Elliptic curve data - 136710.dd2

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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': '136710du', 'Clabel': '136710du4', 'Cnumber': 4, 'abc_quality': 1.0007838605326649, 'absD': 285144529795347600, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 26040, 'ainvs': [1, -1, 0, -8476029, -9495947147], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 31], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 136710, 'degree': 6291456, 'elladic_images': ['8.24.0.18'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5575132707965818780372562418', 'prec': 97}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 1, 'iso_nlabel': 81, 'isogeny_degrees': [1, 2, 4], 'jinv': [785209010066844481, 3324675600], 'lmfdb_iso': '136710.dd', 'lmfdb_label': '136710.dd2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -19220, -1027200], 'min_quad_twist_disc': 21, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.1', '60.24.0.c.1', '84.24.0.?', '120.48.0.?', '140.24.0.?', '168.48.0.?', '248.48.0.?', '280.48.0.?', '420.48.0.?', '840.96.0.?', '3720.96.1.?', '5208.96.0.?', '8680.96.0.?', '26040.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.9933799440823321044642474985', 'prec': 97}, 'semistable': False, 'serre_invariants': [[2, 4, 441], [3, 8, 15190], [5, 6, 27342], [7, 26, 2790], [31, 32, 4410]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0352520519348703797869572516', 'prec': 97}, 'szpiro_ratio': 5.029070372294241, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 1, 1, 0, 0, -1, 0, -1, 4, 0, -6, 0, 0, 1, 2, 0, -4, 1], 'aplist': [-1, 0, 1, 0, 4, -6, 2, -4, 8, -6, 1, -2, 10, -4, 0, 10, -12, 2, -4, 0, -2, 0, 4, -14, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 136710, 'isogeny_matrix': [[1, 2, 4, 8, 4, 8], [2, 1, 2, 4, 2, 4], [4, 2, 1, 8, 4, 8], [8, 4, 8, 1, 2, 4], [4, 2, 4, 2, 1, 2], [8, 4, 8, 4, 2, 1]], 'lmfdb_iso': '136710.dd', 'trace_hash': 789638758597802335}
• 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': '0.0060058184283186425756089186756', 'prec': 97}, 'conductor': 136710, 'gens': [[-1681, 656, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.9933799440823321044642474985', 'prec': 97}], 'lmfdb_label': '136710.dd2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.088481312081513745774679280224', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '5.6534319534785078106615656747463780035', 'prec': 127}, 'tamagawa_product': 256, 'torsion_generators': [[-1678, 839, 1], [3362, -1681, 1]], 'xcoord_integral_points': [-1681, -1678, 3362, 7142, 10089]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [13, 1], '3': 'a', '5': [2, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [3, 0], '29': [1, 0], '31': [2, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '136710.dd2'}
• ec_torsion_growth •

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

  
  
  • id: 6185595
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '136710.dd2', 'torsion': [2, 4]}
  • id: 6185597
    {'degree': 4, 'field': [15, -15, 4, -1, 1], 'lmfdb_label': '136710.dd2', 'torsion': [2, 4]}
  • id: 6185596
    {'degree': 4, 'field': [25, 0, -25, 0, 1], 'lmfdb_label': '136710.dd2', 'torsion': [2, 4]}
  • id: 6185602
    {'degree': 8, 'field': [-3826640, 1104560, 58780, -16832, -688, -488, 4, -4, 1], 'lmfdb_label': '136710.dd2', 'torsion': [2, 6]}
  • id: 6185598
    {'degree': 8, 'field': [225, 0, 105, 0, 16, 0, -7, 0, 1], 'lmfdb_label': '136710.dd2', 'torsion': [4, 4]}
  • id: 6185601
    {'degree': 8, 'field': [1635, -2070, 1005, -630, 586, -98, 9, -2, 1], 'lmfdb_label': '136710.dd2', 'torsion': [2, 8]}
  • id: 6185599
    {'degree': 8, 'field': [26569, 0, 2274, 0, 407, 0, -18, 0, 1], 'lmfdb_label': '136710.dd2', 'torsion': [2, 8]}
  • id: 6185600
    {'degree': 8, 'field': [687646, 71812, -70118, -3380, 1671, 20, -2, -4, 1], 'lmfdb_label': '136710.dd2', 'torsion': [2, 8]}
  • id: 6185604
    {'degree': 16, 'field': [476100, 1076400, 927000, -68400, -109380, 212880, 89580, -112080, 65581, -19756, 4072, -1108, 325, -112, 22, -4, 1], 'lmfdb_label': '136710.dd2', 'torsion': [4, 8]}
  • id: 6185605
    {'degree': 16, 'field': [4040100, 0, -3256875, 0, -318350, 0, 411891, 0, 86307, 0, 7631, 0, 771, 0, 42, 0, 1], 'lmfdb_label': '136710.dd2', 'torsion': [2, 12]}
  • id: 6185603
    {'degree': 16, 'field': [5929225, 0, -5723900, 0, -2293070, 0, 29380, 0, 475411, 0, -72644, 0, 4066, 0, -104, 0, 1], 'lmfdb_label': '136710.dd2', 'torsion': [2, 8]}
• 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: 3372406
    {'conductor': 136710, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '136710.dd2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3372407
    {'conductor': 136710, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '136710.dd2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3372408
    {'conductor': 136710, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '136710.dd2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3372409
    {'conductor': 136710, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '136710.dd2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3372410
    {'conductor': 136710, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '136710.dd2', 'prime': 31, 'reduction_type': 1, '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: 2552656
    {'adelic_gens': [[9241, 7448, 14644, 3753], [26033, 8, 26032, 9], [1, 0, 8, 1], [1, 8, 0, 1], [16745, 8372, 952, 20469], [5, 4, 26036, 26037], [13399, 14882, 17094, 7435], [18607, 12096, 7434, 13945], [24793, 11158, 3738, 18605], [14879, 0, 0, 26039]], 'adelic_image': '26040.192.1.?', 'conductor': 136710, 'lmfdb_label': '136710.dd2', 'prime': 0}
  • id: 529073
    {'conductor': 136710, 'elladic_image': '8.24.0.18', 'lmfdb_label': '136710.dd2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 136710.dd does not appear in ec_padic