Elliptic curve data - 6240.p3

Formats: - HTML - YAML - JSON - 2024-04-29T04:24:53.537803

• 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
  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': '6240z1', 'Cnumber': 1, 'abc_quality': 1.0447549090132258, 'absD': 187388721000000, 'adelic_genus': 3, 'adelic_index': 192, 'adelic_level': 1040, 'ainvs': [0, -1, 0, -16270, -446600], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 6240, 'degree': 24576, 'elladic_images': ['4.24.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4372179322726098224278295356', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [7442744143086784, 2927948765625], 'lmfdb_iso': '6240.p', 'lmfdb_label': '6240.p3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -16270, -446600], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.a.1.1', '40.48.0-40.a.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': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0906443419926371677192134749', 'prec': 100}, 'szpiro_ratio': 4.657985045492758, '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, -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': '0.056447974827166286601453539175', 'prec': 107}, 'conductor': 6240, 'gens': [], 'heights': [], 'lmfdb_label': '6240.p3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.43720368430856236865239353402', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6232221058513742119143612041483218774', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-29, 0, 1], [140, 0, 1]], 'xcoord_integral_points': [-110, -29, 140]}
• 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.p3'}
• ec_torsion_growth •

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

  
  
  • id: 325228
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '6240.p3', 'torsion': [2, 4]}
  • id: 325229
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '6240.p3', 'torsion': [2, 4]}
  • id: 325230
    {'degree': 4, 'field': [25, 0, 0, 0, 1], 'lmfdb_label': '6240.p3', 'torsion': [4, 4]}
  • id: 325233
    {'degree': 8, 'field': [521, -140, -346, -124, -116, -40, -2, -4, 1], 'lmfdb_label': '6240.p3', 'torsion': [2, 6]}
  • id: 325232
    {'degree': 8, 'field': [794, -1216, 1364, -728, 438, -104, 40, -4, 1], 'lmfdb_label': '6240.p3', 'torsion': [2, 8]}
  • id: 325231
    {'degree': 8, 'field': [50625, 0, -21500, 0, -1910, 0, -20, 0, 1], 'lmfdb_label': '6240.p3', 'torsion': [2, 8]}
  • id: 325234
    {'degree': 16, 'field': [225, 1200, -800, -4600, 11720, -11920, 7120, -1400, -1194, 1296, -432, -40, 136, -80, 32, -8, 1], 'lmfdb_label': '6240.p3', 'torsion': [4, 8]}
  • id: 325238
    {'degree': 16, 'field': [6500, -11600, 201280, -186288, 22528, 64328, -1184, -20240, 8028, -200, -760, 32, 140, -84, 32, -8, 1], 'lmfdb_label': '6240.p3', 'torsion': [2, 12]}
  • id: 325236
    {'degree': 16, 'field': [51354, -171288, 418572, -192864, 73606, -14424, 37680, -30596, 7771, -2956, 1352, -604, 358, -148, 44, -8, 1], 'lmfdb_label': '6240.p3', 'torsion': [4, 8]}
  • id: 325237
    {'degree': 16, 'field': [27501201, -131895036, 212706104, -129516764, 27239498, -4624880, -1009108, 1116196, -159276, 28716, -10536, 1804, -694, 136, -8, -4, 1], 'lmfdb_label': '6240.p3', 'torsion': [2, 12]}
  • id: 325235
    {'degree': 16, 'field': [59549841, 155639016, 179005772, 218564264, 203258444, 37946336, 13640588, 10291376, 89568, -610656, 25548, 5312, -1300, 8, 76, -8, 1], 'lmfdb_label': '6240.p3', 'torsion': [4, 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: 124753
    {'conductor': 6240, 'conductor_valuation': 5, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '6240.p3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 124754
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '6240.p3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 124755
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '6240.p3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 124756
    {'conductor': 6240, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '6240.p3', 'prime': 13, '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: 1704881
    {'adelic_gens': [[261, 8, 0, 131], [1, 0, 8, 1], [211, 22, 186, 879], [1, 8, 0, 1], [1, 4, 4, 17], [1033, 8, 1032, 9], [561, 4, 0, 1], [783, 22, 498, 879]], 'adelic_image': '1040.192.3.?', 'conductor': 6240, 'lmfdb_label': '6240.p3', 'prime': 0}
  • id: 30643
    {'conductor': 6240, 'elladic_image': '4.24.0.7', 'lmfdb_label': '6240.p3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 6240.p does not appear in ec_padic