Elliptic curve data - 5070.u4

Formats: - HTML - YAML - JSON - 2025-10-16T01:53:32.842790

• 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': '5070w1', 'Cnumber': 1, 'abc_quality': 0.9770311172779014, 'absD': 12830334847549440, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [1, 0, 0, -48760, 6842432], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 5070, 'degree': 53760, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7865909751416701652022105189', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2, 4], 'jinv': [-2656166199049, 2658140160], 'lmfdb_iso': '5070.u', 'lmfdb_label': '5070.u4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -289, 3092], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.y.1', '30.6.0.a.1', '40.12.0.bb.1', '60.12.0.g.1', '104.12.0.?', '120.24.0.?', '156.12.0.?', '260.12.0.?', '312.24.0.?', '520.24.0.?', '780.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2535], [3, 4, 1690], [5, 6, 507], [13, 98, 30]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.50411629641090179717546679812', 'prec': 103}, 'szpiro_ratio': 5.275012721312635, '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': '0.028066405538944171280106904074', 'prec': 107}, 'conductor': 5070, 'gens': [], 'heights': [], 'lmfdb_label': '5070.u4', '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': [[-272, 136, 1]], 'xcoord_integral_points': [-272]}
• 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.u4'}
• ec_torsion_growth •

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

  
  
  • id: 265906
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '5070.u4', 'torsion': [4]}
  • id: 265905
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '5070.u4', 'torsion': [2, 2]}
  • id: 265907
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '5070.u4', 'torsion': [4]}
  • id: 265908
    {'degree': 4, 'field': [40, 25, -1, -1, 1], 'lmfdb_label': '5070.u4', 'torsion': [2, 4]}
  • id: 265912
    {'degree': 8, 'field': [-3156, 1824, -2004, 359, -176, -7, 7, -4, 1], 'lmfdb_label': '5070.u4', 'torsion': [6]}
  • id: 265911
    {'degree': 8, 'field': [361, 0, 1232, 0, 294, 0, 32, 0, 1], 'lmfdb_label': '5070.u4', 'torsion': [8]}
  • id: 265909
    {'degree': 8, 'field': [456, 1104, 918, 90, 121, 40, 12, -2, 1], 'lmfdb_label': '5070.u4', 'torsion': [2, 4]}
  • id: 265910
    {'degree': 8, 'field': [2960, 1360, -1150, -400, 151, 56, -14, -4, 1], 'lmfdb_label': '5070.u4', 'torsion': [8]}
  • id: 265917
    {'degree': 16, 'field': [-319788160, 400034560, -271029320, 159524220, -70643750, 19494575, -3396104, 125728, 170175, -22100, -982, -5158, 1298, 225, -70, -2, 1], 'lmfdb_label': '5070.u4', 'torsion': [12]}
  • id: 265918
    {'degree': 16, 'field': [6561, 8748, 35721, 28674, 66906, 24246, 43047, -5532, 25786, 1844, 4783, -898, 826, -118, 49, -4, 1], 'lmfdb_label': '5070.u4', 'torsion': [12]}
  • id: 265913
    {'degree': 16, 'field': [207936, 0, 381600, 0, 754356, 0, -136680, 0, 34801, 0, -3500, 0, 546, 0, -20, 0, 1], 'lmfdb_label': '5070.u4', 'torsion': [4, 4]}
  • id: 265916
    {'degree': 16, 'field': [2108304, 0, 7719552, 0, 2467840, 0, 2939799, 0, 296250, 0, 2191, 0, 33, 0, 30, 0, 1], 'lmfdb_label': '5070.u4', 'torsion': [2, 6]}
  • id: 265915
    {'degree': 16, 'field': [2262016, 0, 731424, 0, 536836, 0, 388044, 0, 121329, 0, 18696, 0, 1498, 0, 60, 0, 1], 'lmfdb_label': '5070.u4', 'torsion': [2, 8]}
  • id: 265914
    {'degree': 16, 'field': [13734436, 0, -2388820, 0, 933701, 0, -91170, 0, 11, 0, 0, 0, 11, 0, -10, 0, 1], 'lmfdb_label': '5070.u4', 'torsion': [2, 8]}
• 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: 98617
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 20, 'j_denominator_valuation': 20, 'kodaira_symbol': 24, 'lmfdb_label': '5070.u4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 20}
  • id: 98618
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5070.u4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 98619
    {'conductor': 5070, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5070.u4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 98620
    {'conductor': 5070, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '5070.u4', '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: 1697133
    {'adelic_gens': [[1496, 1443, 845, 482], [1, 0, 8, 1], [1, 8, 0, 1], [404, 481, 1183, 846], [1, 4, 4, 17], [479, 0, 0, 1559], [443, 78, 650, 1067], [833, 468, 1430, 287], [7, 6, 1554, 1555], [1553, 8, 1552, 9]], 'adelic_image': '1560.48.0.?', 'conductor': 5070, 'lmfdb_label': '5070.u4', 'prime': 0}
  • id: 25235
    {'conductor': 5070, 'elladic_image': '4.6.0.1', 'lmfdb_label': '5070.u4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 5070.u does not appear in ec_padic