Elliptic curve data - 121680.l1

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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': '121680w', 'Clabel': '121680w1', 'Cnumber': 1, 'abc_quality': 1.181532960731746, 'absD': 49280400, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 780, 'ainvs': [0, 0, 0, -3783, 89557], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 121680, 'degree': 69120, 'elladic_images': ['2.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.64643538084058550463056522453', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 11, 'isogeny_degrees': [1], 'jinv': [3037375744, 25], 'lmfdb_iso': '121680.l', 'lmfdb_label': '121680.l1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -420, 3457], 'min_quad_twist_disc': 12, 'modell_images': ['2Cn'], 'modm_images': ['2.2.0.a.1', '26.6.0.a.1', '780.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '2.8541270844726596078888063114', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1521], [3, 2, 13520], [5, 6, 24336], [13, 38, 720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56141138325704056688171600801', 'prec': 107}, 'szpiro_ratio': 3.102566892841707, '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, 0, 0, -1, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0], 'aplist': [0, 0, -1, -3, -1, 0, -1, -1, -5, -3, 8, -9, -5, -9, -8, 10, -3, -5, 3, 1, 14, -8, 0, 3, -5], 'class_deg': 1, 'class_size': 1, 'conductor': 121680, 'isogeny_matrix': [[1]], 'lmfdb_iso': '121680.l', 'trace_hash': 1227341453766398089}
• 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': '0.27448167947984998858824359591', 'prec': 103}, 'conductor': 121680, 'gens': [[36, 5, 1], [129, 265, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '0.94230267540495794262921909794', 'prec': 103}, {'__RealLiteral__': 0, 'data': '3.0308425406706602798586850914', 'prec': 100}], 'lmfdb_label': '121680.l1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '1.8035686175246893972359915311', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.295228079964254165797308683768660223', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [-12, 36]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': [2, 0], '11': [6, 0], '13': 'a', '17': [2, 0], '19': [2, 0], '23': [2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '121680.l1'}
• ec_torsion_growth •

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

  
  
  • id: 5556068
    {'degree': 3, 'field': [-1, -4, -1, 1], 'lmfdb_label': '121680.l1', 'torsion': [2, 2]}
  • id: 5556069
    {'degree': 8, 'field': [-783, 918, -212, -530, 254, 22, 8, -2, 1], 'lmfdb_label': '121680.l1', 'torsion': [3]}
  • id: 5556070
    {'degree': 12, 'field': [1248649, -1172896, -35870, 282034, -26526, -16518, -10394, 2094, 669, 8, -42, -2, 1], 'lmfdb_label': '121680.l1', 'torsion': [2, 4]}
• 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: 2994523
    {'conductor': 121680, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '121680.l1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2994524
    {'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '121680.l1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2994525
    {'conductor': 121680, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '121680.l1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2994526
    {'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '121680.l1', 'prime': 13, 'reduction_type': 0, '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: 2458009
    {'adelic_gens': [[1, 0, 4, 1], [1, 2, 2, 5], [1, 4, 0, 1], [424, 261, 123, 1], [211, 264, 216, 271], [3, 2, 772, 775], [389, 516, 390, 779], [777, 4, 776, 5], [259, 0, 0, 779]], 'adelic_image': '780.12.0.?', 'conductor': 121680, 'lmfdb_label': '121680.l1', 'prime': 0}
  • id: 477527
    {'conductor': 121680, 'elladic_image': '2.2.0.1', 'lmfdb_label': '121680.l1', 'modell_image': '2Cn', 'prime': 2}
• ec_padic •

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

  
  
  • id: 6360514
    {'lmfdb_iso': '121680.l', 'p': 7, 'prec': 20, 'unit': 1217929506746303, 'val': 2}
  • id: 6360519
    {'lmfdb_iso': '121680.l', 'p': 11, 'prec': 20, 'unit': 4744346142053741973, 'val': 3}
  • id: 6360520
    {'lmfdb_iso': '121680.l', 'p': 17, 'prec': 20, 'unit': 28633998749309781063224, 'val': 2}
  • id: 6360521
    {'lmfdb_iso': '121680.l', 'p': 19, 'prec': 20, 'unit': 1923118346658197665065167, 'val': 2}
  • id: 6360525
    {'lmfdb_iso': '121680.l', 'p': 23, 'prec': 20, 'unit': 74432372072725475093590001, 'val': 2}
  • id: 6360517
    {'lmfdb_iso': '121680.l', 'p': 29, 'prec': 20, 'unit': 3531646515648973590629525098, 'val': 2}
  • id: 6360530
    {'lmfdb_iso': '121680.l', 'p': 31, 'prec': 20, 'unit': 18770296025718158788822644930, 'val': 2}
  • id: 6360513
    {'lmfdb_iso': '121680.l', 'p': 37, 'prec': 20, 'unit': 150623822748175757719259542693, 'val': 2}
  • id: 6360515
    {'lmfdb_iso': '121680.l', 'p': 41, 'prec': 20, 'unit': 1316183531469706929589558653589, 'val': 2}
  • id: 6360516
    {'lmfdb_iso': '121680.l', 'p': 43, 'prec': 20, 'unit': 6286313581260705798679229304322, 'val': 2}
  • id: 6360528
    {'lmfdb_iso': '121680.l', 'p': 47, 'prec': 20, 'unit': 7348263216417326583077610963900, 'val': 2}
  • id: 6360522
    {'lmfdb_iso': '121680.l', 'p': 53, 'prec': 20, 'unit': 513134171302322771465885226687802, 'val': 2}
  • id: 6360523
    {'lmfdb_iso': '121680.l', 'p': 59, 'prec': 20, 'unit': 3084122522143463307769835946483205, 'val': 2}
  • id: 6360529
    {'lmfdb_iso': '121680.l', 'p': 61, 'prec': 20, 'unit': 6170843901305691745167893141397691, 'val': 2}
  • id: 6360512
    {'lmfdb_iso': '121680.l', 'p': 67, 'prec': 20, 'unit': 31767839402661859299868628058332033, 'val': 2}
  • id: 6360527
    {'lmfdb_iso': '121680.l', 'p': 71, 'prec': 20, 'unit': 1048638635729663522363179344735166, 'val': 0}
  • id: 6360524
    {'lmfdb_iso': '121680.l', 'p': 73, 'prec': 20, 'unit': 229365887498143595263914107038227978, 'val': 2}
  • id: 6360518
    {'lmfdb_iso': '121680.l', 'p': 79, 'prec': 20, 'unit': 773030235979442589481041532680983307, 'val': 2}
  • id: 6360526
    {'lmfdb_iso': '121680.l', 'p': 89, 'prec': 20, 'unit': 8129589087086132544296485328537674395, 'val': 2}
  • id: 6360511
    {'lmfdb_iso': '121680.l', 'p': 97, 'prec': 20, 'unit': 37772127811538398345781458118110347669, 'val': 2}