Elliptic curve data - 6240.p4

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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': '6240z', 'Clabel': '6240z4', 'Cnumber': 4, 'abc_quality': 1.1541079700404029, 'absD': 13689000000000000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 1040, 'ainvs': [0, -1, 0, 52175, -3280223], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6240, 'degree': 49152, 'elladic_images': ['4.24.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7837915225525824771364455964', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [3834800837445824, 3342041015625], 'lmfdb_iso': '6240.p', 'lmfdb_label': '6240.p4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 52175, -3280223], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.1', '40.48.0-40.bf.1.1', '80.96.0.?', '104.48.0.?', '520.96.1.?', '1040.192.3.?'], '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, 1], [3, 4, 416], [5, 6, 1248], [13, 14, 480]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0906443419926371677192134749', 'prec': 100}, 'szpiro_ratio': 5.058015574181806, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 4, 0, 1, 0, 0, 0, 1, 0, -1, 0, 2, 0, 8, 0], 'aplist': [0, -1, 1, 4, 0, 1, 2, 8, 4, 6, -8, 6, -6, -4, 4, 6, 8, -10, 4, 8, -14, 0, 12, -6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 6240, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '6240.p', 'trace_hash': 1890080444446588596}
• 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': '0.028223987413583143300726769587', 'prec': 107}, 'conductor': 6240, 'gens': [], 'heights': [], 'lmfdb_label': '6240.p4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.21860184215428118432619676701', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6232221058513742119143612041483218774', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[309, 6500, 1]], 'xcoord_integral_points': [59, 309]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '13': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '6240.p4'}
• ec_torsion_growth •

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

  
  
  • id: 325265
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '6240.p4', 'torsion': [2, 4]}
  • id: 325267
    {'degree': 4, 'field': [-169, 0, -78, 0, 1], 'lmfdb_label': '6240.p4', 'torsion': [8]}
  • id: 325266
    {'degree': 4, 'field': [169, 0, 0, 0, 1], 'lmfdb_label': '6240.p4', 'torsion': [4, 4]}
  • id: 325268
    {'degree': 8, 'field': [1, 0, 0, 0, 38, 0, 0, 0, 1], 'lmfdb_label': '6240.p4', 'torsion': [2, 8]}
  • id: 325270
    {'degree': 8, 'field': [521, -140, -346, -124, -116, -40, -2, -4, 1], 'lmfdb_label': '6240.p4', 'torsion': [12]}
  • id: 325269
    {'degree': 8, 'field': [281034, 29640, -36572, -3152, 2010, 168, -60, -4, 1], 'lmfdb_label': '6240.p4', 'torsion': [2, 8]}
  • id: 325274
    {'degree': 16, 'field': [6500, -11600, 201280, -186288, 22528, 64328, -1184, -20240, 8028, -200, -760, 32, 140, -84, 32, -8, 1], 'lmfdb_label': '6240.p4', 'torsion': [2, 12]}
  • id: 325272
    {'degree': 16, 'field': [353610, 521400, 302644, -113928, 11614, 16552, 42664, -32916, 11355, -236, -1200, 244, 126, -108, 36, -8, 1], 'lmfdb_label': '6240.p4', 'torsion': [4, 8]}
  • id: 325271
    {'degree': 16, 'field': [153388225, 0, -110533688, 0, 20875456, 0, 168568, 0, 14434, 0, 13768, 0, 64, 0, -8, 0, 1], 'lmfdb_label': '6240.p4', 'torsion': [4, 8]}
  • id: 325273
    {'degree': 16, 'field': [17269832225, 33173218000, 31186447200, 15021136000, 2752662780, -601432000, -339333760, -49462400, 811946, 2738320, 557664, -33280, -14444, 0, 64, 0, 1], 'lmfdb_label': '6240.p4', 'torsion': [16]}
• 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: 124765
    {'conductor': 6240, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '6240.p4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 124766
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6240.p4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 124767
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '6240.p4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 124768
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6240.p4', 'prime': 13, '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: 1704882
    {'adelic_gens': [[5, 16, 64, 205], [1, 16, 0, 1], [1025, 16, 1024, 17], [11, 926, 722, 483], [1, 12, 4, 49], [1, 0, 16, 1], [95, 166, 714, 947], [417, 16, 628, 65], [704, 309, 125, 424]], 'adelic_image': '1040.192.3.?', 'conductor': 6240, 'lmfdb_label': '6240.p4', 'prime': 0}
  • id: 30644
    {'conductor': 6240, 'elladic_image': '4.24.0.11', 'lmfdb_label': '6240.p4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 6240.p does not appear in ec_padic