Elliptic curve data - 41280.k4

Formats: - HTML - YAML - JSON - 2025-10-17T11:28:03.368678

• 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': '41280j', 'Clabel': '41280j1', 'Cnumber': 1, 'abc_quality': 1.0111919436740877, 'absD': 88615321920, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1720, 'ainvs': [0, -1, 0, -76, 14350], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 43], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 41280, 'degree': 36864, 'elladic_images': ['8.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.77960481115274837479896325466', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [-768575296, 1384614405], 'lmfdb_iso': '41280.k', 'lmfdb_label': '41280.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -305, -114495], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.3', '20.12.0.h.1', '40.24.0-20.h.1.1', '344.24.0.?', '1720.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 5], [3, 4, 13760], [5, 6, 8256], [43, 44, 960]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.43303122087277572009034719393', 'prec': 103}, 'szpiro_ratio': 3.073221845227504, '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, -1, 0, -1, 0, 0, 0, 1, 0, -4, 0, 6, 0, 1, 0, 2, 0, 0, 0], 'aplist': [0, -1, -1, 0, -4, 6, 2, 0, 0, 2, 4, 10, -6, 1, 0, 6, -4, 2, 12, -16, 14, 4, -4, 2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 41280, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '41280.k', 'trace_hash': 1368335251162585980}
• 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': '0.21030222371722423547330324640', 'prec': 103}, 'conductor': 41280, 'gens': [], 'heights': [], 'lmfdb_label': '41280.k4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.86492649955330619826685907187', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7298529991066123965337181437357632782', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-25, 0, 1]], 'xcoord_integral_points': [-25]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '43': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '41280.k4'}
• ec_torsion_growth •

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

  
  
  • id: 2028817
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [4]}
  • id: 2028818
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [4]}
  • id: 2028816
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [2, 2]}
  • id: 2028819
    {'degree': 4, 'field': [9, 0, -4, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [2, 4]}
  • id: 2028823
    {'degree': 8, 'field': [-35643, 0, -8816, 0, -654, 0, 0, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [6]}
  • id: 2028820
    {'degree': 8, 'field': [1, 8, 26, -16, 44, -28, 14, -4, 1], 'lmfdb_label': '41280.k4', 'torsion': [2, 4]}
  • id: 2028822
    {'degree': 8, 'field': [7225, 0, -1570, 0, 209, 0, -22, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [8]}
  • id: 2028821
    {'degree': 8, 'field': [42025, 0, -64700, 0, -310, 0, -20, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [8]}
  • id: 2028824
    {'degree': 16, 'field': [1, 0, 0, 0, -36, 0, 0, 0, 646, 0, 0, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [4, 4]}
  • id: 2028828
    {'degree': 16, 'field': [9409, 0, -860564, 0, 754300, 0, -773972, 0, 94090, 0, -452, 0, -68, 0, -20, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [12]}
  • id: 2028826
    {'degree': 16, 'field': [394169, -43496, 1787100, -835424, 2532280, -1603128, 1558668, -685896, 426234, -134568, 56796, -12480, 3704, -536, 108, -8, 1], 'lmfdb_label': '41280.k4', 'torsion': [2, 8]}
  • id: 2028829
    {'degree': 16, 'field': [2788900, 0, -2174000, 0, 852400, 0, -139928, 0, 2692, 0, 1888, 0, -236, 0, 4, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [12]}
  • id: 2028827
    {'degree': 16, 'field': [53114944, 0, 47660416, 0, 104885440, 0, 40989888, 0, 2102160, 0, 2448, 0, -608, 0, 40, 0, 1], 'lmfdb_label': '41280.k4', 'torsion': [2, 6]}
  • id: 2028825
    {'degree': 16, 'field': [5534000566, -1059691240, 1311362116, -512259112, 278476202, -26932384, 9075912, 99020, -236833, 115132, 2388, -12812, 1286, 364, -32, -8, 1], 'lmfdb_label': '41280.k4', '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: 978525
    {'conductor': 41280, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '41280.k4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 978526
    {'conductor': 41280, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '41280.k4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 978527
    {'conductor': 41280, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '41280.k4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 978528
    {'conductor': 41280, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '41280.k4', 'prime': 43, '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: 1939589
    {'adelic_gens': [[7, 6, 1714, 1715], [1, 0, 8, 1], [1, 8, 0, 1], [1504, 637, 645, 644], [1, 4, 4, 17], [1121, 8, 1044, 33], [1713, 8, 1712, 9], [696, 3, 5, 2], [637, 642, 1070, 213]], 'adelic_image': '1720.48.0.?', 'conductor': 41280, 'lmfdb_label': '41280.k4', 'prime': 0}
  • id: 180841
    {'conductor': 41280, 'elladic_image': '8.12.0.7', 'lmfdb_label': '41280.k4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 41280.k does not appear in ec_padic