Elliptic curve data - 369600.qf1

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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': '369600qf', 'Clabel': '369600qf8', 'Cnumber': 8, 'abc_quality': 1.0452427382284861, 'absD': 31297964544000000000000000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [0, 1, 0, -40748781633, -3166068810535137], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 369600, 'degree': 764411904, 'elladic_images': ['8.12.0.12', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.6766807471018618770487221613', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'iso_nlabel': 421, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [1826870018430810435423307849, 7641104625000000000], 'lmfdb_iso': '369600.qf', 'lmfdb_label': '369600.qf1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -25467989, -49471735264], 'min_quad_twist_disc': 40, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '8.12.0-4.c.1.2', '12.24.0.g.1', '20.12.0-4.c.1.1', '24.96.0-24.bu.2.25', '40.24.0-40.y.1.1', '60.48.0-12.g.1.7', '120.192.1.?', '616.24.0.?', '924.48.0.?', '1848.192.1.?', '2310.24.0.?', '3080.48.0.?', '4620.96.0.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '22.703547898280090243821400624', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 1925], [3, 4, 11200], [5, 18, 14784], [7, 8, 52800], [11, 12, 33600]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.8322410200448937256224943125', 'prec': 100}, 'szpiro_ratio': 6.622816587518887, '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, -1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 1, 0, -1, 1, 2, 6, 4, 0, 6, -4, 2, -6, -4, 0, -6, -12, -14, -16, 0, -2, -4, 0, -6, 10], 'class_deg': 12, 'class_size': 8, 'conductor': 369600, 'isogeny_matrix': [[1, 2, 3, 4, 6, 12, 12, 4], [2, 1, 6, 2, 3, 6, 6, 2], [3, 6, 1, 12, 2, 4, 4, 12], [4, 2, 12, 1, 6, 3, 12, 4], [6, 3, 2, 6, 1, 2, 2, 6], [12, 6, 4, 3, 2, 1, 4, 12], [12, 6, 4, 12, 2, 4, 1, 3], [4, 2, 12, 4, 6, 12, 3, 1]], 'lmfdb_iso': '369600.qf', 'trace_hash': 1993416251880600984}
• 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': '0.000086673576131217279920095436812', 'prec': 117}, 'conductor': 369600, 'gens': [[-781118013147, 683732241286524, 2587]], 'heights': [{'__RealLiteral__': 0, 'data': '22.703547898280090243821400624', 'prec': 100}], 'lmfdb_label': '369600.qf1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.010626029240126887424814098819', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.579931063443787809646779451578659163', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[-116727, 0, 1]], 'xcoord_integral_points': [-116727]}
• lmfdb_label 369600.qf1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 15347236
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [2, 2]}
  • id: 15347237
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [4]}
  • id: 15347239
    {'degree': 2, 'field': [30, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [6]}
  • id: 15347238
    {'degree': 2, 'field': [770, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [4]}
  • id: 15347242
    {'degree': 4, 'field': [81, 0, 12, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [12]}
  • id: 15347241
    {'degree': 4, 'field': [2116, 0, -62, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [2, 6]}
  • id: 15347240
    {'degree': 4, 'field': [25281, 0, -298, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [2, 4]}
  • id: 15347243
    {'degree': 4, 'field': [34225, 0, 400, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [12]}
  • id: 15347244
    {'degree': 6, 'field': [2969, -3780, 300, -126, -30, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [6]}
  • id: 15347246
    {'degree': 8, 'field': [42436, 0, 8560, 0, 812, 0, 40, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [8]}
  • id: 15347247
    {'degree': 8, 'field': [128304, -9504, 32208, -24992, 4123, 478, -125, -2, 1], 'lmfdb_label': '369600.qf1', 'torsion': [8]}
  • id: 15347248
    {'degree': 8, 'field': [3218436, 0, -232680, 0, 8488, 0, -140, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [2, 12]}
  • id: 15347245
    {'degree': 8, 'field': [56889295, 120740, -135826, 30176, -15097, 8, 2, -4, 1], 'lmfdb_label': '369600.qf1', 'torsion': [2, 4]}
  • id: 15347249
    {'degree': 12, 'field': [1315609, 0, -159000, 0, 194100, 0, -19706, 0, 1500, 0, -60, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [3, 6]}
  • id: 15347251
    {'degree': 12, 'field': [15928326, -6007932, 1261170, -1046556, 143559, 21168, 23534, 0, 75, -252, -12, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [12]}
  • id: 15347250
    {'degree': 12, 'field': [1269536409, 1901194092, -178808148, -92211084, 34110882, 1377432, -1165186, 0, 24060, -252, -246, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [2, 6]}
  • id: 15347252
    {'degree': 12, 'field': [7200031609, 0, 250959000, 0, 25305900, 0, 147706, 0, 1500, 0, -60, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [12]}
  • id: 15347254
    {'degree': 16, 'field': [2825761, 0, 5809536, 0, 5123952, 0, 2051040, 0, 435586, 0, 51840, 0, 3312, 0, 96, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [2, 8]}
  • id: 15347255
    {'degree': 16, 'field': [539985609, 292277160, 2757240, -523380024, 101787426, 173161592, -27624916, -23617264, 3258419, 1644200, -211492, -60992, 7678, 1120, -140, -8, 1], 'lmfdb_label': '369600.qf1', 'torsion': [2, 8]}
  • id: 15347257
    {'degree': 16, 'field': [1708086241, 0, 737019248, 0, 147131084, 0, 17878512, 0, 1457414, 0, 82512, 0, 3212, 0, 80, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [24]}
  • id: 15347258
    {'degree': 16, 'field': [2586984224400, 49445164800, -51299797440, 3621177840, -1583593151, -291665360, 130232984, -30116748, 9882664, -1689640, 461062, -70336, 14392, -1260, 200, -8, 1], 'lmfdb_label': '369600.qf1', 'torsion': [24]}
  • id: 15347253
    {'degree': 16, 'field': [3236391885597025, 0, 15468668912940, 0, -1706553571434, 0, -3416164608, 0, 341637799, 0, 90696, 0, -30126, 0, 12, 0, 1], 'lmfdb_label': '369600.qf1', 'torsion': [4, 4]}
  • id: 15347256
    {'degree': 16, 'field': [3267472146267505, -47500744635080, 46196066172476, 2619514042992, -1334768090402, 28944199064, -7865533464, -1529246792, 383806095, -673928, -186960, 174728, -28454, -336, 68, -8, 1], 'lmfdb_label': '369600.qf1', 'torsion': [2, 12]}
  • id: 15347259
    {'degree': 18, 'field': [24544851612198984, 8533037028971664, 1950930857591100, 252245071095552, 35908586039430, 1902860029044, -35075879631, -20788995060, 10498645872, 1553801400, 75472155, -18160200, -552690, 159300, 23895, -708, -108, 0, 1], 'lmfdb_label': '369600.qf1', '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: 9145767
    {'conductor': 369600, 'conductor_valuation': 6, 'discriminant_valuation': 27, 'j_denominator_valuation': 9, 'kodaira_symbol': -21, 'lmfdb_label': '369600.qf1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9145768
    {'conductor': 369600, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '369600.qf1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 9145769
    {'conductor': 369600, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '369600.qf1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 9145770
    {'conductor': 369600, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '369600.qf1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9145771
    {'conductor': 369600, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '369600.qf1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 3964905
    {'adelic_gens': [[5543, 9216, 1836, 8951], [15, 106, 7934, 11], [1, 12, 12, 145], [3376, 21, 2235, 8866], [2311, 24, 2322, 289], [9217, 24, 9216, 25], [1, 24, 0, 1], [1336, 21, 1035, 8866], [7314, 8831, 5005, 6544], [7701, 6164, 20, 4701], [1, 0, 24, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 369600, 'lmfdb_label': '369600.qf1', 'prime': 0}
  • id: 1269460
    {'conductor': 369600, 'elladic_image': '8.12.0.12', 'lmfdb_label': '369600.qf1', 'modell_image': '2B', 'prime': 2}
  • id: 1269461
    {'conductor': 369600, 'elladic_image': '3.4.0.1', 'lmfdb_label': '369600.qf1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 369600.qf does not appear in ec_padic