Elliptic curve data - 51744.o1

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• 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': '51744e', 'Clabel': '51744e2', 'Cnumber': 2, 'abc_quality': 1.0521235750322544, 'absD': 1619991356239872, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [0, -1, 0, -217233, -38850111], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 51744, 'degree': 286720, 'elladic_images': ['4.6.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8211885707457319055242833323', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2], 'jinv': [6859000000, 9801], 'lmfdb_iso': '51744.o', 'lmfdb_label': '51744.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -4433, -111999], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.e.1', '24.12.0.bv.1', '28.12.0.l.1', '88.12.0.?', '168.24.0.?', '264.24.0.?', '616.24.0.?', '1848.48.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 7], [3, 4, 17248], [7, 20, 1056], [11, 12, 4704]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33139122160569838272196334674', 'prec': 107}, 'szpiro_ratio': 4.4665100615794255, '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, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -8, 0], 'aplist': [0, -1, 0, 0, -1, 0, 0, -8, -4, 2, -4, 2, 8, 8, 12, 6, -4, 8, -8, -12, 4, -8, 0, -12, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 51744, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '51744.o', 'trace_hash': 2230470596905330714}
• 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': '0.026190012544254874713874263604', 'prec': 107}, 'conductor': 51744, 'gens': [], 'heights': [], 'lmfdb_label': '51744.o1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.22115929981426192593598067563', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.88463719925704770374392270253115984092', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-261, 0, 1]], 'xcoord_integral_points': [-261]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '7': 'a', '11': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '51744.o1'}
• ec_torsion_growth •

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

  
  
  • id: 2505491
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '51744.o1', 'torsion': [2, 2]}
  • id: 2505492
    {'degree': 4, 'field': [2, -4, 3, -1, 1], 'lmfdb_label': '51744.o1', 'torsion': [4]}
  • id: 2505495
    {'degree': 8, 'field': [-190512, 0, 112896, 0, 1512, 0, 0, 0, 1], 'lmfdb_label': '51744.o1', 'torsion': [6]}
  • id: 2505494
    {'degree': 8, 'field': [1, -2, 2, 4, -1, 4, 2, -2, 1], 'lmfdb_label': '51744.o1', 'torsion': [2, 4]}
  • id: 2505493
    {'degree': 8, 'field': [14641, 0, -5324, 0, -121, 0, -44, 0, 1], 'lmfdb_label': '51744.o1', 'torsion': [2, 4]}
  • id: 2505498
    {'degree': 16, 'field': [-253230519, -538467876, -219844616, 12774832, -102521300, -59492804, -34227200, -10194872, -1810318, -569668, -148456, 3472, -5012, 28, 16, -8, 1], 'lmfdb_label': '51744.o1', 'torsion': [2, 6]}
  • id: 2505497
    {'degree': 16, 'field': [35153041, 0, 11869858, 0, 4760987, 0, 561330, 0, 81008, 0, -5394, 0, -373, 0, -2, 0, 1], 'lmfdb_label': '51744.o1', 'torsion': [8]}
  • id: 2505496
    {'degree': 16, 'field': [83777409, 64803240, 25063200, -15160596, 5415682, 826172, 390632, -286312, 119379, 9412, 2200, -1424, 558, 44, 8, -4, 1], 'lmfdb_label': '51744.o1', 'torsion': [4, 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: 1238198
    {'conductor': 51744, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '51744.o1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1238199
    {'conductor': 51744, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '51744.o1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1238200
    {'conductor': 51744, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '51744.o1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1238201
    {'conductor': 51744, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '51744.o1', 'prime': 11, '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: 2007941
    {'adelic_gens': [[617, 8, 620, 33], [1517, 2, 22, 9], [1, 1394, 1390, 33], [3, 8, 1840, 1827], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1841, 8, 1840, 9], [468, 1405, 917, 1364], [270, 19, 1841, 1826], [5, 8, 48, 77]], 'adelic_image': '1848.48.1.?', 'conductor': 51744, 'lmfdb_label': '51744.o1', 'prime': 0}
  • id: 221437
    {'conductor': 51744, 'elladic_image': '4.6.0.4', 'lmfdb_label': '51744.o1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 51744.o does not appear in ec_padic