Elliptic curve data - 5040.j5

Formats: - HTML - YAML - JSON - 2024-05-05T21:32:02.017632

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '5040i', 'Clabel': '5040i4', 'Cnumber': 4, 'abc_quality': 1.0496242487576335, 'absD': 193653039928320, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, 0, 0, 1437, 669202], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 5040, 'degree': 16384, 'elladic_images': ['8.24.0.90'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4204817427315919492265335195', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [439608956, 259416045], 'lmfdb_iso': '5040.j', 'lmfdb_label': '5040.j5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 160, 24732], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.2', '12.12.0-4.c.1.1', '20.12.0.h.1', '24.48.0-8.bb.2.6', '40.48.0.bn.1', '60.24.0-20.h.1.1', '112.48.0.?', '120.96.0.?', '336.96.0.?', '560.96.1.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29355294793091601234788413316', 'prec': 103}, 'szpiro_ratio': 4.733145368410052, '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, 0, 0, 0, -1, 0, -1, 0, 0, 0, 4, 0, -2, 0, 0, 0, 6, 0, -4, 0], 'aplist': [0, 0, -1, -1, 4, -2, 6, -4, 8, 2, 0, -2, -10, -4, 0, -14, 12, -2, 4, 0, 2, 8, -4, 6, -6], 'class_deg': 8, 'class_size': 6, 'conductor': 5040, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '5040.j', 'trace_hash': 503387411415787221}
• 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': '0.058369400794356543321806692574', 'prec': 107}, 'conductor': 5040, 'gens': [], 'heights': [], 'lmfdb_label': '5040.j5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.44109013149755774222749852304', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7643605259902309689099940921534632554', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-82, 0, 1]], 'xcoord_integral_points': [-82]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '5040.j5'}
• ec_torsion_growth •

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

  
  
  • id: 262823
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [4]}
  • id: 262824
    {'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '5040.j5', 'torsion': [4]}
  • id: 262822
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [2, 2]}
  • id: 262826
    {'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [8]}
  • id: 262825
    {'degree': 4, 'field': [4, 0, 1, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [2, 4]}
  • id: 262827
    {'degree': 4, 'field': [25, 0, 20, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [8]}
  • id: 262828
    {'degree': 8, 'field': [1, 2, 0, 12, 19, -12, 0, -2, 1], 'lmfdb_label': '5040.j5', 'torsion': [2, 4]}
  • id: 262830
    {'degree': 8, 'field': [36, 0, -12, 0, 13, 0, 8, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [2, 8]}
  • id: 262829
    {'degree': 8, 'field': [400, 0, 0, 0, 20, 0, 0, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [8]}
  • id: 262831
    {'degree': 8, 'field': [474, -928, 838, 120, -322, 46, 18, -4, 1], 'lmfdb_label': '5040.j5', 'torsion': [6]}
  • id: 262832
    {'degree': 16, 'field': [1, 2, 2, 24, 13, -74, 114, -58, -12, 44, -24, -2, 13, -12, 8, -4, 1], 'lmfdb_label': '5040.j5', 'torsion': [4, 4]}
  • id: 262834
    {'degree': 16, 'field': [1296, 0, 2016, 0, 2560, 0, 1184, 0, 444, 0, -176, 0, 0, 0, -4, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [2, 8]}
  • id: 262839
    {'degree': 16, 'field': [2304, 0, -36096, 0, 2260000, 0, -18048, 0, 525, 0, -2068, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [12]}
  • id: 262833
    {'degree': 16, 'field': [32400, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [2, 8]}
  • id: 262835
    {'degree': 16, 'field': [50625, 0, 94500, 0, 7200, 0, -31920, 0, -2969, 0, 2128, 0, 32, 0, -28, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [16]}
  • id: 262838
    {'degree': 16, 'field': [291600, 0, -658272, 0, 205840, 0, 26016, 0, -7128, 0, -1960, 0, 240, 0, -24, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [12]}
  • id: 262837
    {'degree': 16, 'field': [770884, 0, 12745000, 0, 10610068, 0, 1844548, 0, -204020, 0, 24268, 0, 40, 0, 16, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [2, 6]}
  • id: 262836
    {'degree': 16, 'field': [172922500, 0, 112500000, 0, 28690500, 0, 4635000, 0, 590525, 0, 41100, 0, 2280, 0, 60, 0, 1], 'lmfdb_label': '5040.j5', 'torsion': [16]}
• 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: 97582
    {'conductor': 5040, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '5040.j5', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 97583
    {'conductor': 5040, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '5040.j5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 97584
    {'conductor': 5040, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5040.j5', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 97585
    {'conductor': 5040, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '5040.j5', 'prime': 7, 'reduction_type': -1, '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: 1696907
    {'adelic_gens': [[13, 576, 684, 745], [559, 0, 0, 1679], [1, 16, 0, 1], [352, 1125, 1635, 1666], [241, 576, 1368, 1249], [1, 0, 16, 1], [15, 2, 1582, 1667], [614, 1533, 1377, 1298], [5, 4, 1676, 1677], [1665, 16, 1664, 17]], 'adelic_image': '1680.192.1.?', 'conductor': 5040, 'lmfdb_label': '5040.j5', 'prime': 0}
  • id: 25045
    {'conductor': 5040, 'elladic_image': '8.24.0.90', 'lmfdb_label': '5040.j5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 5040.j does not appear in ec_padic