Elliptic curve data - 60840.a3

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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': '60840r2', 'Cnumber': 2, 'abc_quality': 1.1324456905360707, 'absD': 810718562534400, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 0, 0, -24843, 628342], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 60840, 'degree': 245760, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5546103175948286587498758206', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [470596, 225], 'lmfdb_iso': '60840.a', 'lmfdb_label': '60840.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -16, -16], 'min_quad_twist_disc': -39, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '24.12.0.b.1', '40.12.0.a.1', '52.12.0-2.a.1.1', '60.12.0.b.1', '120.24.0.?', '312.24.0.?', '520.24.0.?', '780.24.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1521], [3, 8, 6760], [5, 6, 12168], [13, 86, 360]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.85479315593661564615551728652', 'prec': 107}, 'szpiro_ratio': 3.810329200548565, '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, 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': '0.044635729304416219347382552593', 'prec': 107}, 'conductor': 60840, 'gens': [], 'heights': [], 'lmfdb_label': '60840.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.44782354961063382060529598540', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7912941984425352824211839415910686255', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[26, 0, 1], [143, 0, 1]], 'xcoord_integral_points': [-169, 26, 143]}
• 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.a3'}
• ec_torsion_growth •

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

  
  
  • id: 2917568
    {'degree': 4, 'field': [3, 18, -17, -2, 1], 'lmfdb_label': '60840.a3', 'torsion': [2, 4]}
  • id: 2917567
    {'degree': 4, 'field': [94, -34, 35, -2, 1], 'lmfdb_label': '60840.a3', 'torsion': [2, 4]}
  • id: 2917566
    {'degree': 4, 'field': [484, 0, 34, 0, 1], 'lmfdb_label': '60840.a3', 'torsion': [2, 4]}
  • id: 2917569
    {'degree': 8, 'field': [-12635, -4918, -4208, -758, -328, -56, 4, -4, 1], 'lmfdb_label': '60840.a3', 'torsion': [2, 6]}
  • id: 2917573
    {'degree': 16, 'field': [-2967, 11400, 8880, -25176, -17816, 16312, 21416, -10656, -10247, 4904, 2284, -1240, -218, 168, -4, -8, 1], 'lmfdb_label': '60840.a3', 'torsion': [2, 8]}
  • id: 2917570
    {'degree': 16, 'field': [2521, -16624, 82702, -109900, 7448, 35840, 18690, -17716, -4699, 3856, 1134, -644, -196, 112, 4, -8, 1], 'lmfdb_label': '60840.a3', 'torsion': [4, 4]}
  • id: 2917572
    {'degree': 16, 'field': [136562596, 0, 27724528, 0, 6169405, 0, 1081318, 0, 115519, 0, 6412, 0, 295, 0, 22, 0, 1], 'lmfdb_label': '60840.a3', 'torsion': [2, 8]}
  • id: 2917571
    {'degree': 16, 'field': [227285776, 0, 170676096, 0, 48957520, 0, 4912704, 0, 194604, 0, 21024, 0, 2740, 0, 96, 0, 1], 'lmfdb_label': '60840.a3', '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: 1465474
    {'conductor': 60840, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '60840.a3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1465475
    {'conductor': 60840, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '60840.a3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1465476
    {'conductor': 60840, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '60840.a3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1465477
    {'conductor': 60840, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '60840.a3', 'prime': 13, '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: 2067223
    {'adelic_gens': [[1, 0, 4, 1], [183, 962, 598, 599], [1, 4, 0, 1], [1039, 1196, 1118, 831], [1557, 4, 1556, 5], [391, 364, 182, 729], [479, 0, 0, 1559], [937, 962, 0, 1]], 'adelic_image': '1560.48.0.?', 'conductor': 60840, 'lmfdb_label': '60840.a3', 'prime': 0}
  • id: 256664
    {'conductor': 60840, 'elladic_image': '2.6.0.1', 'lmfdb_label': '60840.a3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 60840.a does not appear in ec_padic