Elliptic curve data - 5070.u1

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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': '5070w', 'Clabel': '5070w4', 'Cnumber': 4, 'abc_quality': 1.0375259015845228, 'absD': 48943843260000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [1, 0, 0, -14623320, 21522489312], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 5070, 'degree': 215040, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4797381557016154746194426404', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2, 4], 'jinv': [71647584155243142409, 10140000], 'lmfdb_iso': '5070.u', 'lmfdb_label': '5070.u1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -86529, 9789652], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.s.1', '40.12.0.bb.1', '104.12.0.?', '120.24.0.?', '156.12.0.?', '312.24.0.?', '520.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 507], [3, 4, 1690], [5, 6, 507], [13, 98, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1972634769708471065926989196', 'prec': 100}, 'szpiro_ratio': 7.16297021663192, '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, -4, 1, 1, 1, 0, 1, 0, -4, 1, 1, -2, 1, -4, 1], 'aplist': [1, 1, 1, -4, 0, 0, -2, -4, 8, 2, 8, -2, 6, 12, 0, 10, 0, -10, 4, 16, 6, -8, 4, 14, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 5070, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '5070.u', 'trace_hash': 2052601981830525834}
• 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': '0.0070166013847360428200267260186', 'prec': 110}, 'conductor': 5070, 'gens': [], 'heights': [], 'lmfdb_label': '5070.u1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.36353709925010161753614196949', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.6353709925010161753614196949144148365', 'prec': 130}, 'tamagawa_product': 40, 'torsion_generators': [[8831, -8831, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 0], '5': [3, 0], '13': 'a'}, 'iwp0': 7, 'lmfdb_label': '5070.u1'}
• ec_torsion_growth •

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

  
  
  • id: 265943
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '5070.u1', 'torsion': [4]}
  • id: 265942
    {'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '5070.u1', 'torsion': [4]}
  • id: 265941
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '5070.u1', 'torsion': [2, 2]}
  • id: 265944
    {'degree': 4, 'field': [25, 0, -16, 0, 1], 'lmfdb_label': '5070.u1', 'torsion': [2, 4]}
  • id: 265948
    {'degree': 8, 'field': [-3156, 1824, -2004, 359, -176, -7, 7, -4, 1], 'lmfdb_label': '5070.u1', 'torsion': [6]}
  • id: 265946
    {'degree': 8, 'field': [-100, 2000, -2200, 0, 576, -40, -52, 0, 1], 'lmfdb_label': '5070.u1', 'torsion': [8]}
  • id: 265945
    {'degree': 8, 'field': [4300, 3600, 1928, 384, 216, -24, 20, 0, 1], 'lmfdb_label': '5070.u1', 'torsion': [2, 4]}
  • id: 265947
    {'degree': 8, 'field': [68149, 31324, -4091, -2450, 646, 148, -35, -2, 1], 'lmfdb_label': '5070.u1', 'torsion': [8]}
  • id: 265949
    {'degree': 16, 'field': [62500, -180000, 259200, -166080, -7604, 75168, 35712, 2112, 8541, 2856, 288, -432, -38, -24, 0, 0, 1], 'lmfdb_label': '5070.u1', 'torsion': [4, 4]}
  • id: 265951
    {'degree': 16, 'field': [221841, 0, -1729056, 0, 2677084, 0, -1591584, 0, 419670, 0, -53344, 0, 3324, 0, -96, 0, 1], 'lmfdb_label': '5070.u1', 'torsion': [2, 8]}
  • id: 265954
    {'degree': 16, 'field': [2402500, 0, 10764632, 0, 6679084, 0, 421744, 0, -252100, 0, 13240, 0, 133, 0, -34, 0, 1], 'lmfdb_label': '5070.u1', 'torsion': [12]}
  • id: 265950
    {'degree': 16, 'field': [6358465, 10336500, -356236, -5773604, 167303, 1548648, -187486, -271356, 57940, 33204, -9080, -2716, 831, 128, -38, -4, 1], 'lmfdb_label': '5070.u1', 'torsion': [2, 8]}
  • id: 265952
    {'degree': 16, 'field': [300843000, 134852400, -122946660, -21931512, 6309678, 5483520, -1711271, 11128, -137844, 84578, -12091, -1836, -331, 266, -18, -8, 1], 'lmfdb_label': '5070.u1', 'torsion': [2, 6]}
  • id: 265953
    {'degree': 16, 'field': [321624710, -15779680, -9722760, 55210536, -38481138, 14085432, -6484775, 1668472, -592440, 128050, -36731, 5988, -907, -70, 30, -8, 1], 'lmfdb_label': '5070.u1', 'torsion': [12]}
• 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: 98629
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '5070.u1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 98630
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5070.u1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 98631
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '5070.u1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 98632
    {'conductor': 5070, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '5070.u1', 'prime': 13, '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: 1697130
    {'adelic_gens': [[1, 0, 8, 1], [1, 8, 0, 1], [479, 0, 0, 1559], [1, 4, 4, 17], [1288, 1443, 325, 482], [976, 923, 1339, 768], [937, 728, 988, 1353], [1553, 8, 1552, 9], [7, 6, 1554, 1555], [768, 1313, 1027, 534]], 'adelic_image': '1560.48.0.?', 'conductor': 5070, 'lmfdb_label': '5070.u1', 'prime': 0}
  • id: 25232
    {'conductor': 5070, 'elladic_image': '4.6.0.1', 'lmfdb_label': '5070.u1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 5070.u does not appear in ec_padic