Elliptic curve data - 320.c4

Formats: - HTML - YAML - JSON - 2025-04-09T09:15:18.236933

• 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': '320b', 'Clabel': '320b4', 'Cnumber': 4, 'abc_quality': 1.0467057018818753, 'absD': 40960000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 80, 'ainvs': [0, 0, 0, 52, -272], 'analytic_rank': 1, 'bad_primes': [2, 5], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 320, 'degree': 64, 'elladic_images': ['8.48.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.14435980828378274197013612451', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [237276, 625], 'lmfdb_iso': '320.c', 'lmfdb_label': '320.c4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 13, -34], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0.c.1', '8.48.0-4.c.1.1', '40.96.1-40.dk.1.4', '80.192.3.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.72220533806442561466600769222', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 1], [5, 6, 64]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.77983643246281100391950670410', 'prec': 107}, 'szpiro_ratio': 4.288032806814417, '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, -4, 0, -3, 0, -4, 0, 2, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, -1, -4, -4, 2, 2, -4, 4, 2, -8, -6, -6, 8, 4, -6, 4, 2, -8, 0, -6, 0, 16, -6, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 320, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '320.c', 'trace_hash': 971571875835069198}
• 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': '0.74922224546025562003508944220', 'prec': 103}, 'conductor': 320, 'gens': [[6, 16, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.72220533806442561466600769222', 'prec': 103}], 'lmfdb_label': '320.c4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0496381260348652101600003978', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5161085153166400206694335278852594000', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[4, 0, 1]], 'xcoord_integral_points': [4, 6, 13, 54]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 1, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '320.c4'}
• ec_torsion_growth •

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

  
  
  • id: 13390
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '320.c4', 'torsion': [4]}
  • id: 13389
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '320.c4', 'torsion': [2, 2]}
  • id: 13391
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '320.c4', 'torsion': [4]}
  • id: 13392
    {'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '320.c4', 'torsion': [4, 4]}
  • id: 13395
    {'degree': 8, 'field': [-3, 0, 6, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '320.c4', 'torsion': [6]}
  • id: 13393
    {'degree': 8, 'field': [1, 0, -6, 0, 7, 0, -4, 0, 1], 'lmfdb_label': '320.c4', 'torsion': [8]}
  • id: 13394
    {'degree': 8, 'field': [1, 0, 6, 0, 7, 0, 4, 0, 1], 'lmfdb_label': '320.c4', 'torsion': [8]}
  • id: 13396
    {'degree': 16, 'field': [1, 4, 0, -12, 14, 52, -28, -108, 28, 108, -28, -52, 14, 12, 0, -4, 1], 'lmfdb_label': '320.c4', 'torsion': [4, 8]}
  • id: 13397
    {'degree': 16, 'field': [1, 4, 2, -8, 2, -36, 126, -204, 199, -128, 74, -68, 72, -56, 28, -8, 1], 'lmfdb_label': '320.c4', 'torsion': [4, 8]}
  • id: 13398
    {'degree': 16, 'field': [9, 0, 0, 0, 108, 0, 0, 0, 30, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '320.c4', 'torsion': [2, 6]}
  • id: 13399
    {'degree': 16, 'field': [16, 0, -64, 0, 64, 0, -112, 0, 136, 0, 8, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '320.c4', 'torsion': [12]}
  • id: 13400
    {'degree': 16, 'field': [25, 0, 100, 0, 100, 0, -68, 0, -98, 0, 28, 0, 4, 0, 4, 0, 1], 'lmfdb_label': '320.c4', '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: 2979
    {'conductor': 320, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '320.c4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 2980
    {'conductor': 320, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '320.c4', 'prime': 5, '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: 1667096
    {'adelic_gens': [[65, 16, 64, 17], [47, 28, 24, 59], [17, 16, 44, 33], [1, 12, 4, 49], [16, 1, 33, 24], [1, 0, 16, 1], [5, 16, 64, 45], [1, 16, 0, 1]], 'adelic_image': '80.192.3.?', 'conductor': 320, 'lmfdb_label': '320.c4', 'prime': 0}
  • id: 1297
    {'conductor': 320, 'elladic_image': '8.48.0.4', 'lmfdb_label': '320.c4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 3548
    {'lmfdb_iso': '320.c', 'p': 7, 'prec': 20, 'unit': 7082179443523715, 'val': 1}
  • id: 3546
    {'lmfdb_iso': '320.c', 'p': 11, 'prec': 20, 'unit': 30520976350301497666, 'val': 1}
  • id: 3552
    {'lmfdb_iso': '320.c', 'p': 13, 'prec': 20, 'unit': 1235534910997243523564, 'val': 1}
  • id: 3554
    {'lmfdb_iso': '320.c', 'p': 17, 'prec': 20, 'unit': 103328718452063962389640, 'val': 1}
  • id: 3555
    {'lmfdb_iso': '320.c', 'p': 19, 'prec': 20, 'unit': 1311734103107924185300559, 'val': 1}
  • id: 3558
    {'lmfdb_iso': '320.c', 'p': 23, 'prec': 20, 'unit': 58354208061993463597220397, 'val': 1}
  • id: 3551
    {'lmfdb_iso': '320.c', 'p': 29, 'prec': 20, 'unit': 5673221001717859858165118730, 'val': 1}
  • id: 3563
    {'lmfdb_iso': '320.c', 'p': 31, 'prec': 20, 'unit': 20924389529762472083360238417, 'val': 1}
  • id: 3547
    {'lmfdb_iso': '320.c', 'p': 37, 'prec': 20, 'unit': 595537504211320926048195232702, 'val': 1}
  • id: 3549
    {'lmfdb_iso': '320.c', 'p': 41, 'prec': 20, 'unit': 3474230272332535317543572618479, 'val': 1}
  • id: 3550
    {'lmfdb_iso': '320.c', 'p': 43, 'prec': 20, 'unit': 1552396231495596303611272972572, 'val': 1}
  • id: 3553
    {'lmfdb_iso': '320.c', 'p': 47, 'prec': 20, 'unit': 48175846397724683042775705187247, 'val': 1}
  • id: 3556
    {'lmfdb_iso': '320.c', 'p': 53, 'prec': 20, 'unit': 177869094119749003741375396793252, 'val': 1}
  • id: 3560
    {'lmfdb_iso': '320.c', 'p': 59, 'prec': 20, 'unit': 2490728566105690539427503356118774, 'val': 1}
  • id: 3561
    {'lmfdb_iso': '320.c', 'p': 61, 'prec': 20, 'unit': 7351303351354795189741264474769352, 'val': 1}
  • id: 3545
    {'lmfdb_iso': '320.c', 'p': 67, 'prec': 20, 'unit': 28935211101193013860308911924858033, 'val': 1}
  • id: 3557
    {'lmfdb_iso': '320.c', 'p': 73, 'prec': 20, 'unit': 168983298055699367030209917125841081, 'val': 1}
  • id: 3562
    {'lmfdb_iso': '320.c', 'p': 83, 'prec': 20, 'unit': 2236762835720496421712929161152448262, 'val': 1}
  • id: 3559
    {'lmfdb_iso': '320.c', 'p': 89, 'prec': 20, 'unit': 1386924426205889079829607374634171565, 'val': 1}
  • id: 3544
    {'lmfdb_iso': '320.c', 'p': 97, 'prec': 20, 'unit': 21543825089234432354669901565995075185, 'val': 1}