Elliptic curve data - 41616.ca1

Formats: - HTML - YAML - JSON - 2024-06-16T06:47:31.059109

• 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': '41616a', 'Clabel': '41616a1', 'Cnumber': 1, 'abc_quality': 0.8034383677671774, 'absD': 2836260907776, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 102, 'ainvs': [0, 0, 0, 3468, -19652], 'analytic_rank': 1, 'bad_primes': [2, 3, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 41616, 'degree': 36864, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0786152753055889906191101854', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 52, 'isogeny_degrees': [1], 'jinv': [27648, 17], 'lmfdb_iso': '41616.ca', 'lmfdb_label': '41616.ca1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 12, 4], 'min_quad_twist_disc': -68, 'modell_images': [], 'modm_images': ['102.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.6812105145287943268347567006', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0747425892628433452992898471', 'prec': 103}, 'szpiro_ratio': 3.3910106473879513, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, 0, 0, 0, 3, 0, -1, 0, 0, 0, 0, 0, 3, 0], 'aplist': [0, 0, 1, -2, 3, -1, 0, 3, 3, 2, -4, 6, 3, 5, 0, -8, -2, 10, -4, -8, -4, -10, -16, -2, 4], 'class_deg': 1, 'class_size': 1, 'conductor': 41616, 'isogeny_matrix': [[1]], 'lmfdb_iso': '41616.ca', 'trace_hash': 417435958072888387}
• 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': '0.11564495079578023758750472460', 'prec': 103}, 'conductor': 41616, 'gens': [[153, 2023, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.6812105145287943268347567006', 'prec': 100}], 'lmfdb_label': '41616.ca1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.46558593595904061355655671222', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.2619837676085516356278808224675903689', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [153]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '41616.ca1'}
• ec_torsion_growth •

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

  
  
  • id: 2045461
    {'degree': 3, 'field': [-3, 1, -1, 1], 'lmfdb_label': '41616.ca1', 'torsion': [2]}
  • id: 2045462
    {'degree': 6, 'field': [9, -27, 30, -15, 4, -1, 1], 'lmfdb_label': '41616.ca1', 'torsion': [2, 2]}
  • id: 2045463
    {'degree': 8, 'field': [-1453, -1890, 304, 1388, 540, -50, -46, 0, 1], 'lmfdb_label': '41616.ca1', 'torsion': [3]}
  • id: 2045464
    {'degree': 12, 'field': [444, -912, 552, 360, -296, 92, -292, 344, -158, 64, -16, -2, 1], 'lmfdb_label': '41616.ca1', 'torsion': [4]}
• 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: 987514
    {'conductor': 41616, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '41616.ca1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 987515
    {'conductor': 41616, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '41616.ca1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 987516
    {'conductor': 41616, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '41616.ca1', 'prime': 17, '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

  
  {'adelic_gens': [[1, 2, 0, 1], [1, 1, 101, 0], [1, 0, 2, 1], [35, 2, 35, 3], [37, 2, 37, 3], [101, 2, 100, 3]], 'adelic_image': '102.2.0.?', 'conductor': 41616, 'lmfdb_label': '41616.ca1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2068321
    {'lmfdb_iso': '41616.ca', 'p': 5, 'prec': 20, 'unit': 84382207899823, 'val': -1}
  • id: 2068322
    {'lmfdb_iso': '41616.ca', 'p': 7, 'prec': 20, 'unit': 419885911183279, 'val': 1}
  • id: 2068329
    {'lmfdb_iso': '41616.ca', 'p': 11, 'prec': 20, 'unit': 24005900947202717624, 'val': 1}
  • id: 2068327
    {'lmfdb_iso': '41616.ca', 'p': 13, 'prec': 20, 'unit': 870497639045976309714, 'val': 1}
  • id: 2068330
    {'lmfdb_iso': '41616.ca', 'p': 19, 'prec': 20, 'unit': 84861613556316957527224, 'val': 1}
  • id: 2068333
    {'lmfdb_iso': '41616.ca', 'p': 23, 'prec': 20, 'unit': 60785260645646627222200155, 'val': 1}
  • id: 2068326
    {'lmfdb_iso': '41616.ca', 'p': 29, 'prec': 20, 'unit': 2512722106149000577166539665, 'val': 1}
  • id: 2068323
    {'lmfdb_iso': '41616.ca', 'p': 31, 'prec': 20, 'unit': 5801113117856872398548522147, 'val': 1}
  • id: 2068338
    {'lmfdb_iso': '41616.ca', 'p': 37, 'prec': 20, 'unit': 153641967659775371903408225884, 'val': 1}
  • id: 2068324
    {'lmfdb_iso': '41616.ca', 'p': 41, 'prec': 20, 'unit': 2652587968036199850426852117893, 'val': 1}
  • id: 2068325
    {'lmfdb_iso': '41616.ca', 'p': 43, 'prec': 20, 'unit': 724800198060549552361123977560, 'val': 1}
  • id: 2068331
    {'lmfdb_iso': '41616.ca', 'p': 53, 'prec': 20, 'unit': 153941003945303175235851531873029, 'val': 1}
  • id: 2068336
    {'lmfdb_iso': '41616.ca', 'p': 59, 'prec': 20, 'unit': 3985993466065882590636551045161651, 'val': 1}
  • id: 2068337
    {'lmfdb_iso': '41616.ca', 'p': 61, 'prec': 20, 'unit': 7883476725490112968607828654560880, 'val': 1}
  • id: 2068320
    {'lmfdb_iso': '41616.ca', 'p': 67, 'prec': 20, 'unit': 12382466177258854322905171526336045, 'val': 1}
  • id: 2068335
    {'lmfdb_iso': '41616.ca', 'p': 71, 'prec': 20, 'unit': 44175078704392801602135600235507772, 'val': 1}
  • id: 2068332
    {'lmfdb_iso': '41616.ca', 'p': 73, 'prec': 20, 'unit': 252303208140332399131850031132903083, 'val': 1}
  • id: 2068328
    {'lmfdb_iso': '41616.ca', 'p': 79, 'prec': 20, 'unit': 3668346270436870783664757224674313, 'val': 2}
  • id: 2068319
    {'lmfdb_iso': '41616.ca', 'p': 83, 'prec': 20, 'unit': 1670554712688203716956852856677534337, 'val': 1}
  • id: 2068334
    {'lmfdb_iso': '41616.ca', 'p': 89, 'prec': 20, 'unit': 533539079173748730119520996331198082, 'val': 1}
  • id: 2068318
    {'lmfdb_iso': '41616.ca', 'p': 97, 'prec': 20, 'unit': 53170187667228587094773712131028614494, 'val': 1}