Elliptic curve data - 20400.dp4

Formats: - HTML - YAML - JSON - 2024-06-01T04:34:29.737155

• 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': '20400dk', 'Clabel': '20400dk4', 'Cnumber': 4, 'abc_quality': 1.053583581360511, 'absD': 64066128740352000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 2040, 'ainvs': [0, 1, 0, 723792, 303765588], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 20400, 'degree': 497664, 'elladic_images': ['8.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4858660477383878059744057067', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 93, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [655215969476375, 1001033261568], 'lmfdb_iso': '20400.dp', 'lmfdb_label': '20400.dp4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 1809, -37790], 'min_quad_twist_disc': -20, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.a.1', '24.24.0.p.1', '60.24.0-6.a.1.2', '68.6.0.c.1', '120.48.0.?', '136.12.0.?', '204.24.0.?', '408.48.1.?', '1020.48.0.?', '2040.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.98799991096139230925679391863', 'prec': 103}, 'szpiro_ratio': 5.29915876746438, '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, 0, 0, 2, 0, 1, 0, 0, 0, -2, 0, 0, 0, 1, 0, 4, 0], 'aplist': [0, 1, 0, 2, 0, -2, 1, 4, -6, 0, 10, -8, 6, -4, 12, -6, 12, 8, -4, -6, -2, 10, 12, -18, -14], 'class_deg': 6, 'class_size': 4, 'conductor': 20400, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '20400.dp', 'trace_hash': 1539529953623668049}
• 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': '0.0069311322486889862733872163353', 'prec': 110}, 'conductor': 20400, 'gens': [], 'heights': [], 'lmfdb_label': '20400.dp4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.13350858323258461152198979619', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2042059975820306765277551085382050542', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-357, 0, 1]], 'xcoord_integral_points': [-357]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [5, 0], '5': 'a', '17': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '20400.dp4'}
• ec_torsion_growth •

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

  
  
  • id: 1043072
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [6]}
  • id: 1043071
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [2, 2]}
  • id: 1043073
    {'degree': 4, 'field': [-4, 26, 12, -1, 1], 'lmfdb_label': '20400.dp4', 'torsion': [4]}
  • id: 1043074
    {'degree': 4, 'field': [49, 0, 16, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [2, 6]}
  • id: 1043075
    {'degree': 6, 'field': [134, 90, 75, -6, 15, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [6]}
  • id: 1043076
    {'degree': 8, 'field': [81, 0, 44, 0, -8, 0, -4, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [2, 4]}
  • id: 1043078
    {'degree': 8, 'field': [306, -918, 423, 54, -149, 50, -1, -2, 1], 'lmfdb_label': '20400.dp4', 'torsion': [12]}
  • id: 1043077
    {'degree': 8, 'field': [544, -1088, 848, -320, 38, 16, -1, -2, 1], 'lmfdb_label': '20400.dp4', 'torsion': [2, 4]}
  • id: 1043080
    {'degree': 12, 'field': [1206, -972, 1890, -2316, 999, 1008, -226, 0, 75, -12, -12, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [2, 6]}
  • id: 1043079
    {'degree': 12, 'field': [14884, 0, 21000, 0, 8925, 0, 2506, 0, 375, 0, 30, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [3, 6]}
  • id: 1043082
    {'degree': 16, 'field': [16641, 0, -14304, 0, -9968, 0, 2128, 0, 5346, 0, 1760, 0, 336, 0, 16, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [2, 12]}
  • id: 1043083
    {'degree': 16, 'field': [118354, -790364, 2045694, -2595996, 2127287, -1172564, 407658, -69484, -1875, -1220, 3378, -1396, 233, -12, 6, -4, 1], 'lmfdb_label': '20400.dp4', 'torsion': [2, 12]}
  • id: 1043081
    {'degree': 16, 'field': [640000, 0, -204000, 0, -416450, 0, -134385, 0, 5349, 0, 7548, 0, 970, 0, 51, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [8]}
  • id: 1043084
    {'degree': 18, 'field': [-60255704, -89972196, 146591985, -211351108, 222651405, -106647816, 86764286, -15711960, 14099463, -1218484, 784002, -84372, -15925, -2592, -2514, -16, -39, 0, 1], 'lmfdb_label': '20400.dp4', 'torsion': [18]}
• 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: 463767
    {'conductor': 20400, 'conductor_valuation': 4, 'discriminant_valuation': 21, 'j_denominator_valuation': 9, 'kodaira_symbol': -17, 'lmfdb_label': '20400.dp4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 463768
    {'conductor': 20400, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '20400.dp4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 463769
    {'conductor': 20400, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '20400.dp4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 463770
    {'conductor': 20400, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '20400.dp4', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1800524
    {'adelic_gens': [[1614, 1535, 595, 934], [1223, 0, 0, 2039], [11, 2, 1990, 2031], [1361, 420, 340, 1], [826, 1635, 585, 1216], [1, 0, 12, 1], [1, 6, 6, 37], [241, 420, 630, 481], [1, 12, 0, 1], [2029, 12, 2028, 13]], 'adelic_image': '2040.96.1.?', 'conductor': 20400, 'lmfdb_label': '20400.dp4', 'prime': 0}
  • id: 95115
    {'conductor': 20400, 'elladic_image': '8.6.0.5', 'lmfdb_label': '20400.dp4', 'modell_image': '2B', 'prime': 2}
  • id: 95116
    {'conductor': 20400, 'elladic_image': '3.4.0.1', 'lmfdb_label': '20400.dp4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 20400.dp does not appear in ec_padic