Elliptic curve data - 6840.d1

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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': '6840e', 'Clabel': '6840e5', 'Cnumber': 5, 'abc_quality': 1.0217291045785974, 'absD': 24253655040, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 4560, 'ainvs': [0, 0, 0, -6238083, 5996872798], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 19], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 6840, 'degree': 65536, 'elladic_images': ['16.24.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1878984246678536177322937869', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [17981241677724245762, 16245], 'lmfdb_iso': '6840.d', 'lmfdb_label': '6840.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -693120, -222337440], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '12.12.0-4.c.1.1', '16.24.0.f.2', '24.24.0-8.n.1.10', '40.24.0.bp.1', '48.48.0-16.f.2.10', '80.48.0.?', '120.48.0.?', '152.24.0.?', '240.96.0.?', '304.48.0.?', '456.48.0.?', '760.48.0.?', '912.96.0.?', '1520.96.1.?', '2280.96.0.?', '4560.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 45], [3, 8, 760], [5, 6, 1368], [19, 20, 360]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0032073648205155717355417238', 'prec': 100}, 'szpiro_ratio': 6.630640200399103, '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, -4, 0, -2, 0, 0, 0, -2, 0, -1, 0], 'aplist': [0, 0, -1, 0, -4, -2, -2, -1, 0, -6, 0, 6, 6, 4, -8, -6, 12, -2, 4, -8, -6, 16, 4, 6, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 6840, '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': '6840.d', 'trace_hash': 379124748565284470}
• 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': '0.012578115385128180076524560184', 'prec': 107}, 'conductor': 6840, 'gens': [], 'heights': [], 'lmfdb_label': '6840.d1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.52667026358742219489321323761', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0533405271748443897864264752298837585', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[1442, 0, 1]], 'xcoord_integral_points': [1442]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '19': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '6840.d1'}
• ec_torsion_growth •

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

  
  
  • id: 359428
    {'degree': 2, 'field': [-30, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [4]}
  • id: 359426
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [2, 2]}
  • id: 359427
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [4]}
  • id: 359429
    {'degree': 4, 'field': [25, 0, -20, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [2, 4]}
  • id: 359431
    {'degree': 4, 'field': [361, 0, -76, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [8]}
  • id: 359430
    {'degree': 4, 'field': [529, 0, -49, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [8]}
  • id: 359435
    {'degree': 8, 'field': [-33708, 0, 10236, 0, 396, 0, 20, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [6]}
  • id: 359433
    {'degree': 8, 'field': [1600, 0, 0, 0, -40, 0, 0, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [8]}
  • id: 359434
    {'degree': 8, 'field': [3481, 0, -4008, 0, 743, 0, -48, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [2, 8]}
  • id: 359432
    {'degree': 8, 'field': [208513600, 0, 0, 0, 14440, 0, 0, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [2, 4]}
  • id: 359437
    {'degree': 16, 'field': [12321, 0, 25716, 0, 16810, 0, 3584, 0, -81, 0, -296, 0, 30, 0, -4, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [2, 8]}
  • id: 359440
    {'degree': 16, 'field': [81000000, 0, -726064000, 0, -26441600, 0, 3163200, 0, 898400, 0, 48760, 0, 1740, 0, 20, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [2, 6]}
  • id: 359441
    {'degree': 16, 'field': [250652224, 0, 46576768, 0, -2785472, 0, -1199968, 0, -84208, 0, 8960, 0, 628, 0, -56, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [12]}
  • id: 359442
    {'degree': 16, 'field': [1361610000, 0, -2083080000, 0, -206614400, 0, -7885200, 0, 160200, 0, -1480, 0, 2580, 0, -60, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [12]}
  • id: 359438
    {'degree': 16, 'field': [199434589561, 0, -209361696556, 0, 46614714272, 0, -4247899468, 0, 194009350, 0, -4748852, 0, 62192, 0, -404, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [16]}
  • id: 359439
    {'degree': 16, 'field': [57608479500625, 0, -9206396724000, 0, 646755687000, 0, -25815081120, 0, 632410991, 0, -9634368, 0, 88920, 0, -456, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [16]}
  • id: 359436
    {'degree': 16, 'field': [169741577737081, 0, 564967483676, 0, 189930078110, 0, 260930784, 0, 77795519, 0, 14424, 0, 14450, 0, -4, 0, 1], 'lmfdb_label': '6840.d1', 'torsion': [4, 4]}
• 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: 139510
    {'conductor': 6840, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '6840.d1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 139511
    {'conductor': 6840, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '6840.d1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 139512
    {'conductor': 6840, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6840.d1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 139513
    {'conductor': 6840, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6840.d1', 'prime': 19, 'reduction_type': -1, '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: 1709183
    {'adelic_gens': [[15, 2, 4462, 4547], [5, 4, 4556, 4557], [1, 16, 0, 1], [2668, 4185, 2283, 3802], [2173, 1536, 3744, 2725], [616, 1521, 3423, 10], [1, 0, 16, 1], [1519, 0, 0, 4559], [4545, 16, 4544, 17], [2851, 1536, 2478, 4309]], 'adelic_image': '4560.192.1.?', 'conductor': 6840, 'lmfdb_label': '6840.d1', 'prime': 0}
  • id: 33784
    {'conductor': 6840, 'elladic_image': '16.24.0.6', 'lmfdb_label': '6840.d1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6840.d does not appear in ec_padic