179
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [2, 2]}
  • id: 2360180
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [4]}
  • id: 2360181
    {'degree': 2, 'field': [462, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [4]}
  • id: 2360182
    {'degree': 4, 'field': [1849, 0, -2, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [2, 4]}
  • id: 2360186
    {'degree': 8, 'field': [-654080, 62153, 32200, -259, -833, 35, 25, -4, 1], 'lmfdb_label': '48510.j1', 'torsion': [6]}
  • id: 2360184
    {'degree': 8, 'field': [16, -16, 160, -112, 90, 22, -17, -2, 1], 'lmfdb_label': '48510.j1', 'torsion': [8]}
  • id: 2360183
    {'degree': 8, 'field': [484, 0, 0, 0, -506, 0, 0, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [2, 4]}
  • id: 2360185
    {'degree': 8, 'field': [302500, 0, 48400, 0, 7194, 0, 88, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [8]}
  • id: 2360190
    {'degree': 16, 'field': [-573153200802, 977867238348, -532742283675, 182365446312, -56023111872, 5035618938, -913167717, -364300104, 34071433, 3750634, -401369, -40472, 6763, 718, -110, -8, 1], 'lmfdb_label': '48510.j1', 'torsion': [2, 6]}
  • id: 2360187
    {'degree': 16, 'field': [441, 0, 3937920, 0, 1131400, 0, 1025432, 0, 274278, 0, 2080, 0, -984, 0, 8, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [4, 4]}
  • id: 2360188
    {'degree': 16, 'field': [1185921, 0, 2635380, 0, 4706416, 0, 2268024, 0, 794607, 0, 134552, 0, 16368, 0, 132, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [2, 8]}
  • id: 2360189
    {'degree': 16, 'field': [3545518, -3812836, 648862, 67448, 44867, -9748, 80622, -84688, 51185, -20708, 10074, -3776, 1085, -260, 58, -8, 1], 'lmfdb_label': '48510.j1', 'torsion': [2, 8]}
  • id: 2360191
    {'degree': 16, 'field': [8538084, 0, 9399573, 0, 1608490, 0, 1689459, 0, 171915, 0, 10271, 0, 555, 0, 42, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [12]}
  • id: 2360192
    {'degree': 16, 'field': [50456121075360000, 0, 112218034585272, 0, 5000545280500, 0, -17406276888, 0, -1365736680, 0, 12352340, 0, -264, 0, -330, 0, 1], 'lmfdb_label': '48510.j1', 'torsion': [12]}
• 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: 1158304
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '48510.j1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1158305
    {'conductor': 48510, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '48510.j1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1158306
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '48510.j1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1158307
    {'conductor': 48510, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '48510.j1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1158308
    {'conductor': 48510, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '48510.j1', '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: 1987105
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [7, 6, 1842, 1843], [232, 1779, 1467, 880], [1231, 0, 0, 1847], [263, 1224, 1668, 1199], [844, 1233, 1311, 622], [1312, 393, 531, 1750]], 'adelic_image': '1848.48.0.?', 'conductor': 48510, 'lmfdb_label': '48510.j1', 'prime': 0}
  • id: 209232
    {'conductor': 48510, 'elladic_image': '4.6.0.1', 'lmfdb_label': '48510.j1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2434384
    {'lmfdb_iso': '48510.j', 'p': 13, 'prec': 20, 'unit': 1053547429809338096635, 'val': 1}
  • id: 2434386
    {'lmfdb_iso': '48510.j', 'p': 17, 'prec': 20, 'unit': 209852501622474152912545, 'val': 1}
  • id: 2434387
    {'lmfdb_iso': '48510.j', 'p': 19, 'prec': 20, 'unit': 1547809503856902102440461, 'val': 1}
  • id: 2434383
    {'lmfdb_iso': '48510.j', 'p': 29, 'prec': 20, 'unit': 5697404867485893628890564517, 'val': 1}
  • id: 2434394
    {'lmfdb_iso': '48510.j', 'p': 31, 'prec': 20, 'unit': 18484179035611239353656364403, 'val': 1}
  • id: 2434379
    {'lmfdb_iso': '48510.j', 'p': 37, 'prec': 20, 'unit': 341624180965713395919280728310, 'val': 1}
  • id: 2434381
    {'lmfdb_iso': '48510.j', 'p': 41, 'prec': 20, 'unit': 1769638740938692340690273242371, 'val': 1}
  • id: 2434382
    {'lmfdb_iso': '48510.j', 'p': 43, 'prec': 20, 'unit': 4137176543483309014151479588615, 'val': 1}
  • id: 2434392
    {'lmfdb_iso': '48510.j', 'p': 47, 'prec': 20, 'unit': 9755626330066202980014237066996, 'val': 1}
  • id: 2434388
    {'lmfdb_iso': '48510.j', 'p': 53, 'prec': 20, 'unit': 4111206965182245980577877387621, 'val': 1}
  • id: 2434389
    {'lmfdb_iso': '48510.j', 'p': 59, 'prec': 20, 'unit': 210490521715965910174946909632274, 'val': 1}
  • id: 2434393
    {'lmfdb_iso': '48510.j', 'p': 61, 'prec': 20, 'unit': 4937727622969158587241229539420723, 'val': 1}
  • id: 2434378
    {'lmfdb_iso': '48510.j', 'p': 67, 'prec': 20, 'unit': 38904774084724033607913902489792397, 'val': 1}
  • id: 2434380
    {'lmfdb_iso': '48510.j', 'p': 71, 'prec': 20, 'unit': 108005729810206319979537777073566894, 'val': 1}
  • id: 2434390
    {'lmfdb_iso': '48510.j', 'p': 73, 'prec': 20, 'unit': 155217096728561641060916034013254516, 'val': 1}
  • id: 2434385
    {'lmfdb_iso': '48510.j', 'p': 79, 'prec': 20, 'unit': 605359528075148831220953649691871543, 'val': 1}
  • id: 2434377
    {'lmfdb_iso': '48510.j', 'p': 83, 'prec': 20, 'unit': 658291968530160291385224116648824445, 'val': 1}
  • id: 2434391
    {'lmfdb_iso': '48510.j', 'p': 89, 'prec': 20, 'unit': 5357677324696725603436514000196249077, 'val': 1}
  • id: 2434376
    {'lmfdb_iso': '48510.j', 'p': 97, 'prec': 20, 'unit': 45799096195104970752164783482744719391, 'val': 1}