Elliptic curve data - 70.a1

Formats: - HTML - YAML - JSON - 2023-06-08T13:02:50.298531

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '70a', 'Clabel': '70a3', 'Cnumber': 3, 'absD': 120050, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 56, 'ainvs': [1, -1, 1, -268, -1619], 'analytic_rank': 0, 'bad_primes': [2, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 70, 'degree': 16, 'elladic_images': ['8.24.0.58'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.038987671614636246397705984290', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [2121328796049, 120050], 'lmfdb_iso': '70.a', 'lmfdb_label': '70.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -268, -1619], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.k.1.3', '56.48.0-56.v.1.4'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.038987671614636246397705984290', 'prec': 107}, '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, 0, 1, -1, 0, -1, 1, -3, -1, 4, 0, -6, -1, 0, 1, 2, -3, 0, -1], 'aplist': [1, 0, -1, -1, 4, -6, 2, 0, 0, 6, 8, -10, 2, 4, 8, -2, -8, -14, -12, -16, 2, -8, 8, 10, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 70, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '70.a', 'trace_hash': 1338735293501548123}
• 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': '0.92498723346050697017099802840', 'prec': 103}, 'conductor': 70, 'gens': [], 'heights': [], 'lmfdb_label': '70.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1803043465576622803337375426', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1803043465576622803337375426010351971', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-37, 33, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 1], '5': [0, 0], '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '70.a1'}
• ec_torsion_growth •

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

  
  
  • id: 2470
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [2, 2]}
  • id: 2471
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [4]}
  • id: 2472
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [4]}
  • id: 2473
    {'degree': 4, 'field': [-50, 0, 0, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [2, 4]}
  • id: 2474
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [2, 4]}
  • id: 2478
    {'degree': 8, 'field': [-48, 0, -36, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [6]}
  • id: 2477
    {'degree': 8, 'field': [16, 0, 0, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [8]}
  • id: 2476
    {'degree': 8, 'field': [196, 0, 189, 0, 67, 0, 11, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [8]}
  • id: 2475
    {'degree': 8, 'field': [625, 0, -500, 0, 200, 0, -20, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [4, 4]}
  • id: 2480
    {'degree': 16, 'field': [16, 0, -32, 0, 32, 0, -88, 0, 161, 0, -44, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [2, 8]}
  • id: 2483
    {'degree': 16, 'field': [16, 0, 10124, 0, 7561, 0, 2762, 0, 763, 0, 332, 0, 91, 0, 14, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [12]}
  • id: 2481
    {'degree': 16, 'field': [196, 392, 392, 532, 589, 496, 536, 164, -529, -184, 152, -116, 103, -32, 8, -4, 1], 'lmfdb_label': '70.a1', 'torsion': [2, 8]}
  • id: 2479
    {'degree': 16, 'field': [40000, 0, 0, 0, -80000, 0, 0, 0, -1650, 0, 0, 0, -400, 0, 0, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [2, 8]}
  • id: 2482
    {'degree': 16, 'field': [129600, 0, -106272, 0, 42336, 0, -13392, 0, 3348, 0, -666, 0, 96, 0, -12, 0, 1], 'lmfdb_label': '70.a1', 'torsion': [2, 6]}
  • id: 2484
    {'degree': 16, 'field': [129600, 0, 106272, 0, 42336, 0, 13392, 0, 3348, 0, 666, 0, 96, 0, 12, 0, 1], 'lmfdb_label': '70.a1', '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: 384
    {'conductor': 70, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '70.a1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 385
    {'conductor': 70, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '70.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 386
    {'conductor': 70, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '70.a1', '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: 1666061
    {'adelic_gens': [[17, 8, 12, 33], [49, 8, 48, 9], [1, 0, 8, 1], [1, 4, 4, 17], [7, 6, 50, 51], [43, 36, 26, 13], [24, 1, 27, 14], [1, 8, 0, 1]], 'adelic_image': '56.48.0.?', 'conductor': 70, 'lmfdb_label': '70.a1', 'prime': 0}
  • id: 218
    {'conductor': 70, 'elladic_image': '8.24.0.58', 'lmfdb_label': '70.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 70.a does not appear in ec_padic