Elliptic curve data - 31680.df4

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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': '31680dw', 'Clabel': '31680dw1', 'Cnumber': 1, 'abc_quality': 0.7920712085843463, 'absD': 10510663680, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1320, 'ainvs': [0, 0, 0, 468, 3024], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 31680, 'degree': 16384, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.61021425463926859974325126955', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 83, 'isogeny_degrees': [1, 2, 4], 'jinv': [59319, 55], 'lmfdb_iso': '31680.df', 'lmfdb_label': '31680.df4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 1, 0], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.6', '40.12.0.z.1', '88.12.0.?', '110.6.0.?', '120.24.0.?', '220.12.0.?', '264.24.0.?', '440.24.0.?', '1320.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.4877903046049773270448825621', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 495], [3, 6, 3520], [5, 6, 6336], [11, 12, 2880]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.97881266053470421008021953110', 'prec': 107}, 'szpiro_ratio': 2.900485308630515, '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, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 1, 0, 1, -2, -6, -4, 4, 6, 8, 2, -2, 4, -12, -2, -4, 10, -16, 8, 14, -8, 4, -10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 31680, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '31680.df', 'trace_hash': 1043229114407515041}
• 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': '0.29510368515942341321693226906', 'prec': 103}, 'conductor': 31680, 'gens': [[250, 3968, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.4877903046049773270448825621', 'prec': 100}], 'lmfdb_label': '31680.df4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.83990542047290706305065492786', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.8588279646211441708987968327369152926', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-6, 0, 1]], 'xcoord_integral_points': [-6, 250]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': [1, 1, 0], '11': [4, 0], '13': [1, 0], '17': [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': '31680.df4'}
• ec_torsion_growth •

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

  
  
  • id: 1579616
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [4]}
  • id: 1579615
    {'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '31680.df4', 'torsion': [2, 2]}
  • id: 1579617
    {'degree': 2, 'field': [66, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [4]}
  • id: 1579618
    {'degree': 4, 'field': [576, 0, 18, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [2, 4]}
  • id: 1579622
    {'degree': 8, 'field': [-432, 0, 0, 0, 72, 0, -6, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [6]}
  • id: 1579620
    {'degree': 8, 'field': [1420, -440, -1120, -80, 171, 42, -21, -2, 1], 'lmfdb_label': '31680.df4', 'torsion': [8]}
  • id: 1579621
    {'degree': 8, 'field': [11185, 8140, 4626, 1012, 183, -44, 2, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [8]}
  • id: 1579619
    {'degree': 8, 'field': [32400, 0, -9450, 0, 585, 0, 30, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [2, 4]}
  • id: 1579627
    {'degree': 16, 'field': [-1005845, -683720, 440220, 768650, 184280, -228870, -93209, -1910, 23151, 2566, -1679, -810, 260, 2, 12, -8, 1], 'lmfdb_label': '31680.df4', 'torsion': [12]}
  • id: 1579628
    {'degree': 16, 'field': [932875, -506300, 1630980, -593746, -37393, 133848, 13891, -94070, 23520, 8104, -785, -1398, 230, 26, 12, -8, 1], 'lmfdb_label': '31680.df4', 'torsion': [12]}
  • id: 1579624
    {'degree': 16, 'field': [2725801, 0, -1437350, 0, 532701, 0, -240370, 0, 74516, 0, -12430, 0, 1101, 0, -50, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [2, 8]}
  • id: 1579623
    {'degree': 16, 'field': [3632836, 0, 2192360, 0, 1639936, 0, 571220, 0, 202501, 0, 15860, 0, -194, 0, -40, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [4, 4]}
  • id: 1579625
    {'degree': 16, 'field': [14891881, 0, 8794582, 0, 2270037, 0, 393722, 0, 62708, 0, 8246, 0, 693, 0, 34, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [2, 8]}
  • id: 1579626
    {'degree': 16, 'field': [31443795, 11823570, 1601775, 6476760, 3336930, 775170, 506844, 256716, 25218, -6858, 6705, 4356, 672, -114, -36, 0, 1], 'lmfdb_label': '31680.df4', 'torsion': [2, 6]}
• 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: 740127
    {'conductor': 31680, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '31680.df4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 740128
    {'conductor': 31680, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '31680.df4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 740129
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '31680.df4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 740130
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '31680.df4', 'prime': 11, '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: 1875655
    {'adelic_gens': [[821, 822, 702, 485], [808, 3, 285, 442], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1151, 1152, 42, 1145], [1313, 8, 1312, 9], [439, 0, 0, 1319], [268, 441, 111, 886], [7, 6, 1314, 1315]], 'adelic_image': '1320.48.0.?', 'conductor': 31680, 'lmfdb_label': '31680.df4', 'prime': 0}
  • id: 141626
    {'conductor': 31680, 'elladic_image': '4.6.0.1', 'lmfdb_label': '31680.df4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1541440
    {'lmfdb_iso': '31680.df', 'p': 13, 'prec': 20, 'unit': 1213965274603342269945, 'val': 1}
  • id: 1541442
    {'lmfdb_iso': '31680.df', 'p': 17, 'prec': 20, 'unit': 181161581033185923980028, 'val': 1}
  • id: 1541443
    {'lmfdb_iso': '31680.df', 'p': 19, 'prec': 20, 'unit': 1256283816997089663430463, 'val': 1}
  • id: 1541447
    {'lmfdb_iso': '31680.df', 'p': 23, 'prec': 20, 'unit': 3391820724298546185234817, 'val': 1}
  • id: 1541439
    {'lmfdb_iso': '31680.df', 'p': 29, 'prec': 20, 'unit': 52716832429606525699347404, 'val': 1}
  • id: 1541451
    {'lmfdb_iso': '31680.df', 'p': 31, 'prec': 20, 'unit': 9850198721891575489663339381, 'val': 1}
  • id: 1541435
    {'lmfdb_iso': '31680.df', 'p': 37, 'prec': 20, 'unit': 110639288156739263011660070970, 'val': 1}
  • id: 1541437
    {'lmfdb_iso': '31680.df', 'p': 41, 'prec': 20, 'unit': 3475949659663742695925250041103, 'val': 1}
  • id: 1541438
    {'lmfdb_iso': '31680.df', 'p': 43, 'prec': 20, 'unit': 3808130597353143957026973649356, 'val': 1}
  • id: 1541449
    {'lmfdb_iso': '31680.df', 'p': 47, 'prec': 20, 'unit': 24898664215998811063479137928643, 'val': 1}
  • id: 1541444
    {'lmfdb_iso': '31680.df', 'p': 53, 'prec': 20, 'unit': 211890313183213869912196349764614, 'val': 1}
  • id: 1541445
    {'lmfdb_iso': '31680.df', 'p': 59, 'prec': 20, 'unit': 2350129169078354512327985918983148, 'val': 1}
  • id: 1541450
    {'lmfdb_iso': '31680.df', 'p': 61, 'prec': 20, 'unit': 6409102914431880159846216277137920, 'val': 1}
  • id: 1541434
    {'lmfdb_iso': '31680.df', 'p': 67, 'prec': 20, 'unit': 8928299817156088834166060668642718, 'val': 1}
  • id: 1541436
    {'lmfdb_iso': '31680.df', 'p': 71, 'prec': 20, 'unit': 61167611357933844746813723320459264, 'val': 1}
  • id: 1541446
    {'lmfdb_iso': '31680.df', 'p': 73, 'prec': 20, 'unit': 22144367429994910387327094145675010, 'val': 1}
  • id: 1541441
    {'lmfdb_iso': '31680.df', 'p': 79, 'prec': 20, 'unit': 224126245760489753375832521111549580, 'val': 1}
  • id: 1541433
    {'lmfdb_iso': '31680.df', 'p': 83, 'prec': 20, 'unit': 2744308531786715667386188886096200256, 'val': 1}
  • id: 1541448
    {'lmfdb_iso': '31680.df', 'p': 89, 'prec': 20, 'unit': 8298781947525436634955712941711712562, 'val': 1}
  • id: 1541432
    {'lmfdb_iso': '31680.df', 'p': 97, 'prec': 20, 'unit': 34245841035922891271163131719544569593, 'val': 1}