Elliptic curve isogeny class data - 8670.v

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• 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, 0, 2, -8, -6, 6, -4, 0, -10, -4, 2, 4, 0, 6, -8, -12, -6, 14], 'class_deg': 16, 'class_size': 8, 'conductor': 8670, 'isogeny_matrix': [[1, 16, 2, 4, 8, 16, 8, 4], [16, 1, 8, 4, 2, 4, 8, 16], [2, 8, 1, 2, 4, 8, 4, 2], [4, 4, 2, 1, 2, 4, 2, 4], [8, 2, 4, 2, 1, 2, 4, 8], [16, 4, 8, 4, 2, 1, 8, 16], [8, 8, 4, 2, 4, 8, 1, 8], [4, 16, 2, 4, 8, 16, 8, 1]], 'lmfdb_iso': '8670.v', 'trace_hash': 48406145217345363}
• ec_padic •

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

  
  
  • id: 359571
    {'lmfdb_iso': '8670.v', 'p': 11, 'prec': 20, 'unit': 13996202793224408928, 'val': 1}
  • id: 359569
    {'lmfdb_iso': '8670.v', 'p': 13, 'prec': 20, 'unit': 675068187442049791604, 'val': 1}
  • id: 359572
    {'lmfdb_iso': '8670.v', 'p': 19, 'prec': 20, 'unit': 150846914049377824542958, 'val': 1}
  • id: 359568
    {'lmfdb_iso': '8670.v', 'p': 29, 'prec': 20, 'unit': 5789923948311056993965520889, 'val': 1}
  • id: 359578
    {'lmfdb_iso': '8670.v', 'p': 31, 'prec': 20, 'unit': 15795778693296627642411827908, 'val': 1}
  • id: 359565
    {'lmfdb_iso': '8670.v', 'p': 37, 'prec': 20, 'unit': 5834886356063184146421215772, 'val': 2}
  • id: 359566
    {'lmfdb_iso': '8670.v', 'p': 41, 'prec': 20, 'unit': 1450145482935207596653135955755, 'val': 1}
  • id: 359567
    {'lmfdb_iso': '8670.v', 'p': 43, 'prec': 20, 'unit': 8245995097187571479617816076888, 'val': 1}
  • id: 359573
    {'lmfdb_iso': '8670.v', 'p': 53, 'prec': 20, 'unit': 264070251959860975164248823743520, 'val': 1}
  • id: 359576
    {'lmfdb_iso': '8670.v', 'p': 59, 'prec': 20, 'unit': 3279687491870816483027866444936426, 'val': 1}
  • id: 359577
    {'lmfdb_iso': '8670.v', 'p': 61, 'prec': 20, 'unit': 256136801749568211848430033645817, 'val': 1}
  • id: 359564
    {'lmfdb_iso': '8670.v', 'p': 67, 'prec': 20, 'unit': 23635108252040992123365229060653862, 'val': 1}
  • id: 359574
    {'lmfdb_iso': '8670.v', 'p': 73, 'prec': 20, 'unit': 28099545204390546499413866502358957, 'val': 1}
  • id: 359570
    {'lmfdb_iso': '8670.v', 'p': 79, 'prec': 20, 'unit': 803151841496943099698749224441788342, 'val': 1}
  • id: 359563
    {'lmfdb_iso': '8670.v', 'p': 83, 'prec': 20, 'unit': 2474403757319322642195420704007025252, 'val': 1}
  • id: 359575
    {'lmfdb_iso': '8670.v', 'p': 89, 'prec': 20, 'unit': 3759971848594044952531598369022040259, 'val': 1}
  • id: 359562
    {'lmfdb_iso': '8670.v', 'p': 97, 'prec': 20, 'unit': 2323263223297366656883352925489279965, 'val': 1}
• 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[]

  
  
  • id: 55850
    {'Ciso': '8670v', 'Clabel': '8670v7', 'Cnumber': 7, 'abc_quality': 1.0337884894740492, 'absD': 22079667965176541250, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 8160, 'ainvs': [1, 0, 0, -32792836, -72282118834], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 589824, 'elladic_images': ['16.96.0.242'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9033465489412446850164223181', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 16, 'intrinsic_torsion': 2, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [161572377633716256481, 914742821250], 'lmfdb_iso': '8670.v', 'lmfdb_label': '8670.v1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -113470, -14759143], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0-8.bb.1.4', '16.96.0-16.x.1.3', '68.12.0-4.c.1.1', '136.96.0.?', '272.192.1.?', '480.192.1.?', '1360.384.5.?', '1632.384.5.?', '8160.768.13.?'], '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': '3.4629487283130357633637508309', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 2890], [5, 6, 1734], [17, 162, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4867398769131366448916550092', 'prec': 100}, 'szpiro_ratio': 7.0063298224935915, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 55847
    {'Ciso': '8670v', 'Clabel': '8670v4', 'Cnumber': 4, 'abc_quality': 1.0170027108062862, 'absD': 98481281520, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 8160, 'ainvs': [1, 0, 0, -6288646, 6069408116], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 147456, 'elladic_images': ['32.96.0.30'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2101993683812993755991901966', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [1139466686381936641, 4080], 'lmfdb_iso': '8670.v', 'lmfdb_label': '8670.v2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -21760, 1226417], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.1', '16.48.0-16.g.1.1', '32.96.0-32.e.2.15', '60.12.0-4.c.1.1', '68.12.0-4.c.1.2', '120.48.0.?', '136.48.0.?', '240.96.0.?', '272.96.0.?', '480.192.1.?', '544.192.1.?', '816.192.2.?', '1020.24.0.?', '1360.192.2.?', '1632.384.5.?', '2040.96.0.?', '2720.384.5.?', '4080.384.5.?', '8160.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.4629487283130357633637508309', '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': '0.79359269635319133547442288766', 'prec': 103}, 'szpiro_ratio': 6.459947128539045, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 55848
    {'Ciso': '8670v', 'Clabel': '8670v5', 'Cnumber': 5, 'abc_quality': 1.0054946838642063, 'absD': 71512413391251562500, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 4080, 'ainvs': [1, 0, 0, -2086586, -1086607584], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 294912, 'elladic_images': ['8.96.0.139'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5567729586612720303078062574', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'intrinsic_torsion': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [41623544884956481, 2962701562500], 'lmfdb_iso': '8670.v', 'lmfdb_label': '8670.v3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -7220, -224143], 'min_quad_twist_disc': 17, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.96.0-8.k.2.6', '68.24.0-4.b.1.1', '136.192.1.?', '240.192.1.?', '816.384.5.?', '1360.384.5.?', '4080.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.9258974566260715267275016618', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 2890], [5, 6, 1734], [17, 162, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1401662866331639901830389485', 'prec': 100}, 'szpiro_ratio': 6.094950785778734, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 55846
    {'Ciso': '8670v', 'Clabel': '8670v3', 'Cnumber': 3, 'abc_quality': 1.0677360670200853, 'absD': 1632955059363690000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 4080, 'ainvs': [1, 0, 0, -416166, 83020500], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 147456, 'elladic_images': ['8.96.0.82'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2101993683812993755991901966', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4], 'jinv': [330240275458561, 67652010000], 'lmfdb_iso': '8670.v', 'lmfdb_label': '8670.v4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1440, 16305], 'min_quad_twist_disc': 17, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0.b.1', '8.96.0-8.b.1.6', '68.48.0-4.b.1.1', '120.192.1.?', '136.192.1.?', '816.384.5.?', '1360.384.5.?', '2040.384.5.?', '4080.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.4629487283130357633637508309', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 2890], [5, 6, 1734], [17, 162, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.79359269635319133547442288766', 'prec': 103}, 'szpiro_ratio': 5.561558495277205, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 55845
    {'Ciso': '8670v', 'Clabel': '8670v2', 'Cnumber': 2, 'abc_quality': 0.9796429838987872, 'absD': 401803628601600, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 4080, 'ainvs': [1, 0, 0, -393046, 94807076], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 73728, 'elladic_images': ['16.96.0.36'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8636257781013267208905741359', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [278202094583041, 16646400], 'lmfdb_iso': '8670.v', 'lmfdb_label': '8670.v5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -1360, 18737], 'min_quad_twist_disc': 17, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.i.1.3', '16.96.0-16.d.1.3', '60.24.0-4.b.1.2', '68.24.0-4.b.1.3', '120.96.0.?', '136.96.0.?', '240.192.1.?', '272.192.1.?', '816.384.5.?', '1020.48.0.?', '1360.384.5.?', '2040.192.1.?', '4080.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7314743641565178816818754154', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 2890], [5, 6, 1734], [17, 162, 30]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.44701910607321868076580682696', 'prec': 103}, 'szpiro_ratio': 5.542648063268354, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
  • id: 55844
    {'Ciso': '8670v', 'Clabel': '8670v1', 'Cnumber': 1, 'abc_quality': 1.0017576460079456, 'absD': 403379329105920, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 8160, 'ainvs': [1, 0, 0, -23126, 1661220], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 36864, 'elladic_images': ['32.96.0.30'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5170521878213540661819580752', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-56667352321, 16711680], 'lmfdb_iso': '8670.v', 'lmfdb_label': '8670.v6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -80, 305], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.1', '16.48.0-16.g.1.1', '32.96.0-32.e.2.15', '60.12.0-4.c.1.2', '68.12.0-4.c.1.2', '120.48.0.?', '136.48.0.?', '240.96.0.?', '272.96.0.?', '480.192.1.?', '510.6.0.?', '544.192.1.?', '816.192.2.?', '1020.24.0.?', '1360.192.2.?', '1632.384.5.?', '2040.96.0.?', '2720.384.5.?', '4080.384.5.?', '8160.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.86573718207825894084093770772', 'prec': 103}, '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': '0.10044551579324602605719076626', 'prec': 103}, 'szpiro_ratio': 4.650787208687644, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 55849
    {'Ciso': '8670v', 'Clabel': '8670v6', 'Cnumber': 6, 'abc_quality': 1.0137929987603158, 'absD': 151540043903460836100, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 8160, 'ainvs': [1, 0, 0, 884334, 498400200], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 294912, 'elladic_images': ['16.96.0.208'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5567729586612720303078062574', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'intrinsic_torsion': 2, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [3168685387909439, 6278181696900], 'lmfdb_iso': '8670.v', 'lmfdb_label': '8670.v7', 'lmfdb_number': 7, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 3060, 102705], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0.n.1', '16.96.0-8.n.1.3', '60.24.0.h.1', '68.24.0-4.d.1.1', '120.96.1.?', '136.96.0.?', '240.192.1.?', '272.192.1.?', '1020.48.0.?', '1632.384.5.?', '2040.192.1.?', '2720.384.5.?', '4080.384.5.?', '8160.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.9258974566260715267275016618', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 2890], [5, 6, 1734], [17, 162, 30]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1401662866331639901830389485', 'prec': 100}, 'szpiro_ratio': 5.908568466527, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
  • id: 55851
    {'Ciso': '8670v', 'Clabel': '8670v8', 'Cnumber': 8, 'abc_quality': 1.042914731101016, 'absD': 10143259433898925781250, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 8160, 'ainvs': [1, 0, 0, 1892944, -4740612030], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 8670, 'degree': 589824, 'elladic_images': ['16.96.0.265'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9033465489412446850164223181', 'prec': 100}, 'faltings_index': 7, 'faltings_ratio': 16, 'intrinsic_torsion': 2, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [31077313442863199, 420227050781250], 'lmfdb_iso': '8670.v', 'lmfdb_label': '8670.v8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 6550, -962215], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.48.0-8.ba.1.4', '16.96.0-16.u.1.3', '68.12.0-4.c.1.1', '136.96.0.?', '272.192.1.?', '480.192.1.?', '816.384.5.?', '2720.384.5.?', '8160.768.13.?'], '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': '13.851794913252143053455003324', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 2890], [5, 6, 1734], [17, 162, 30]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4867398769131366448916550092', 'prec': 100}, 'szpiro_ratio': 6.405434963925024, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}