Elliptic curve data - 48400.w3

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '48400cp', 'Clabel': '48400cp2', 'Cnumber': 2, 'abc_quality': 0.8781924989889901, 'absD': 1217948187500000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 660, 'ainvs': [0, 1, 0, -303508, -36469512], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 48400, 'degree': 829440, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1688107342875638289639312018', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 22, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [436334416, 171875], 'lmfdb_iso': '48400.w', 'lmfdb_label': '48400.w3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -100, -252], 'min_quad_twist_disc': 220, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0-6.a.1.1', '20.6.0.c.1', '30.24.0-6.a.1.3', '44.6.0.a.1', '60.48.0-60.q.1.6', '132.48.0.?', '220.12.0.?', '660.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7184901589889144619324843983', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3025], [5, 18, 1936], [11, 72, 400]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.29695397870196850331224166810', 'prec': 107}, 'szpiro_ratio': 4.58718141428078, '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, -2, 0, 0, 0, 4, 0, 1, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, 0], 'aplist': [0, -2, 0, 4, 0, -4, 0, -4, -6, 6, -8, -2, -6, -8, 6, 6, 12, -2, -10, 12, -16, 8, 0, 6, -14], 'class_deg': 6, 'class_size': 4, 'conductor': 48400, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '48400.w', 'trace_hash': 2230800722424669058}
• 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': '0.013067572901199394198460306245', 'prec': 107}, 'conductor': 48400, 'gens': [[-297, 5250, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.7184901589889144619324843983', 'prec': 100}], 'lmfdb_label': '48400.w3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.21038742871308788431436293584', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9708440478307478351581052577823117431', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-477, 0, 1]], 'xcoord_integral_points': [-477, -297]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': 'a', '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 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': '48400.w3'}
• ec_torsion_growth •

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

  
  
  • id: 2355960
    {'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '48400.w3', 'torsion': [6]}
  • id: 2355959
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '48400.w3', 'torsion': [2, 2]}
  • id: 2355961
    {'degree': 4, 'field': [11, 0, 7, 0, 1], 'lmfdb_label': '48400.w3', 'torsion': [4]}
  • id: 2355962
    {'degree': 4, 'field': [89, 24, -23, -2, 1], 'lmfdb_label': '48400.w3', 'torsion': [2, 6]}
  • id: 2355963
    {'degree': 6, 'field': [4125, 0, 1375, 0, 55, 0, 1], 'lmfdb_label': '48400.w3', 'torsion': [6]}
  • id: 2355964
    {'degree': 8, 'field': [25, -80, -726, 56, -372, -52, 22, -4, 1], 'lmfdb_label': '48400.w3', 'torsion': [2, 4]}
  • id: 2355965
    {'degree': 8, 'field': [229, -374, 350, -22, 55, -22, -8, 0, 1], 'lmfdb_label': '48400.w3', 'torsion': [2, 12]}
  • id: 2355967
    {'degree': 12, 'field': [6340, 9960, -1236, -18640, 12540, -4560, 2753, -1206, 495, -140, 39, -6, 1], 'lmfdb_label': '48400.w3', 'torsion': [2, 6]}
  • id: 2355966
    {'degree': 12, 'field': [30239001, 32994, 82521, -220050, 82590, 32874, -10859, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '48400.w3', 'torsion': [3, 6]}
  • id: 2355969
    {'degree': 16, 'field': [3025, 0, -67760, 0, 374066, 0, -52668, 0, 17779, 0, -2604, 0, 294, 0, -28, 0, 1], 'lmfdb_label': '48400.w3', 'torsion': [2, 12]}
  • id: 2355968
    {'degree': 16, 'field': [698896, 0, -170368, 0, 67408, 0, 15664, 0, 940, 0, 744, 0, 308, 0, 32, 0, 1], 'lmfdb_label': '48400.w3', 'torsion': [8]}
  • id: 2355970
    {'degree': 18, 'field': [-3852119, -20428484, 45263081, -43418284, 40530405, -26005644, 8878366, -2674094, 980106, -333510, 111521, 1976, -13049, 2226, -235, 56, 6, -4, 1], 'lmfdb_label': '48400.w3', 'torsion': [18]}
• 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: 1155908
    {'conductor': 48400, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48400.w3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1155909
    {'conductor': 48400, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '48400.w3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1155910
    {'conductor': 48400, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '48400.w3', 'prime': 11, '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

  
  
  • id: 1986294
    {'adelic_gens': [[449, 2, 498, 13], [1, 0, 12, 1], [263, 648, 258, 587], [54, 263, 55, 274], [1, 6, 6, 37], [649, 12, 648, 13], [1, 12, 0, 1], [11, 2, 610, 651], [530, 657, 87, 8]], 'adelic_image': '660.96.1.?', 'conductor': 48400, 'lmfdb_label': '48400.w3', 'prime': 0}
  • id: 208648
    {'conductor': 48400, 'elladic_image': '2.3.0.1', 'lmfdb_label': '48400.w3', 'modell_image': '2B', 'prime': 2}
  • id: 208649
    {'conductor': 48400, 'elladic_image': '3.4.0.1', 'lmfdb_label': '48400.w3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 2429039
    {'lmfdb_iso': '48400.w', 'p': 7, 'prec': 20, 'unit': 5365178328202192, 'val': 1}
  • id: 2429043
    {'lmfdb_iso': '48400.w', 'p': 13, 'prec': 20, 'unit': 1409041425703414855816, 'val': 1}
  • id: 2429046
    {'lmfdb_iso': '48400.w', 'p': 19, 'prec': 20, 'unit': 1733850489108151237034507, 'val': 1}
  • id: 2429049
    {'lmfdb_iso': '48400.w', 'p': 23, 'prec': 20, 'unit': 30169632443036714938250939, 'val': 1}
  • id: 2429042
    {'lmfdb_iso': '48400.w', 'p': 29, 'prec': 20, 'unit': 936814035665558130075398007, 'val': 1}
  • id: 2429054
    {'lmfdb_iso': '48400.w', 'p': 31, 'prec': 20, 'unit': 16874701844769066864972091069, 'val': 1}
  • id: 2429038
    {'lmfdb_iso': '48400.w', 'p': 37, 'prec': 20, 'unit': 475686406414500193998646947806, 'val': 1}
  • id: 2429040
    {'lmfdb_iso': '48400.w', 'p': 41, 'prec': 20, 'unit': 3628590629261356922685770159890, 'val': 1}
  • id: 2429041
    {'lmfdb_iso': '48400.w', 'p': 43, 'prec': 20, 'unit': 1546927590057511278017190164207, 'val': 1}
  • id: 2429052
    {'lmfdb_iso': '48400.w', 'p': 47, 'prec': 20, 'unit': 46040131512789273962059380548045, 'val': 1}
  • id: 2429047
    {'lmfdb_iso': '48400.w', 'p': 53, 'prec': 20, 'unit': 195239039099905359506668575858637, 'val': 1}
  • id: 2429045
    {'lmfdb_iso': '48400.w', 'p': 59, 'prec': 20, 'unit': 3616880940258084279898147167584236, 'val': 1}
  • id: 2429053
    {'lmfdb_iso': '48400.w', 'p': 61, 'prec': 20, 'unit': 3774809740626930521989945322736621, 'val': 1}
  • id: 2429037
    {'lmfdb_iso': '48400.w', 'p': 67, 'prec': 20, 'unit': 38266001864905996864587354606532847, 'val': 1}
  • id: 2429051
    {'lmfdb_iso': '48400.w', 'p': 71, 'prec': 20, 'unit': 73640004383629122376450731889458161, 'val': 1}
  • id: 2429048
    {'lmfdb_iso': '48400.w', 'p': 73, 'prec': 20, 'unit': 127422539726652460567262976272694733, 'val': 1}
  • id: 2429044
    {'lmfdb_iso': '48400.w', 'p': 79, 'prec': 20, 'unit': 286692997440006545514804836400306553, 'val': 1}
  • id: 2429050
    {'lmfdb_iso': '48400.w', 'p': 89, 'prec': 20, 'unit': 362950152612001327222842641213917096, 'val': 1}
  • id: 2429036
    {'lmfdb_iso': '48400.w', 'p': 97, 'prec': 20, 'unit': 21838838975020155898833056483125633938, 'val': 1}