Elliptic curve data - 4560.k4

Formats: - HTML - YAML - JSON - 2022-06-29T00:27:14.384408

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  absD	numeric
  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[]
  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': '4560u', 'Clabel': '4560u1', 'Cnumber': 1, 'absD': 504299520, 'ainvs': [0, -1, 0, -160, -1280], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4560, 'degree': 2304, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.36451530780700678110066664938', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [-111284641, 123120], 'lmfdb_iso': '4560.k', 'lmfdb_label': '4560.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -10, 20], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], '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, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.32863187275293852831656547208', '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, 0, -1, 0, 1, 0, -4, 0, 1, 0, 4, 0, -2, 0, -1, 0, -2, 0, 1, 0], 'aplist': [0, -1, 1, -4, 4, -2, -2, 1, 8, 6, -4, -10, -2, -12, 0, 6, 0, -10, 4, 8, 2, 12, 8, 6, 18], 'class_deg': 4, 'class_size': 4, 'conductor': 4560, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '4560.k', 'trace_hash': 1162779962427262450}
• 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': '0.48237637164025071293221075912', 'prec': 103}, 'conductor': 4560, 'gens': [], 'heights': [], 'lmfdb_label': '4560.k4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.64295475827020151422413311712', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2859095165404030284482662342299814852', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[16, 0, 1]], 'xcoord_integral_points': [16]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [1, 0], '19': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '4560.k4'}
• ec_torsion_growth •

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

  
  
  • id: 238060
    {'degree': 2, 'field': [-95, 0, 1], 'lmfdb_label': '4560.k4', 'torsion': [4]}
  • id: 238061
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '4560.k4', 'torsion': [4]}
  • id: 238059
    {'degree': 2, 'field': [24, -1, 1], 'lmfdb_label': '4560.k4', 'torsion': [2, 2]}
  • id: 238062
    {'degree': 4, 'field': [95, 0, 0, 0, 1], 'lmfdb_label': '4560.k4', 'torsion': [2, 4]}
  • id: 238063
    {'degree': 4, 'field': [576, 0, -47, 0, 1], 'lmfdb_label': '4560.k4', 'torsion': [2, 4]}
  • id: 238067
    {'degree': 8, 'field': [-3, 0, 1528, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '4560.k4', 'torsion': [6]}
  • id: 238066
    {'degree': 8, 'field': [36, 0, 12, 0, -11, 0, 2, 0, 1], 'lmfdb_label': '4560.k4', 'torsion': [8]}
  • id: 238064
    {'degree': 8, 'field': [576, -48, 2, 90, -39, -10, 8, -4, 1], 'lmfdb_label': '4560.k4', 'torsion': [4, 4]}
  • id: 238065
    {'degree': 8, 'field': [91296, 31392, -29448, -3960, 2161, -220, 78, -4, 1], 'lmfdb_label': '4560.k4', 'torsion': [8]}
  • id: 238073
    {'degree': 16, 'field': [36, 0, 288, 0, 576, 0, -59, 0, -154, 0, 49, 0, 1, 0, 2, 0, 1], 'lmfdb_label': '4560.k4', 'torsion': [12]}
  • id: 238070
    {'degree': 16, 'field': [576, -4608, 18432, -46176, 78676, -92472, 73032, -34132, 4697, 4508, -2776, 908, -30, -84, 32, -8, 1], 'lmfdb_label': '4560.k4', 'torsion': [2, 8]}
  • id: 238072
    {'degree': 16, 'field': [8456, -472888, 4859004, -13629480, 19490970, -16701606, 8041369, -2096768, 482610, 45820, -27215, 9768, -1537, -70, 30, -8, 1], 'lmfdb_label': '4560.k4', 'torsion': [12]}
  • id: 238071
    {'degree': 16, 'field': [11664, 0, 130788, 0, 408060, 0, 214596, 0, 28725, 0, -356, 0, 498, 0, 0, 0, 1], 'lmfdb_label': '4560.k4', 'torsion': [2, 6]}
  • id: 238068
    {'degree': 16, 'field': [54720, 0, -9120, 9120, 18620, -55480, 63080, -32300, 3231, 3792, -732, -436, 260, -56, 28, -8, 1], 'lmfdb_label': '4560.k4', 'torsion': [2, 8]}
  • id: 238069
    {'degree': 16, 'field': [150297930, 9170820, -143280090, 5613300, 20382111, -6039684, 10136610, -2117340, 2503521, -318420, 214674, -18900, 8461, -460, 150, -4, 1], 'lmfdb_label': '4560.k4', '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: 87064
    {'conductor': 4560, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '4560.k4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 87065
    {'conductor': 4560, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '4560.k4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 87066
    {'conductor': 4560, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4560.k4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 87067
    {'conductor': 4560, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4560.k4', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  {'conductor': 4560, 'elladic_image': '4.12.0.8', 'lmfdb_label': '4560.k4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4560.k does not appear in ec_padic