Elliptic curve data - 31680.eh1

Formats: - HTML - YAML - JSON - 2024-05-30T15:35:52.747563

• 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': '31680ee', 'Clabel': '31680ee4', 'Cnumber': 4, 'abc_quality': 0.9734387724171747, 'absD': 397434470400, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 1320, 'ainvs': [0, 0, 0, -255612, -49741616], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 31680, 'degree': 165888, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6103300206194107157364410439', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 111, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [154639330142416, 33275], 'lmfdb_iso': '31680.eh', 'lmfdb_label': '31680.eh1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -7100, -232652], 'min_quad_twist_disc': 24, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '20.6.0.c.1', '24.24.0-6.a.1.6', '44.6.0.a.1', '60.24.0.q.1', '120.48.0.?', '132.24.0.?', '220.12.0.?', '264.48.0.?', '660.48.1.?', '1320.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.8153314128440614101295710933', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.25235216563208634238538095040', 'prec': 103}, 'szpiro_ratio': 4.725057208985107, '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, 0, 0, 1, 0, 4, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, -4, 0], 'aplist': [0, 0, 1, 4, 1, 4, 0, -4, -6, -6, -8, -2, -6, 8, 6, -6, 12, -2, -10, -12, -16, -8, 0, -6, 14], 'class_deg': 6, 'class_size': 4, 'conductor': 31680, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '31680.eh', 'trace_hash': 602626319524054203}
• 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': '0.039928694975887037828628713527', 'prec': 107}, 'conductor': 31680, 'gens': [[4208, 270900, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.8153314128440614101295710933', 'prec': 100}], 'lmfdb_label': '31680.eh1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.21232652434694710606223177550', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.4084946408888055064063217259200507081', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-292, 0, 1]], 'xcoord_integral_points': [-292, 4208]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '31680.eh1'}
• ec_torsion_growth •

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

  
  
  • id: 1579811
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [2, 2]}
  • id: 1579812
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [6]}
  • id: 1579814
    {'degree': 4, 'field': [25, 0, 12, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [2, 6]}
  • id: 1579813
    {'degree': 4, 'field': [396, 0, 42, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [4]}
  • id: 1579815
    {'degree': 6, 'field': [-24, 0, 28, 0, -2, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [6]}
  • id: 1579818
    {'degree': 8, 'field': [361, 0, 426, 0, 167, 0, 24, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [12]}
  • id: 1579817
    {'degree': 8, 'field': [6229, -1628, 2276, -1340, 781, -136, 50, -4, 1], 'lmfdb_label': '31680.eh1', 'torsion': [2, 4]}
  • id: 1579816
    {'degree': 8, 'field': [62500, 0, -17000, 0, 1580, 0, -64, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [2, 4]}
  • id: 1579819
    {'degree': 12, 'field': [4, 0, -24, 0, 156, 0, 76, 0, 24, 0, 6, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [3, 6]}
  • id: 1579820
    {'degree': 12, 'field': [140625, 0, -157500, 0, 37675, 0, -4584, 0, 683, 0, -12, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [2, 6]}
  • id: 1579823
    {'degree': 16, 'field': [2401, 0, 117404, 0, 507698, 0, 706776, 0, 307883, 0, 47352, 0, 3122, 0, 92, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [2, 12]}
  • id: 1579822
    {'degree': 16, 'field': [228484, 0, -193736, 0, 217684, 0, -93512, 0, 22117, 0, -3116, 0, 298, 0, -20, 0, 1], 'lmfdb_label': '31680.eh1', 'torsion': [2, 12]}
  • id: 1579821
    {'degree': 16, 'field': [3748921, -7354732, 4159672, 378884, -1187204, 329648, 122000, -46928, -14841, 9776, 1520, -1384, 116, 92, -12, -4, 1], 'lmfdb_label': '31680.eh1', 'torsion': [8]}
  • id: 1579824
    {'degree': 18, 'field': [275747859, 532825722, 541675791, 311801358, 89189937, -10249074, -14123916, -2534070, 1501242, 629860, 38787, -36564, -3607, 1254, 351, -22, 12, 0, 1], 'lmfdb_label': '31680.eh1', '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: 740207
    {'conductor': 31680, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '31680.eh1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 740208
    {'conductor': 31680, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '31680.eh1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 740209
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '31680.eh1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 740210
    {'conductor': 31680, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '31680.eh1', '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: 1875745
    {'adelic_gens': [[659, 0, 0, 1319], [606, 397, 605, 386], [923, 1308, 918, 1247], [11, 2, 1270, 1311], [1309, 1318, 710, 669], [1, 0, 12, 1], [1, 6, 6, 37], [221, 12, 220, 1], [130, 3, 573, 652], [671, 1308, 672, 1307], [1, 12, 0, 1], [1309, 12, 1308, 13]], 'adelic_image': '1320.96.1.?', 'conductor': 31680, 'lmfdb_label': '31680.eh1', 'prime': 0}
  • id: 141717
    {'conductor': 31680, 'elladic_image': '2.3.0.1', 'lmfdb_label': '31680.eh1', 'modell_image': '2B', 'prime': 2}
  • id: 141718
    {'conductor': 31680, 'elladic_image': '3.4.0.1', 'lmfdb_label': '31680.eh1', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 1541593
    {'lmfdb_iso': '31680.eh', 'p': 7, 'prec': 20, 'unit': 10346133951417939, 'val': 1}
  • id: 1541597
    {'lmfdb_iso': '31680.eh', 'p': 13, 'prec': 20, 'unit': 1003509291242061524877, 'val': 1}
  • id: 1541600
    {'lmfdb_iso': '31680.eh', 'p': 19, 'prec': 20, 'unit': 1843525232566659724397281, 'val': 1}
  • id: 1541603
    {'lmfdb_iso': '31680.eh', 'p': 23, 'prec': 20, 'unit': 17821600479124384115077846, 'val': 1}
  • id: 1541596
    {'lmfdb_iso': '31680.eh', 'p': 29, 'prec': 20, 'unit': 4696047864405283817571002522, 'val': 1}
  • id: 1541608
    {'lmfdb_iso': '31680.eh', 'p': 31, 'prec': 20, 'unit': 20367637534608904854924990420, 'val': 1}
  • id: 1541592
    {'lmfdb_iso': '31680.eh', 'p': 37, 'prec': 20, 'unit': 524802799816590683825014564736, 'val': 1}
  • id: 1541594
    {'lmfdb_iso': '31680.eh', 'p': 41, 'prec': 20, 'unit': 625974195627784033018523565261, 'val': 1}
  • id: 1541595
    {'lmfdb_iso': '31680.eh', 'p': 43, 'prec': 20, 'unit': 4541882554617245652196486438020, 'val': 1}
  • id: 1541606
    {'lmfdb_iso': '31680.eh', 'p': 47, 'prec': 20, 'unit': 53211872198784497645052544653902, 'val': 1}
  • id: 1541601
    {'lmfdb_iso': '31680.eh', 'p': 53, 'prec': 20, 'unit': 250949151362794772528575006288040, 'val': 1}
  • id: 1541599
    {'lmfdb_iso': '31680.eh', 'p': 59, 'prec': 20, 'unit': 2530816199956773151387614114787913, 'val': 1}
  • id: 1541607
    {'lmfdb_iso': '31680.eh', 'p': 61, 'prec': 20, 'unit': 175340851721736993985735481235977, 'val': 1}
  • id: 1541591
    {'lmfdb_iso': '31680.eh', 'p': 67, 'prec': 20, 'unit': 15470588836622740252166148960709152, 'val': 1}
  • id: 1541605
    {'lmfdb_iso': '31680.eh', 'p': 71, 'prec': 20, 'unit': 109918129253960359496159116114034343, 'val': 1}
  • id: 1541602
    {'lmfdb_iso': '31680.eh', 'p': 73, 'prec': 20, 'unit': 237897777885955650863443499222044049, 'val': 1}
  • id: 1541598
    {'lmfdb_iso': '31680.eh', 'p': 79, 'prec': 20, 'unit': 513476415722784860637078481603145564, 'val': 1}
  • id: 1541604
    {'lmfdb_iso': '31680.eh', 'p': 89, 'prec': 20, 'unit': 3941343484754148032527855810571874988, 'val': 1}
  • id: 1541590
    {'lmfdb_iso': '31680.eh', 'p': 97, 'prec': 20, 'unit': 47627294054904473515711246130714344529, 'val': 1}