Elliptic curve data - 5200.x2

Formats: - HTML - YAML - JSON - 2024-06-15T06:11:41.760376

• 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': '5200p', 'Clabel': '5200p2', 'Cnumber': 2, 'abc_quality': 0.947172997962475, 'absD': 1124864000000, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 4680, 'ainvs': [0, 1, 0, -1808, 58388], 'analytic_rank': 0, 'bad_primes': [2, 5, 13], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 5200, 'degree': 5184, 'elladic_images': ['3.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0029464185763173067931996803', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 23, 'isogeny_degrees': [1, 3], 'jinv': [-10218313, 17576], 'lmfdb_iso': '5200.x', 'lmfdb_label': '5200.x2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5, -8], 'min_quad_twist_disc': -20, 'modell_images': ['3Cs'], 'modm_images': ['3.12.0.a.1', '60.24.0-3.a.1.1', '104.2.0.?', '117.36.0.?', '312.24.1.?', '936.72.3.?', '1560.48.1.?', '2340.72.0.?', '4680.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.49491971820067818992441210777', 'prec': 107}, 'szpiro_ratio': 4.148165046878086, '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, 1, 0, 0, 0, -1, 0, -2, 0, -6, 0, -1, 0, 0, 0, 3, 0, -2, 0], 'aplist': [0, 1, 0, -1, -6, -1, 3, -2, 0, 6, 4, 7, 0, -1, 3, 0, 6, 8, 14, 3, -2, -8, 12, -6, 10], 'class_deg': 9, 'class_size': 3, 'conductor': 5200, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '5200.x', 'trace_hash': 795811706764272201}
• 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': '0.13454011963733221754127263767', 'prec': 103}, 'conductor': 5200, 'gens': [], 'heights': [], 'lmfdb_label': '5200.x2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.77800485460237768913372512428', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5560097092047553782674502485584634900', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '5200.x2'}
• ec_torsion_growth •

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

  
  
  • id: 272207
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '5200.x2', 'torsion': [3]}
  • id: 272208
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '5200.x2', 'torsion': [3]}
  • id: 272209
    {'degree': 3, 'field': [-2, -1, 0, 1], 'lmfdb_label': '5200.x2', 'torsion': [2]}
  • id: 272210
    {'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '5200.x2', 'torsion': [3, 3]}
  • id: 272212
    {'degree': 6, 'field': [-686, -294, 217, -4, 34, -2, 1], 'lmfdb_label': '5200.x2', 'torsion': [6]}
  • id: 272211
    {'degree': 6, 'field': [26, 0, 29, 0, 8, 0, 1], 'lmfdb_label': '5200.x2', 'torsion': [2, 2]}
  • id: 272213
    {'degree': 6, 'field': [54, -54, 57, -4, -6, -2, 1], 'lmfdb_label': '5200.x2', 'torsion': [6]}
  • id: 272214
    {'degree': 12, 'field': [-17656, 14270, -16562, -16477, 4153, 148, -748, 494, -190, -26, 22, -5, 1], 'lmfdb_label': '5200.x2', 'torsion': [4]}
  • id: 272215
    {'degree': 12, 'field': [2916, -2916, -162, -2646, 3357, -984, 358, 198, -29, 20, 10, -2, 1], 'lmfdb_label': '5200.x2', 'torsion': [3, 6]}
  • id: 272217
    {'degree': 12, 'field': [5006, -14244, 13178, -1960, -3047, 140, 1786, -1028, 132, 72, -16, -4, 1], 'lmfdb_label': '5200.x2', 'torsion': [2, 6]}
  • id: 272216
    {'degree': 12, 'field': [1152826, 383756, 991318, -594920, 186913, -76220, 21606, -4628, 1592, -208, 64, -4, 1], 'lmfdb_label': '5200.x2', 'torsion': [2, 6]}
  • id: 272218
    {'degree': 18, 'field': [-85184, 0, 0, 485969568, 0, 0, 309572772, 0, 0, 1577576, 0, 0, -35688, 0, 0, -84, 0, 0, 1], 'lmfdb_label': '5200.x2', 'torsion': [9]}
  • id: 272219
    {'degree': 18, 'field': [2418001, 1282200, 2944125, 1554770, 2560425, 715950, 1335106, 169110, 410625, 18808, 80220, 450, 10489, -90, 900, -6, 45, 0, 1], 'lmfdb_label': '5200.x2', 'torsion': [9]}
• 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: 101400
    {'conductor': 5200, 'conductor_valuation': 4, 'discriminant_valuation': 15, 'j_denominator_valuation': 3, 'kodaira_symbol': -11, 'lmfdb_label': '5200.x2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 101401
    {'conductor': 5200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '5200.x2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 101402
    {'conductor': 5200, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5200.x2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1698018
    {'adelic_gens': [[1, 18, 0, 1], [4663, 18, 4662, 19], [1169, 2790, 225, 1709], [1, 9, 9, 82], [1, 6, 6, 37], [2821, 1890, 2025, 511], [1, 0, 18, 1], [2341, 1890, 3285, 2971], [1, 12, 0, 1], [3521, 4230, 4050, 541], [3743, 0, 0, 4679]], 'adelic_image': '4680.144.3.?', 'conductor': 5200, 'lmfdb_label': '5200.x2', 'prime': 0}
  • id: 25922
    {'conductor': 5200, 'elladic_image': '3.12.0.1', 'lmfdb_label': '5200.x2', 'modell_image': '3Cs', 'prime': 3}
• lmfdb_iso 5200.x does not appear in ec_padic