Elliptic curve data - 27735.k7

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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': '27735g', 'Clabel': '27735g1', 'Cnumber': 1, 'abc_quality': 1.1980768440515948, 'absD': 94820445735, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 20640, 'ainvs': [1, 0, 1, -39, -14819], 'analytic_rank': 1, 'bad_primes': [3, 5, 43], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 27735, 'degree': 20160, 'elladic_images': ['32.48.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.78517530520399211487559263805', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-1, 15], 'lmfdb_iso': '27735.k', 'lmfdb_label': '27735.k7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 0, 0], 'min_quad_twist_disc': -43, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0.g.1', '24.24.0.bz.1', '30.6.0.a.1', '32.48.0.e.1', '40.24.0.cb.2', '48.48.0.bv.1', '60.12.0.g.1', '80.96.2.?', '96.96.1.?', '120.48.0.?', '160.192.5.?', '172.12.0.?', '240.192.5.?', '344.24.0.?', '480.384.13.?', '688.48.0.?', '1032.48.0.?', '1376.96.0.?', '1720.48.0.?', '2064.96.0.?', '2580.24.0.?', '3440.192.2.?', '4128.192.1.?', '5160.96.0.?', '6880.384.5.?', '10320.384.5.?', '20640.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '25.926579597785233703770754705', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 4, 9245], [5, 6, 5547], [43, 926, 15]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0954247526427890968608286186', 'prec': 103}, 'szpiro_ratio': 3.1992735451987557, '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, 0, -3, 1, -1, -4, -1, -2, 0, -1, -1, 2, 1, -4, 1], 'aplist': [1, 1, -1, 0, -4, -2, 2, -4, 0, 2, 0, 10, 10, 0, 8, -10, -4, 2, 12, 8, -10, 0, 12, 6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 27735, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '27735.k', 'trace_hash': 512768579550082875}
• 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': '0.20797225233651433504806909601', 'prec': 103}, 'conductor': 27735, 'gens': [[175608467329, 71829520009567697, 20083]], 'heights': [{'__RealLiteral__': 0, 'data': '25.926579597785233703770754705', 'prec': 100}], 'lmfdb_label': '27735.k7', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.48684931355927389705403744770', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.3111687400608082795801419247052479412', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[25, -13, 1]], 'xcoord_integral_points': [25]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [4, 0], '5': [1, 0], '7': [3, 1, 0], '11': [1, 0], '13': [1, 0], '17': [3, 0], '19': [3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': 'a', '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '27735.k7'}
• ec_torsion_growth •

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

  
  
  • id: 1387985
    {'degree': 2, 'field': [-161, -1, 1], 'lmfdb_label': '27735.k7', 'torsion': [4]}
  • id: 1387984
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '27735.k7', 'torsion': [2, 2]}
  • id: 1387986
    {'degree': 2, 'field': [11, -1, 1], 'lmfdb_label': '27735.k7', 'torsion': [4]}
  • id: 1387987
    {'degree': 4, 'field': [49, 0, 29, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [2, 4]}
  • id: 1387988
    {'degree': 4, 'field': [121, -11, -10, -1, 1], 'lmfdb_label': '27735.k7', 'torsion': [8]}
  • id: 1387989
    {'degree': 4, 'field': [144, 0, 19, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [8]}
  • id: 1387995
    {'degree': 8, 'field': [-40059, 360, -11787, 429, -498, -28, -3, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [6]}
  • id: 1387991
    {'degree': 8, 'field': [1156, 0, -4552, 0, 909, 0, -58, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [8]}
  • id: 1387993
    {'degree': 8, 'field': [14641, -1331, -1210, 231, 89, 21, -10, -1, 1], 'lmfdb_label': '27735.k7', 'torsion': [16]}
  • id: 1387992
    {'degree': 8, 'field': [20736, 0, -2736, 0, 217, 0, -19, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [2, 8]}
  • id: 1387994
    {'degree': 8, 'field': [27061, -1629, 6319, -538, 659, -56, 36, -2, 1], 'lmfdb_label': '27735.k7', 'torsion': [16]}
  • id: 1387990
    {'degree': 8, 'field': [3423876, -461664, 287889, -22398, 9604, -386, 156, -2, 1], 'lmfdb_label': '27735.k7', 'torsion': [2, 4]}
  • id: 1387997
    {'degree': 16, 'field': [10214416, 0, -27582552, 0, 24267625, 0, -7652832, 0, 1184184, 0, -99618, 0, 4600, 0, -108, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [2, 8]}
  • id: 1387996
    {'degree': 16, 'field': [125014761, 0, 126017892, 0, 44715570, 0, 8379492, 0, 973459, 0, 72028, 0, 3330, 0, 88, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [4, 4]}
  • id: 1388000
    {'degree': 16, 'field': [149108521, 0, 140498264, 0, 47727592, 0, 8677097, 0, 970180, 0, 69983, 0, 3217, 0, 86, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [32]}
  • id: 1388003
    {'degree': 16, 'field': [178302609, 0, 131595291, 0, 43247880, 0, 8078167, 0, 937385, 0, 69577, 0, 3235, 0, 86, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [12]}
  • id: 1387999
    {'degree': 16, 'field': [214358881, -19487171, 19487171, -5153632, 468512, 264869, -103818, 70048, -21009, 6368, -858, 199, 32, -32, 11, -1, 1], 'lmfdb_label': '27735.k7', 'torsion': [2, 16]}
  • id: 1387998
    {'degree': 16, 'field': [261674073, 31756032, 166925817, 13035456, 48182553, 2092980, 8228034, 154722, 906463, 3864, 65554, -114, 3030, -6, 82, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [16]}
  • id: 1388002
    {'degree': 16, 'field': [1674982269, -764085681, 664634730, -173476842, 71778981, -8901801, 607161, 1290810, -522776, 172483, -53078, 5423, -2185, -43, -11, -2, 1], 'lmfdb_label': '27735.k7', 'torsion': [12]}
  • id: 1388001
    {'degree': 16, 'field': [1729145889, 0, 864434751, 0, 161141920, 0, 12087003, 0, 273855, 0, -2252, 0, -1398, 0, 0, 0, 1], 'lmfdb_label': '27735.k7', 'torsion': [2, 6]}
• 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: 640623
    {'conductor': 27735, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27735.k7', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 640624
    {'conductor': 27735, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27735.k7', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 640625
    {'conductor': 27735, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '27735.k7', 'prime': 43, '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: 1848962
    {'adelic_gens': [[1, 9632, 11610, 3871], [15094, 8643, 19565, 5548], [1, 0, 32, 1], [20512, 989, 19307, 9762], [1, 32, 0, 1], [5, 28, 68, 381], [20609, 32, 20608, 33], [8343, 5762, 10234, 10063], [23, 18, 18078, 18635], [5759, 0, 0, 20639]], 'adelic_image': '20640.768.13.?', 'conductor': 27735, 'lmfdb_label': '27735.k7', 'prime': 0}
  • id: 125378
    {'conductor': 27735, 'elladic_image': '32.48.0.1', 'lmfdb_label': '27735.k7', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1329049
    {'lmfdb_iso': '27735.k', 'p': 11, 'prec': 20, 'unit': 40879464271524253180, 'val': 1}
  • id: 1329051
    {'lmfdb_iso': '27735.k', 'p': 13, 'prec': 20, 'unit': 678262326205482375468, 'val': 1}
  • id: 1329053
    {'lmfdb_iso': '27735.k', 'p': 17, 'prec': 20, 'unit': 526300767743413471817, 'val': 2}
  • id: 1329054
    {'lmfdb_iso': '27735.k', 'p': 19, 'prec': 20, 'unit': 34863066262508768535404, 'val': 2}
  • id: 1329050
    {'lmfdb_iso': '27735.k', 'p': 29, 'prec': 20, 'unit': 3047112413454121642194924457, 'val': 1}
  • id: 1329046
    {'lmfdb_iso': '27735.k', 'p': 37, 'prec': 20, 'unit': 482398635338791802518811947572, 'val': 1}
  • id: 1329048
    {'lmfdb_iso': '27735.k', 'p': 41, 'prec': 20, 'unit': 3506072121479282151539931611332, 'val': 1}
  • id: 1329052
    {'lmfdb_iso': '27735.k', 'p': 47, 'prec': 20, 'unit': 40842158126065742497012224916256, 'val': 1}
  • id: 1329055
    {'lmfdb_iso': '27735.k', 'p': 53, 'prec': 20, 'unit': 529786011144410565264530981581755, 'val': 1}
  • id: 1329058
    {'lmfdb_iso': '27735.k', 'p': 59, 'prec': 20, 'unit': 4083378574535776479445180751821056, 'val': 1}
  • id: 1329059
    {'lmfdb_iso': '27735.k', 'p': 61, 'prec': 20, 'unit': 5685758835835201915873174819220861, 'val': 1}
  • id: 1329045
    {'lmfdb_iso': '27735.k', 'p': 67, 'prec': 20, 'unit': 18989583067876005321428817399227445, 'val': 1}
  • id: 1329047
    {'lmfdb_iso': '27735.k', 'p': 71, 'prec': 20, 'unit': 22732089217265808909403927395867202, 'val': 1}
  • id: 1329056
    {'lmfdb_iso': '27735.k', 'p': 73, 'prec': 20, 'unit': 130101805959184543590563070677240547, 'val': 1}
  • id: 1329044
    {'lmfdb_iso': '27735.k', 'p': 83, 'prec': 20, 'unit': 401887033779570119442062354822300236, 'val': 1}
  • id: 1329057
    {'lmfdb_iso': '27735.k', 'p': 89, 'prec': 20, 'unit': 991397941110913322190808719816039010, 'val': 1}
  • id: 1329043
    {'lmfdb_iso': '27735.k', 'p': 97, 'prec': 20, 'unit': 33960474489626684930375542515154904903, 'val': 1}