Elliptic curve data - 60840.a2

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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': '60840r', 'Clabel': '60840r3', 'Cnumber': 3, 'abc_quality': 0.9792461634823973, 'absD': 13511976042240000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -207363, -35912162], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 60840, 'degree': 491520, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9011839078748013134584918814', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [136835858, 1875], 'lmfdb_iso': '60840.a', 'lmfdb_label': '60840.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -136, 560], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0.s.1', '40.12.0.bb.1', '52.12.0-4.c.1.1', '120.24.0.?', '312.24.0.?', '520.24.0.?', '1560.48.0.?'], '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, 1521], [3, 8, 6760], [5, 6, 12168], [13, 86, 360]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56598183070330510056500390251', 'prec': 107}, 'szpiro_ratio': 4.388187133263068, '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, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0], 'aplist': [0, 0, -1, -4, 0, 0, 2, -4, 8, 6, 0, 6, 10, -4, 8, -10, 0, 6, 4, 0, 14, 16, 12, 2, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 60840, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '60840.a', 'trace_hash': 1990866380342487379}
• 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': '0.022317864652208109673691276296', 'prec': 107}, 'conductor': 60840, 'gens': [], 'heights': [], 'lmfdb_label': '60840.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.22391177480531691030264799270', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7912941984425352824211839415910686255', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-286, 0, 1]], 'xcoord_integral_points': [-286]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '60840.a2'}
• ec_torsion_growth •

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

  
  
  • id: 2917574
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [2, 2]}
  • id: 2917575
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [4]}
  • id: 2917576
    {'degree': 2, 'field': [78, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [4]}
  • id: 2917577
    {'degree': 4, 'field': [361, 0, 14, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [2, 4]}
  • id: 2917581
    {'degree': 8, 'field': [-12635, -4918, -4208, -758, -328, -56, 4, -4, 1], 'lmfdb_label': '60840.a2', 'torsion': [6]}
  • id: 2917578
    {'degree': 8, 'field': [-69, 348, -306, -72, 7, 32, -6, -4, 1], 'lmfdb_label': '60840.a2', 'torsion': [2, 4]}
  • id: 2917580
    {'degree': 8, 'field': [11236, 0, 1968, 0, 658, 0, 48, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [8]}
  • id: 2917579
    {'degree': 8, 'field': [45796, 0, 9064, 0, 957, 0, 46, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [8]}
  • id: 2917582
    {'degree': 16, 'field': [4761, 0, 78876, 0, 142782, 0, 30912, 0, 10975, 0, 2296, 0, 306, 0, 28, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [4, 4]}
  • id: 2917583
    {'degree': 16, 'field': [5764801, 0, -7058940, 0, 4266577, 0, -1719900, 0, 399408, 0, -35100, 0, 1777, 0, -60, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [2, 8]}
  • id: 2917586
    {'degree': 16, 'field': [14516100, 0, 19630152, 0, 7894620, 0, 1220124, 0, 129912, 0, 37020, 0, 3460, 0, 104, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [12]}
  • id: 2917584
    {'degree': 16, 'field': [20711601, 0, 9923244, 0, 2986150, 0, 332016, 0, 28599, 0, -2344, 0, 690, 0, -36, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [2, 8]}
  • id: 2917585
    {'degree': 16, 'field': [141786193, 93742408, 63689700, 35473236, 7111968, 7584900, 1284200, 1588040, 127026, 102056, -25336, -1164, -312, -60, 12, -8, 1], 'lmfdb_label': '60840.a2', 'torsion': [2, 6]}
  • id: 2917587
    {'degree': 16, 'field': [305165961, 0, 22700670, 0, 9250912, 0, 2916186, 0, 242046, 0, 6434, 0, 312, 0, 30, 0, 1], 'lmfdb_label': '60840.a2', 'torsion': [12]}
• 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: 1465478
    {'conductor': 60840, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '60840.a2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1465479
    {'conductor': 60840, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '60840.a2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1465480
    {'conductor': 60840, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '60840.a2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1465481
    {'conductor': 60840, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '60840.a2', 'prime': 13, 'reduction_type': 0, '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: 2067222
    {'adelic_gens': [[272, 117, 1235, 1078], [1, 0, 8, 1], [1, 8, 0, 1], [479, 0, 0, 1559], [1, 4, 4, 17], [937, 728, 988, 1353], [976, 923, 1339, 768], [1553, 8, 1552, 9], [7, 6, 1554, 1555], [768, 1313, 1027, 534]], 'adelic_image': '1560.48.0.?', 'conductor': 60840, 'lmfdb_label': '60840.a2', 'prime': 0}
  • id: 256663
    {'conductor': 60840, 'elladic_image': '4.6.0.1', 'lmfdb_label': '60840.a2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 60840.a does not appear in ec_padic