Elliptic curve data - 4046.f6

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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': '4046b', 'Clabel': '4046b3', 'Cnumber': 3, 'abc_quality': 0.9869508090989833, 'absD': 529867914688, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 8568, 'ainvs': [1, 1, 0, 1295, -29547], 'analytic_rank': 1, 'bad_primes': [2, 7, 17], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 4046, 'degree': 4608, 'elladic_images': ['8.6.0.1', '3.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.93382791783716499729931098458', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [9938375, 21952], 'lmfdb_iso': '4046.f', 'lmfdb_label': '4046.f6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 4, -6], 'min_quad_twist_disc': 17, 'modell_images': ['2B', '3Cs'], 'modm_images': ['2.3.0.a.1', '3.12.0.a.1', '6.36.0.a.1', '8.6.0.c.1', '14.6.0.b.1', '24.72.1.n.1', '42.72.1.d.1', '51.24.0-3.a.1.1', '56.12.0.n.1', '63.36.0.a.1', '102.72.0.?', '126.216.7.?', '168.144.5.?', '408.144.1.?', '504.432.21.?', '714.144.1.?', '1071.72.0.?', '2142.432.7.?', '2856.288.5.?', '8568.864.21.?'], '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': '7.4039624769253249188223145184', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2023], [3, 2, 289], [7, 8, 578], [17, 146, 14]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.48277875419094304282545632436', 'prec': 107}, 'szpiro_ratio': 4.11135643356374, '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, -1, 2, 1, 0, -2, -1, -1, 1, 0, 0, 2, -4, 1, 0, 1, 0, -1, 2, 0], 'aplist': [-1, 2, 0, -1, 0, -4, 0, 2, 0, 6, 4, -2, -6, 8, -12, 6, -6, -8, -4, 0, -2, -8, -6, -6, 10], 'class_deg': 18, 'class_size': 6, 'conductor': 4046, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '4046.f', 'trace_hash': 1270343409320887797}
• 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': '0.15448537679894212861752088052', 'prec': 103}, 'conductor': 4046, 'gens': [[4626, 312375, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '7.4039624769253249188223145184', 'prec': 100}], 'lmfdb_label': '4046.f6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.48054600972539211182301482201', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5579446244429954577635333142715749000', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[18, -9, 1]], 'xcoord_integral_points': [18, 4626]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [11, 1], '5': [5, 1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [3, 0], '17': 'a', '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4046.f6'}
• ec_torsion_growth •

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

  
  
  • id: 211147
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '4046.f6', 'torsion': [6]}
  • id: 211146
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '4046.f6', 'torsion': [2, 2]}
  • id: 211148
    {'degree': 2, 'field': [13, -1, 1], 'lmfdb_label': '4046.f6', 'torsion': [6]}
  • id: 211149
    {'degree': 4, 'field': [-137, 26, 9, -2, 1], 'lmfdb_label': '4046.f6', 'torsion': [4]}
  • id: 211150
    {'degree': 4, 'field': [16, 4, 5, -1, 1], 'lmfdb_label': '4046.f6', 'torsion': [3, 6]}
  • id: 211151
    {'degree': 4, 'field': [36, 0, -5, 0, 1], 'lmfdb_label': '4046.f6', 'torsion': [2, 6]}
  • id: 211152
    {'degree': 4, 'field': [121, 0, 29, 0, 1], 'lmfdb_label': '4046.f6', 'torsion': [2, 6]}
  • id: 211156
    {'degree': 8, 'field': [239, 208, -284, -32, 113, -4, -18, 0, 1], 'lmfdb_label': '4046.f6', 'torsion': [12]}
  • id: 211154
    {'degree': 8, 'field': [953, -1150, 505, -278, 206, -54, 15, -2, 1], 'lmfdb_label': '4046.f6', 'torsion': [2, 4]}
  • id: 211155
    {'degree': 8, 'field': [1296, 0, 180, 0, -11, 0, 5, 0, 1], 'lmfdb_label': '4046.f6', 'torsion': [6, 6]}
  • id: 211157
    {'degree': 8, 'field': [1993, -1194, 1115, 442, 78, 70, -3, -2, 1], 'lmfdb_label': '4046.f6', 'torsion': [12]}
  • id: 211153
    {'degree': 8, 'field': [19826, -8706, -159, -114, 477, -34, -17, -2, 1], 'lmfdb_label': '4046.f6', 'torsion': [2, 4]}
  • id: 211159
    {'degree': 16, 'field': [57121, -49712, 111140, 43776, 60305, 38876, 25344, 9632, 7290, 1396, 1482, -40, 211, -8, 18, 0, 1], 'lmfdb_label': '4046.f6', 'torsion': [3, 12]}
  • id: 211161
    {'degree': 16, 'field': [226444, -656536, 941786, -274092, -549941, 676102, 13272, -189202, 31760, 4864, 4228, -2478, 140, 98, 6, -8, 1], 'lmfdb_label': '4046.f6', 'torsion': [2, 12]}
  • id: 211160
    {'degree': 16, 'field': [521168, 474808, -276130, -447706, 68105, 183730, -14300, -47834, 6316, 8402, -1810, -950, 256, 70, -18, -4, 1], 'lmfdb_label': '4046.f6', 'torsion': [2, 12]}
  • id: 211158
    {'degree': 16, 'field': [535024, 2246720, 3446112, 2016512, -84000, -531008, -219120, -49344, 9044, 14752, 3784, -32, -404, -88, 8, 0, 1], 'lmfdb_label': '4046.f6', 'torsion': [8]}
  • id: 211162
    {'degree': 16, 'field': [876164, -5928, -801850, -11184, 345531, 30972, -89134, -17088, 14806, 4760, -1688, -832, 170, 84, -16, -4, 1], 'lmfdb_label': '4046.f6', 'torsion': [2, 12]}
  • id: 211163
    {'degree': 16, 'field': [1469476, -1541408, 2213442, -1536152, 1288217, -739892, 451604, -201020, 84486, -26920, 9674, -2600, 676, -140, 40, -8, 1], 'lmfdb_label': '4046.f6', 'torsion': [2, 12]}
  • id: 211164
    {'degree': 18, 'field': [-262144, 0, 0, 159744, 0, 0, 112896, 0, 0, 14677, 0, 0, -133, 0, 0, -52, 0, 0, 1], 'lmfdb_label': '4046.f6', 'torsion': [18]}
  • id: 211165
    {'degree': 18, 'field': [49815336591, -32743680921, 34989368697, -15679296024, 9367097274, -3113197158, 1310031094, -334136640, 108062757, -21734003, 5746131, -955944, 218994, -31806, 6378, -764, 123, -9, 1], 'lmfdb_label': '4046.f6', '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: 75754
    {'conductor': 4046, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '4046.f6', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 75755
    {'conductor': 4046, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '4046.f6', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 75756
    {'conductor': 4046, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4046.f6', 'prime': 17, 'reduction_type': 0, '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: 1690299
    {'adelic_gens': [[1, 36, 0, 1], [1, 0, 36, 1], [4285, 3060, 0, 8093], [1837, 6324, 1530, 5203], [8533, 36, 8532, 37], [3023, 0, 0, 8567], [3622, 4539, 4437, 3724], [1, 6, 6, 37], [4285, 3060, 1530, 3673], [19, 24, 1440, 1819]], 'adelic_image': '8568.864.21.?', 'conductor': 4046, 'lmfdb_label': '4046.f6', 'prime': 0}
  • id: 20112
    {'conductor': 4046, 'elladic_image': '8.6.0.1', 'lmfdb_label': '4046.f6', 'modell_image': '2B', 'prime': 2}
  • id: 20113
    {'conductor': 4046, 'elladic_image': '3.12.0.1', 'lmfdb_label': '4046.f6', 'modell_image': '3Cs', 'prime': 3}
• ec_padic •

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

  
  
  • id: 141641
    {'lmfdb_iso': '4046.f', 'p': 13, 'prec': 20, 'unit': 10783700463631680124, 'val': 2}
  • id: 141644
    {'lmfdb_iso': '4046.f', 'p': 19, 'prec': 20, 'unit': 1030318058929618210679832, 'val': 1}
  • id: 141640
    {'lmfdb_iso': '4046.f', 'p': 29, 'prec': 20, 'unit': 4804433183793178350286744055, 'val': 1}
  • id: 141650
    {'lmfdb_iso': '4046.f', 'p': 31, 'prec': 20, 'unit': 6149359113587449272957944979, 'val': 1}
  • id: 141637
    {'lmfdb_iso': '4046.f', 'p': 37, 'prec': 20, 'unit': 436552429367243104649678945577, 'val': 1}
  • id: 141638
    {'lmfdb_iso': '4046.f', 'p': 41, 'prec': 20, 'unit': 276297385970004580238647714326, 'val': 1}
  • id: 141639
    {'lmfdb_iso': '4046.f', 'p': 43, 'prec': 20, 'unit': 2543695517689872184227280443989, 'val': 1}
  • id: 141648
    {'lmfdb_iso': '4046.f', 'p': 47, 'prec': 20, 'unit': 46591678029211758216382860941925, 'val': 1}
  • id: 141645
    {'lmfdb_iso': '4046.f', 'p': 53, 'prec': 20, 'unit': 512112870930437737494712567992235, 'val': 1}
  • id: 141643
    {'lmfdb_iso': '4046.f', 'p': 59, 'prec': 20, 'unit': 2119116164327620355118660079066492, 'val': 1}
  • id: 141649
    {'lmfdb_iso': '4046.f', 'p': 61, 'prec': 20, 'unit': 7688668691400720625888370500791614, 'val': 1}
  • id: 141636
    {'lmfdb_iso': '4046.f', 'p': 67, 'prec': 20, 'unit': 6826246686587649501976225256645287, 'val': 1}
  • id: 141646
    {'lmfdb_iso': '4046.f', 'p': 73, 'prec': 20, 'unit': 137494866688124776508168085032784539, 'val': 1}
  • id: 141642
    {'lmfdb_iso': '4046.f', 'p': 79, 'prec': 20, 'unit': 907267043997245963598705554760537527, 'val': 1}
  • id: 141635
    {'lmfdb_iso': '4046.f', 'p': 83, 'prec': 20, 'unit': 1250244293282702161841485988357519099, 'val': 1}
  • id: 141647
    {'lmfdb_iso': '4046.f', 'p': 89, 'prec': 20, 'unit': 8339891231135128407882127885753285398, 'val': 1}
  • id: 141634
    {'lmfdb_iso': '4046.f', 'p': 97, 'prec': 20, 'unit': 52999091543673748514877834124485974873, 'val': 1}