Elliptic curve data - 127050.gv8

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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': '127050ga', 'Clabel': '127050ga1', 'Cnumber': 1, 'abc_quality': 0.9990919448660593, 'absD': 7218827625240000000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [1, 1, 1, 4806662, -505870969], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 127050, 'degree': 9953280, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8836348989236650691414503726', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 177, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [443688652450511, 260789760000], 'lmfdb_iso': '127050.gv', 'lmfdb_label': '127050.gv8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 1589, 3185], 'min_quad_twist_disc': -55, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.48.0-12.g.1.3', '60.48.0-12.g.1.4', '84.48.0.?', '88.12.0.?', '120.96.0.?', '132.48.0.?', '165.8.0.?', '168.96.0.?', '210.24.0.?', '264.96.0.?', '280.12.0.?', '330.24.0.?', '420.96.0.?', '462.24.0.?', '660.96.0.?', '840.192.1.?', '924.96.1.?', '1320.192.1.?', '1540.12.0.?', '1848.192.1.?', '2310.48.0.?', '3080.24.0.?', '4620.192.1.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 63525], [3, 4, 3025], [5, 18, 5082], [7, 8, 18150], [11, 72, 1050]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.87996830630742960981009891700', 'prec': 103}, 'szpiro_ratio': 4.915630676817457, '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, 0, -1, 1, 1, 1, 0, 0, -1, 2, 1, 0, 1, 6, 1, 4, 0], 'aplist': [1, -1, 0, 1, 0, 2, 6, 4, 0, -6, 8, 10, 6, 8, 0, -6, 12, -2, 4, 12, -10, 4, -12, 6, 10], 'class_deg': 12, 'class_size': 8, 'conductor': 127050, 'isogeny_matrix': [[1, 4, 2, 12, 3, 4, 6, 12], [4, 1, 2, 3, 12, 4, 6, 12], [2, 2, 1, 6, 6, 2, 3, 6], [12, 3, 6, 1, 4, 12, 2, 4], [3, 12, 6, 4, 1, 12, 2, 4], [4, 4, 2, 12, 12, 1, 6, 3], [6, 6, 3, 2, 2, 6, 1, 2], [12, 12, 6, 4, 4, 3, 2, 1]], 'lmfdb_iso': '127050.gv', 'trace_hash': 253269235380836645}
• 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': '0.0031282867207770403276624466925', 'prec': 110}, 'conductor': 127050, 'gens': [], 'heights': [], 'lmfdb_label': '127050.gv8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.077808424034440219267665908595', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6022065304796957872719454188098266426', 'prec': 130}, 'tamagawa_product': 288, 'torsion_generators': [[105, -53, 1]], 'xcoord_integral_points': [105]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [2, 0], '5': 'a', '7': [3, 0], '11': 'a'}, 'iwp0': 5, 'lmfdb_label': '127050.gv8'}
• ec_torsion_growth •

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

  
  
  • id: 5784156
    {'degree': 2, 'field': [-96, -1, 1], 'lmfdb_label': '127050.gv8', 'torsion': [4]}
  • id: 5784157
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '127050.gv8', 'torsion': [4]}
  • id: 5784158
    {'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '127050.gv8', 'torsion': [6]}
  • id: 5784155
    {'degree': 2, 'field': [58, -1, 1], 'lmfdb_label': '127050.gv8', 'torsion': [2, 2]}
  • id: 5784162
    {'degree': 4, 'field': [34, -23, 5, -1, 1], 'lmfdb_label': '127050.gv8', 'torsion': [12]}
  • id: 5784161
    {'degree': 4, 'field': [144, 0, 31, 0, 1], 'lmfdb_label': '127050.gv8', 'torsion': [12]}
  • id: 5784160
    {'degree': 4, 'field': [364, 133, 23, -1, 1], 'lmfdb_label': '127050.gv8', 'torsion': [2, 6]}
  • id: 5784159
    {'degree': 4, 'field': [1464, 153, -17, -1, 1], 'lmfdb_label': '127050.gv8', 'torsion': [2, 4]}
  • id: 5784163
    {'degree': 6, 'field': [-116, -38, 25, 25, -10, -3, 1], 'lmfdb_label': '127050.gv8', 'torsion': [6]}
  • id: 5784165
    {'degree': 8, 'field': [-336, 1344, -1162, -336, 99, 80, -22, -4, 1], 'lmfdb_label': '127050.gv8', 'torsion': [8]}
  • id: 5784167
    {'degree': 8, 'field': [1024, 1056, 160, -46, 77, 16, 18, -2, 1], 'lmfdb_label': '127050.gv8', 'torsion': [2, 12]}
  • id: 5784164
    {'degree': 8, 'field': [18760, 42560, 44254, 20426, 3613, 38, -8, -4, 1], 'lmfdb_label': '127050.gv8', 'torsion': [2, 4]}
  • id: 5784166
    {'degree': 8, 'field': [43681, 0, 10648, 0, 1518, 0, 88, 0, 1], 'lmfdb_label': '127050.gv8', 'torsion': [8]}
  • id: 5784171
    {'degree': 12, 'field': [144, -696, 832, 670, 165, -81, 59, -48, 0, 10, 7, -3, 1], 'lmfdb_label': '127050.gv8', 'torsion': [12]}
  • id: 5784170
    {'degree': 12, 'field': [3025, 0, 0, 0, 0, 0, -6050, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '127050.gv8', 'torsion': [12]}
  • id: 5784168
    {'degree': 12, 'field': [3136, -336, -804, 2150, -735, -456, 251, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '127050.gv8', 'torsion': [3, 6]}
  • id: 5784169
    {'degree': 12, 'field': [5017600, 0, 703675, 0, 171075, 0, 11195, 0, 705, 0, 25, 0, 1], 'lmfdb_label': '127050.gv8', 'torsion': [2, 6]}
  • id: 5784176
    {'degree': 16, 'field': [11022400, 0, 8090080, 0, -748076, 0, -798924, 0, 145089, 0, -8568, 0, 826, 0, -44, 0, 1], 'lmfdb_label': '127050.gv8', 'torsion': [24]}
  • id: 5784177
    {'degree': 16, 'field': [41583600, -5198400, 73507410, 13802400, 8102751, 27604920, -964542, -3135588, 2436619, -463648, 86686, -13336, 3397, -376, 46, -4, 1], 'lmfdb_label': '127050.gv8', 'torsion': [24]}
  • id: 5784173
    {'degree': 16, 'field': [100000000, 0, 18200000, 0, -7603900, 0, -601020, 0, 211361, 0, -3192, 0, 554, 0, -28, 0, 1], 'lmfdb_label': '127050.gv8', 'torsion': [2, 8]}
  • id: 5784174
    {'degree': 16, 'field': [429697024, 29207552, -44167360, 32131584, -21235048, 5148808, 177118, -1904556, 849211, -282096, 91078, -20548, 4820, -672, 116, -8, 1], 'lmfdb_label': '127050.gv8', 'torsion': [2, 8]}
  • id: 5784172
    {'degree': 16, 'field': [2679097600, -97308800, 1767200, 40012320, 69321104, -4799968, 427408, 318096, 116008, 40776, -3566, -782, 857, -18, 8, -4, 1], 'lmfdb_label': '127050.gv8', 'torsion': [4, 4]}
  • id: 5784175
    {'degree': 16, 'field': [36842499136, 0, 6376774560, 0, 73174132, 0, -25428168, 0, 977409, 0, 29052, 0, -1646, 0, -12, 0, 1], 'lmfdb_label': '127050.gv8', 'torsion': [2, 12]}
  • id: 5784178
    {'degree': 18, 'field': [152234233687936, 63008102016, 28960133003424, -226309864512, 2802273169176, -32317048656, 187310598258, -3973039758, 8628812892, -251101635, 287281953, -9635742, 6432132, -279036, 85788, -2748, 504, -9, 1], 'lmfdb_label': '127050.gv8', '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: 3131514
    {'conductor': 127050, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '127050.gv8', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 3131515
    {'conductor': 127050, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '127050.gv8', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3131516
    {'conductor': 127050, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '127050.gv8', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 3131517
    {'conductor': 127050, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '127050.gv8', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 3131518
    {'conductor': 127050, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '127050.gv8', 'prime': 11, '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: 2492244
    {'adelic_gens': [[1929, 388, 8900, 7349], [5543, 9216, 1836, 8951], [5864, 9219, 7005, 374], [15, 106, 7934, 11], [1, 12, 12, 145], [1336, 3, 6141, 9154], [16, 4641, 7415, 5786], [9217, 24, 9216, 25], [1, 24, 0, 1], [6937, 24, 7422, 1687], [1, 0, 24, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 127050, 'lmfdb_label': '127050.gv8', 'prime': 0}
  • id: 496042
    {'conductor': 127050, 'elladic_image': '4.6.0.1', 'lmfdb_label': '127050.gv8', 'modell_image': '2B', 'prime': 2}
  • id: 496043
    {'conductor': 127050, 'elladic_image': '3.4.0.1', 'lmfdb_label': '127050.gv8', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 127050.gv does not appear in ec_padic