Elliptic curve data - 8670.r2

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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': '8670r', 'Clabel': '8670r4', 'Cnumber': 4, 'abc_quality': 0.9394020799048373, 'absD': 60479817013470, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2040, 'ainvs': [1, 1, 1, -47980, 4007855], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 8670, 'degree': 36864, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4919811128951952771091875525', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [506071034209, 2505630], 'lmfdb_iso': '8670.r', 'lmfdb_label': '8670.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -166, 806], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '120.24.0.?', '136.24.0.?', '1020.12.0.?', '2040.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.1020993201320873228240417642', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 4335], [3, 4, 2890], [5, 6, 1734], [17, 162, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.075374440867087236984420243563', 'prec': 107}, 'szpiro_ratio': 4.846828960524284, '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, -1, 1, 1, -1, 0, 1, 1, 1, -4, -1, 2, 0, -1, 1, 0, 1, -4, 1], 'aplist': [1, -1, 1, 0, -4, 2, 0, -4, -4, -2, 4, 6, 10, -8, 0, 6, -8, -10, -8, -8, 2, -4, 4, -14, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 8670, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '8670.r', 'trace_hash': 1635604046090819867}
• 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': '0.050591979366799950246836307043', 'prec': 107}, 'conductor': 8670, 'gens': [[8995, 840437, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '9.1020993201320873228240417642', 'prec': 100}], 'lmfdb_label': '8670.r2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.62715919548526469599328567285', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.7084652868410146385366207214614461516', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[531, -535, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 0], '3': [1, 0], '5': [4, 0], '7': [1, 1, 0], '11': [1, 0], '13': [3, 0], '17': 'a', '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '8670.r2'}
• ec_torsion_growth •

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

  
  
  • id: 452743
    {'degree': 2, 'field': [-255, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [4]}
  • id: 452742
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [4]}
  • id: 452741
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [2, 2]}
  • id: 452744
    {'degree': 4, 'field': [1, 0, -32, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [2, 4]}
  • id: 452745
    {'degree': 4, 'field': [120, 0, -32, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [8]}
  • id: 452749
    {'degree': 8, 'field': [-195, -660, -580, -504, -174, -52, -12, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [6]}
  • id: 452748
    {'degree': 8, 'field': [18241, -2040, -11904, 1680, 1862, -120, -96, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [2, 8]}
  • id: 452747
    {'degree': 8, 'field': [18496, 0, -4556, 0, 441, 0, -26, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [8]}
  • id: 452746
    {'degree': 8, 'field': [140896, 97920, 31264, 7680, 276, -240, 4, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [2, 4]}
  • id: 452754
    {'degree': 16, 'field': [4734976, 0, -10723328, 0, 10771456, 0, -2603136, 0, -97344, 0, 7296, 0, 916, 0, -62, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [12]}
  • id: 452755
    {'degree': 16, 'field': [5253264, 0, 440832, 0, -440060, 0, 18384, 0, -35160, 0, -64, 0, -192, 0, 0, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [12]}
  • id: 452751
    {'degree': 16, 'field': [10601536, -2396416, 270848, 4017888, -1283884, -1266776, 1080520, -556116, 123769, 18108, -11480, 4172, -574, -84, 32, -8, 1], 'lmfdb_label': '8670.r2', 'torsion': [2, 8]}
  • id: 452750
    {'degree': 16, 'field': [77545636, -107785440, 74908800, -30926400, 14057236, -7715520, 3312000, -576960, 6741, -120, 7200, 2160, -134, -120, 0, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [4, 4]}
  • id: 452753
    {'degree': 16, 'field': [207360000, 0, -926208000, 0, -96537600, 0, -2008800, 0, -338400, 0, -11640, 0, 2340, 0, -60, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [2, 6]}
  • id: 452752
    {'degree': 16, 'field': [207360000, 0, -221184000, 0, 64051200, 0, -8985600, 0, 885600, 0, -74880, 0, 4448, 0, -128, 0, 1], 'lmfdb_label': '8670.r2', 'torsion': [16]}
• 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: 180947
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8670.r2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 180948
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8670.r2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 180949
    {'conductor': 8670, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8670.r2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 180950
    {'conductor': 8670, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '8670.r2', 'prime': 17, '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: 1721289
    {'adelic_gens': [[256, 1283, 259, 288], [688, 3, 685, 2], [416, 3, 5, 2], [1, 0, 8, 1], [2033, 8, 2032, 9], [7, 6, 2034, 2035], [768, 1793, 1267, 1254], [1799, 2032, 1076, 2007], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '2040.48.0.?', 'conductor': 8670, 'lmfdb_label': '8670.r2', 'prime': 0}
  • id: 42416
    {'conductor': 8670, 'elladic_image': '8.12.0.6', 'lmfdb_label': '8670.r2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 359532
    {'lmfdb_iso': '8670.r', 'p': 11, 'prec': 20, 'unit': 51639674274547402473, 'val': 1}
  • id: 359530
    {'lmfdb_iso': '8670.r', 'p': 13, 'prec': 20, 'unit': 103731423372074664820, 'val': 2}
  • id: 359533
    {'lmfdb_iso': '8670.r', 'p': 19, 'prec': 20, 'unit': 734562605961666411297909, 'val': 1}
  • id: 359536
    {'lmfdb_iso': '8670.r', 'p': 23, 'prec': 20, 'unit': 7897295881139444317990057, 'val': 1}
  • id: 359529
    {'lmfdb_iso': '8670.r', 'p': 29, 'prec': 20, 'unit': 4031083441568332763745106229, 'val': 1}
  • id: 359540
    {'lmfdb_iso': '8670.r', 'p': 31, 'prec': 20, 'unit': 15292350303151443604207324884, 'val': 1}
  • id: 359525
    {'lmfdb_iso': '8670.r', 'p': 37, 'prec': 20, 'unit': 74925229250435554040682472073, 'val': 1}
  • id: 359527
    {'lmfdb_iso': '8670.r', 'p': 41, 'prec': 20, 'unit': 66699843366199011773777113812, 'val': 2}
  • id: 359528
    {'lmfdb_iso': '8670.r', 'p': 43, 'prec': 20, 'unit': 4257437756113911602291969460137, 'val': 1}
  • id: 359534
    {'lmfdb_iso': '8670.r', 'p': 53, 'prec': 20, 'unit': 65218772364735013336502385899063, 'val': 1}
  • id: 359538
    {'lmfdb_iso': '8670.r', 'p': 59, 'prec': 20, 'unit': 3295917933281499500770451940566376, 'val': 1}
  • id: 359539
    {'lmfdb_iso': '8670.r', 'p': 61, 'prec': 20, 'unit': 1872275558272190752777210279201762, 'val': 1}
  • id: 359524
    {'lmfdb_iso': '8670.r', 'p': 67, 'prec': 20, 'unit': 196235758000452701475386696970455, 'val': 2}
  • id: 359526
    {'lmfdb_iso': '8670.r', 'p': 71, 'prec': 20, 'unit': 916248175268592796257181728602463, 'val': 1}
  • id: 359535
    {'lmfdb_iso': '8670.r', 'p': 73, 'prec': 20, 'unit': 256841955642536834052662136950446, 'val': 1}
  • id: 359531
    {'lmfdb_iso': '8670.r', 'p': 79, 'prec': 20, 'unit': 538460071387966504587098318754261688, 'val': 1}
  • id: 359523
    {'lmfdb_iso': '8670.r', 'p': 83, 'prec': 20, 'unit': 2094220208358785953138364878551230355, 'val': 1}
  • id: 359537
    {'lmfdb_iso': '8670.r', 'p': 89, 'prec': 20, 'unit': 992957867511438814468726349357373593, 'val': 1}
  • id: 359522
    {'lmfdb_iso': '8670.r', 'p': 97, 'prec': 20, 'unit': 8045414982684460709671540699340257157, 'val': 1}