Elliptic curve data - 18259.a1

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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': '18259a', 'Clabel': '18259a3', 'Cnumber': 3, 'abc_quality': 1.104947099482495, 'absD': 16862569939, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 31806, 'ainvs': [0, -1, 1, -739329, 244930132], 'analytic_rank': 1, 'bad_primes': [19, 31], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 18259, 'degree': 90720, 'elladic_images': ['27.36.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7504327592338909264846770459', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9], 'jinv': [-50357871050752, 19], 'lmfdb_iso': '18259.a', 'lmfdb_label': '18259.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -769, -8470], 'min_quad_twist_disc': -31, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '27.36.0.a.1', '38.2.0.a.1', '93.8.0.?', '114.8.0.?', '171.36.0.?', '279.24.0.?', '342.72.3.?', '513.324.16.?', '837.72.0.?', '1026.648.43.?', '3534.16.0.?', '5301.72.0.?', '10602.144.3.?', '15903.648.16.?', '31806.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7478483876626541071717586611', 'prec': 100}, 'semistable': False, 'serre_invariants': [[19, 20, 961], [31, 482, 19]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.033439156991317803520094883627', 'prec': 107}, 'szpiro_ratio': 5.31511435710819, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 2, -2, 3, 0, -1, 0, 1, 0, -3, -4, 4, 0, 6, 4, 3, 0, 1, -6], 'aplist': [0, 2, 3, -1, -3, 4, 3, 1, 0, -6, 0, -2, -6, 1, -3, -12, -6, 1, -4, 6, 7, -8, -12, -12, 8], 'class_deg': 9, 'class_size': 3, 'conductor': 18259, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '18259.a', 'trace_hash': 2176724210810431149}
• 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': '0.030171258336790699664130985633', 'prec': 107}, 'conductor': 18259, 'gens': [[50429, 290683, 10]], 'heights': [{'__RealLiteral__': 0, 'data': '4.7478483876626541071717586611', 'prec': 100}], 'lmfdb_label': '18259.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.74124767550677976128852268986', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.0386631620271090276080882361650144138', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [16, 19, 0], '3': [5, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [2, 0], '23': [1, 1, 0], '29': [1, 0], '31': 'a', '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '18259.a1'}
• ec_torsion_growth •

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

  
  
  • id: 934326
    {'degree': 2, 'field': [-23, -1, 1], 'lmfdb_label': '18259.a1', 'torsion': [3]}
  • id: 934327
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '18259.a1', 'torsion': [2]}
  • id: 934330
    {'degree': 6, 'field': [-24669, -5292, 4653, 327, -180, -3, 1], 'lmfdb_label': '18259.a1', 'torsion': [9]}
  • id: 934331
    {'degree': 6, 'field': [-15573, -531, 1618, 43, -64, -1, 1], 'lmfdb_label': '18259.a1', 'torsion': [6]}
  • id: 934328
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '18259.a1', 'torsion': [2, 2]}
  • id: 934329
    {'degree': 6, 'field': [1880, -904, 208, 21, 11, -1, 1], 'lmfdb_label': '18259.a1', 'torsion': [3]}
  • id: 934332
    {'degree': 12, 'field': [-290180351, 95294746, 13265036, -2263182, -199789, -296148, 92552, 5996, -4205, 274, 12, -6, 1], 'lmfdb_label': '18259.a1', 'torsion': [4]}
  • id: 934333
    {'degree': 12, 'field': [150544, 0, 210692, 0, 58125, 0, 9787, 0, 900, 0, 47, 0, 1], 'lmfdb_label': '18259.a1', 'torsion': [3, 3]}
  • id: 934334
    {'degree': 12, 'field': [265825, -257145, 297924, -133638, 90666, -35430, 16259, -4308, 1446, -258, 63, -6, 1], 'lmfdb_label': '18259.a1', 'torsion': [9]}
  • id: 934335
    {'degree': 12, 'field': [162970756, 0, -40930456, 0, 4367016, 0, -250325, 0, 8079, 0, -139, 0, 1], 'lmfdb_label': '18259.a1', 'torsion': [2, 6]}
  • id: 934336
    {'degree': 18, 'field': [131691982, -2053724, 127514410, -5329979, 57536245, -9801964, 16608462, -4035853, 3458991, -765559, 494347, -82597, 44753, -5363, 2433, -194, 74, -3, 1], 'lmfdb_label': '18259.a1', 'torsion': [6]}
  • id: 934337
    {'degree': 18, 'field': [274687059501, -750119706666, 893735363745, -600474585543, 222145886493, -19596361467, -19301803853, 7131193287, 36610173, -432980360, 42653916, 13136559, -1835011, -237153, 32925, 2294, -285, -9, 1], 'lmfdb_label': '18259.a1', '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: 410049
    {'conductor': 18259, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '18259.a1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 410050
    {'conductor': 18259, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '18259.a1', 'prime': 31, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1785843
    {'adelic_gens': [[30691, 6231, 8835, 11378], [31, 36, 25984, 25045], [8278, 16461, 6541, 30226], [31753, 54, 31752, 55], [1, 54, 0, 1], [20519, 0, 0, 31805], [1, 0, 54, 1], [28, 27, 729, 703]], 'adelic_image': '31806.1296.43.?', 'conductor': 18259, 'lmfdb_label': '18259.a1', 'prime': 0}
  • id: 85479
    {'conductor': 18259, 'elladic_image': '27.36.0.1', 'lmfdb_label': '18259.a1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 838430
    {'lmfdb_iso': '18259.a', 'p': 5, 'prec': 20, 'unit': 6197676438033, 'val': 1}
  • id: 838431
    {'lmfdb_iso': '18259.a', 'p': 7, 'prec': 20, 'unit': 3634219527590605, 'val': 1}
  • id: 838429
    {'lmfdb_iso': '18259.a', 'p': 11, 'prec': 20, 'unit': 27859752386771340626, 'val': 1}
  • id: 838435
    {'lmfdb_iso': '18259.a', 'p': 13, 'prec': 20, 'unit': 1064806087790141162516, 'val': 1}
  • id: 838437
    {'lmfdb_iso': '18259.a', 'p': 17, 'prec': 20, 'unit': 51851128079919743326518, 'val': 1}
  • id: 838434
    {'lmfdb_iso': '18259.a', 'p': 29, 'prec': 20, 'unit': 548282522358662204439314100, 'val': 1}
  • id: 838446
    {'lmfdb_iso': '18259.a', 'p': 37, 'prec': 20, 'unit': 416863972387948516099874440649, 'val': 1}
  • id: 838432
    {'lmfdb_iso': '18259.a', 'p': 41, 'prec': 20, 'unit': 430169689426106785264590862864, 'val': 1}
  • id: 838433
    {'lmfdb_iso': '18259.a', 'p': 43, 'prec': 20, 'unit': 432379610954042807144264049282331, 'val': -1}
  • id: 838444
    {'lmfdb_iso': '18259.a', 'p': 47, 'prec': 20, 'unit': 22025135948744710428750240907405, 'val': 1}
  • id: 838439
    {'lmfdb_iso': '18259.a', 'p': 53, 'prec': 20, 'unit': 301671211911005267012236081158051, 'val': 1}
  • id: 838440
    {'lmfdb_iso': '18259.a', 'p': 59, 'prec': 20, 'unit': 346916101588087322352375816485800, 'val': 1}
  • id: 838445
    {'lmfdb_iso': '18259.a', 'p': 61, 'prec': 20, 'unit': 66651709012718792317372522992116007, 'val': -1}
  • id: 838438
    {'lmfdb_iso': '18259.a', 'p': 67, 'prec': 20, 'unit': 180795838547241089293933329405180, 'val': 2}
  • id: 838443
    {'lmfdb_iso': '18259.a', 'p': 71, 'prec': 20, 'unit': 25779928727604753950640249718629723, 'val': 1}
  • id: 838441
    {'lmfdb_iso': '18259.a', 'p': 73, 'prec': 20, 'unit': 72262843213295607187515401580047594, 'val': 1}
  • id: 838436
    {'lmfdb_iso': '18259.a', 'p': 79, 'prec': 20, 'unit': 520487832595640400130167150868737426, 'val': 1}
  • id: 838428
    {'lmfdb_iso': '18259.a', 'p': 83, 'prec': 20, 'unit': 1942599216580755940447468182386235071, 'val': 1}
  • id: 838442
    {'lmfdb_iso': '18259.a', 'p': 89, 'prec': 20, 'unit': 10552303062668418672922586927523436854, 'val': 1}
  • id: 838427
    {'lmfdb_iso': '18259.a', 'p': 97, 'prec': 20, 'unit': 51770278474042553504946088138480517814, 'val': 1}