Elliptic curve data - 70560.cm1

Formats: - HTML - YAML - JSON - 2024-05-03T23:23:00.221850

• 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': '70560bu', 'Clabel': '70560bu4', 'Cnumber': 4, 'abc_quality': 0.9370477448335434, 'absD': 1729044999360000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 840, 'ainvs': [0, 0, 0, -300027, -63222446], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 70560, 'degree': 393216, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8694510988065073720247342565', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2, 4], 'jinv': [68017239368, 39375], 'lmfdb_iso': '70560.cm', 'lmfdb_label': '70560.cm1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -680, -6600], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.2', '40.12.0.ba.1', '56.12.0.s.1', '84.12.0.?', '120.24.0.?', '168.24.0.?', '280.24.0.?', '840.48.0.?'], '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': '-0.17267050547516310828848882478', 'prec': 107}, 'szpiro_ratio': 4.429193627563612, '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, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 0, 1, 0, -4, 2, -2, 0, 0, -6, -8, 2, -6, 4, 0, 6, 8, 2, 4, 4, 10, 12, 4, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 70560, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '70560.cm', 'trace_hash': 1019208619022800530}
• 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': '0.023780194761529807561551487860', 'prec': 107}, 'conductor': 70560, 'gens': [], 'heights': [], 'lmfdb_label': '70560.cm1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20399736608311729722736605657', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6319789286649383778189284525482607670', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-322, 0, 1]], 'xcoord_integral_points': [-322]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '70560.cm1'}
• ec_torsion_growth •

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

  
  
  • id: 3353378
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [2, 2]}
  • id: 3353380
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [4]}
  • id: 3353379
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [4]}
  • id: 3353381
    {'degree': 4, 'field': [25, 0, -4, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [2, 4]}
  • id: 3353385
    {'degree': 8, 'field': [-1145542, -152868, 46720, 11500, 2832, -100, -118, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [6]}
  • id: 3353382
    {'degree': 8, 'field': [196, 0, 0, 0, -322, 0, 0, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [2, 4]}
  • id: 3353383
    {'degree': 8, 'field': [576, 0, 240, 0, -2, 0, -10, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [8]}
  • id: 3353384
    {'degree': 8, 'field': [108900, 0, -3840, 0, 916, 0, -32, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [8]}
  • id: 3353386
    {'degree': 16, 'field': [15625, 70000, 156800, -212240, 125066, -33208, 37632, -25312, 6831, -1736, 1568, -448, 102, -56, 0, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [4, 4]}
  • id: 3353389
    {'degree': 16, 'field': [52900, 0, -401200, 0, 174400, 0, -46264, 0, 11092, 0, -2704, 0, 316, 0, -28, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [2, 6]}
  • id: 3353388
    {'degree': 16, 'field': [255025, 0, 472460, 0, 395096, 0, 96972, 0, 2174, 0, -2364, 0, 344, 0, -28, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [2, 8]}
  • id: 3353387
    {'degree': 16, 'field': [222159025, 0, 120256960, 0, 31389596, 0, -13698048, 0, 2154614, 0, -162624, 0, 6524, 0, -128, 0, 1], 'lmfdb_label': '70560.cm1', 'torsion': [2, 8]}
  • id: 3353390
    {'degree': 16, 'field': [1570471009, -2066879468, 1488896640, -511836736, 85162748, 16283844, -10617128, 4086280, -860454, -51068, 14848, -4896, 2300, -364, 72, -8, 1], 'lmfdb_label': '70560.cm1', 'torsion': [12]}
  • id: 3353391
    {'degree': 16, 'field': [20477610000, 0, 33048000, 0, 89359200, 0, 10088064, 0, -316008, 0, 53424, 0, -504, 0, 48, 0, 1], 'lmfdb_label': '70560.cm1', '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: 1710488
    {'conductor': 70560, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '70560.cm1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1710489
    {'conductor': 70560, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '70560.cm1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1710490
    {'conductor': 70560, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '70560.cm1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1710491
    {'conductor': 70560, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '70560.cm1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2130941
    {'adelic_gens': [[559, 0, 0, 839], [736, 603, 249, 838], [32, 837, 195, 278], [833, 8, 832, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [337, 288, 228, 313], [104, 237, 525, 524], [7, 6, 834, 835]], 'adelic_image': '840.48.0.?', 'conductor': 70560, 'lmfdb_label': '70560.cm1', 'prime': 0}
  • id: 293977
    {'conductor': 70560, 'elladic_image': '4.6.0.1', 'lmfdb_label': '70560.cm1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 70560.cm does not appear in ec_padic