Elliptic curve data - 21840.cc5

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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': '21840cg', 'Clabel': '21840cg1', 'Cnumber': 1, 'abc_quality': 0.9925267429077052, 'absD': 3283073001062400, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 4368, 'ainvs': [0, 1, 0, -5920, -2764300], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 21840, 'degree': 147456, 'elladic_images': ['16.48.0.48'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6566971369529502416987742584', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 54, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [-5602762882081, 801531494400], 'lmfdb_iso': '21840.cc', 'lmfdb_label': '21840.cc5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -370, 43007], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.n.1.6', '16.48.0-16.e.2.5', '56.48.0-56.bv.1.10', '78.6.0.?', '112.96.0.?', '156.24.0.?', '312.48.0.?', '624.96.0.?', '2184.96.0.?', '4368.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.9608676523980826200309363075', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 39], [3, 4, 7280], [5, 6, 4368], [7, 8, 3120], [13, 14, 1680]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.96354995639300493228154213694', 'prec': 103}, 'szpiro_ratio': 4.32230596267728, '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, 1, 0, -1, 0, 1, 0, 4, 0, 1, 0, 1, 0, -6, 0, 4, 0], 'aplist': [0, 1, 1, -1, 4, 1, -6, 4, 8, -10, 0, -2, -6, -12, -8, -2, -4, -2, 4, -8, -14, -16, 4, -6, -6], 'class_deg': 8, 'class_size': 6, 'conductor': 21840, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '21840.cc', 'trace_hash': 631043050172331488}
• 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': '0.036392437973387612626767514096', 'prec': 107}, 'conductor': 21840, 'gens': [[10945, 573375, 8]], 'heights': [{'__RealLiteral__': 0, 'data': '8.9608676523980826200309363075', 'prec': 100}], 'lmfdb_label': '21840.cc5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19876385436700518087564274622', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.1243863722530403893552840119002856004', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[154, 0, 1]], 'xcoord_integral_points': [154]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [4, 0], '7': [3, 0], '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '21840.cc5'}
• ec_torsion_growth •

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

  
  
  • id: 1110920
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [4]}
  • id: 1110921
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [4]}
  • id: 1110919
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '21840.cc5', 'torsion': [2, 2]}
  • id: 1110924
    {'degree': 4, 'field': [-56, -176, -18, -2, 1], 'lmfdb_label': '21840.cc5', 'torsion': [8]}
  • id: 1110925
    {'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [8]}
  • id: 1110923
    {'degree': 4, 'field': [100, 0, -19, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [2, 4]}
  • id: 1110926
    {'degree': 4, 'field': [4624, 0, 137, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [8]}
  • id: 1110922
    {'degree': 4, 'field': [47775, 0, 0, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [2, 4]}
  • id: 1110930
    {'degree': 8, 'field': [-1457180, -1975840, -1034555, -262540, -33989, -2464, -149, -4, 1], 'lmfdb_label': '21840.cc5', 'torsion': [16]}
  • id: 1110931
    {'degree': 8, 'field': [-768, 0, -463, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [6]}
  • id: 1110929
    {'degree': 8, 'field': [196, 1232, 3872, 764, 109, 106, 2, -2, 1], 'lmfdb_label': '21840.cc5', 'torsion': [2, 8]}
  • id: 1110928
    {'degree': 8, 'field': [17488, 4248, -3758, -950, 401, 86, -24, -4, 1], 'lmfdb_label': '21840.cc5', 'torsion': [2, 8]}
  • id: 1110927
    {'degree': 8, 'field': [9821956, -2168728, 239432, -12496, 6349, -674, 2, -2, 1], 'lmfdb_label': '21840.cc5', 'torsion': [4, 4]}
  • id: 1110939
    {'degree': 16, 'field': [160000, 0, 234500, 0, 388825, 0, 187164, 0, 23052, 0, -486, 0, -164, 0, 8, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [12]}
  • id: 1110937
    {'degree': 16, 'field': [29404008, -75120336, 122340726, -107560650, 87718677, -43972848, 20247190, -5155736, 1763658, -346498, 100478, -18504, 4358, -616, 108, -8, 1], 'lmfdb_label': '21840.cc5', 'torsion': [2, 6]}
  • id: 1110933
    {'degree': 16, 'field': [65830144, 37485760, -37727256, -15798712, 19258020, 10077432, 600826, 522170, 276393, 4210, 14788, 1410, -366, 214, -6, -4, 1], 'lmfdb_label': '21840.cc5', 'torsion': [4, 8]}
  • id: 1110938
    {'degree': 16, 'field': [298865850, 193257150, -189886995, -13367304, 23169582, -19503468, 5877055, 863992, -656565, 339200, -113281, 24708, -4027, -70, 30, -8, 1], 'lmfdb_label': '21840.cc5', 'torsion': [12]}
  • id: 1110932
    {'degree': 16, 'field': [7428888481, 0, -6497989568, 0, 1521773008, 0, -7337456, 0, 2784670, 0, 153664, 0, 5488, 0, 112, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [2, 8]}
  • id: 1110935
    {'degree': 16, 'field': [64552581184, 0, 83830219200, 0, 28824398512, 0, 3325305984, 0, 97967340, 0, -80916, 0, 26197, 0, -90, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [16]}
  • id: 1110934
    {'degree': 16, 'field': [416365629696, 0, 22958229600, 0, 588298833, 0, 94582554, 0, 4477759, 0, -6484, 0, -2129, 0, 26, 0, 1], 'lmfdb_label': '21840.cc5', 'torsion': [16]}
  • id: 1110936
    {'degree': 16, 'field': [5161370863936, -25993714432, -381860493616, -28920758496, 35447270384, -4522578560, -99180248, -177311232, 109763668, -22913952, 2092777, -16090, -15841, 1764, -61, -2, 1], 'lmfdb_label': '21840.cc5', 'torsion': [2, 16]}
• 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: 498584
    {'conductor': 21840, 'conductor_valuation': 4, 'discriminant_valuation': 36, 'j_denominator_valuation': 24, 'kodaira_symbol': -32, 'lmfdb_label': '21840.cc5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 498585
    {'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21840.cc5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 498586
    {'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21840.cc5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 498587
    {'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21840.cc5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 498588
    {'conductor': 21840, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21840.cc5', 'prime': 13, '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: 1810096
    {'adelic_gens': [[15, 2, 4270, 4355], [3133, 16, 3488, 4053], [5, 4, 4364, 4365], [1, 16, 0, 1], [1472, 5, 4323, 4354], [4353, 16, 4352, 17], [1696, 5, 963, 4354], [1, 0, 16, 1], [1, 16, 1092, 1093], [2719, 4352, 3622, 801]], 'adelic_image': '4368.192.1.?', 'conductor': 21840, 'lmfdb_label': '21840.cc5', 'prime': 0}
  • id: 101009
    {'conductor': 21840, 'elladic_image': '16.48.0.48', 'lmfdb_label': '21840.cc5', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1027614
    {'lmfdb_iso': '21840.cc', 'p': 11, 'prec': 20, 'unit': 2558478274867265855, 'val': 1}
  • id: 1027615
    {'lmfdb_iso': '21840.cc', 'p': 17, 'prec': 20, 'unit': 186737386629733250786590, 'val': 1}
  • id: 1027616
    {'lmfdb_iso': '21840.cc', 'p': 19, 'prec': 20, 'unit': 1922664869618716390352043, 'val': 1}
  • id: 1027620
    {'lmfdb_iso': '21840.cc', 'p': 23, 'prec': 20, 'unit': 19530334613514543195854119, 'val': 1}
  • id: 1027612
    {'lmfdb_iso': '21840.cc', 'p': 29, 'prec': 20, 'unit': 1810486134470484368592192036, 'val': 1}
  • id: 1027608
    {'lmfdb_iso': '21840.cc', 'p': 37, 'prec': 20, 'unit': 532896593233853705431281681113, 'val': 1}
  • id: 1027610
    {'lmfdb_iso': '21840.cc', 'p': 41, 'prec': 20, 'unit': 1374697643429766203342771112253, 'val': 1}
  • id: 1027611
    {'lmfdb_iso': '21840.cc', 'p': 43, 'prec': 20, 'unit': 1592762805285438514179926586486, 'val': 1}
  • id: 1027622
    {'lmfdb_iso': '21840.cc', 'p': 47, 'prec': 20, 'unit': 14721648058810219634973950896816, 'val': 1}
  • id: 1027617
    {'lmfdb_iso': '21840.cc', 'p': 53, 'prec': 20, 'unit': 133569875563068756709893297132686, 'val': 1}
  • id: 1027618
    {'lmfdb_iso': '21840.cc', 'p': 59, 'prec': 20, 'unit': 3925948115057142275483229156782642, 'val': 1}
  • id: 1027623
    {'lmfdb_iso': '21840.cc', 'p': 61, 'prec': 20, 'unit': 6941827036403681718044746400052009, 'val': 1}
  • id: 1027607
    {'lmfdb_iso': '21840.cc', 'p': 67, 'prec': 20, 'unit': 1413574514323115227818081371229294, 'val': 1}
  • id: 1027609
    {'lmfdb_iso': '21840.cc', 'p': 71, 'prec': 20, 'unit': 80943037530102936359701464619648870, 'val': 1}
  • id: 1027619
    {'lmfdb_iso': '21840.cc', 'p': 73, 'prec': 20, 'unit': 208264952650339713986388270393075076, 'val': 1}
  • id: 1027613
    {'lmfdb_iso': '21840.cc', 'p': 79, 'prec': 20, 'unit': 217322721309876832328300437327458457, 'val': 1}
  • id: 1027606
    {'lmfdb_iso': '21840.cc', 'p': 83, 'prec': 20, 'unit': 1019484414938619327316555505921631020, 'val': 1}
  • id: 1027621
    {'lmfdb_iso': '21840.cc', 'p': 89, 'prec': 20, 'unit': 5198817552563819791734410047273855903, 'val': 1}
  • id: 1027605
    {'lmfdb_iso': '21840.cc', 'p': 97, 'prec': 20, 'unit': 7013730459854280356139329971259966663, 'val': 1}