Elliptic curve data - 98736.ca1

Formats: - HTML - YAML - JSON - 2025-10-22T18:10:55.140874

• 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': '98736by', 'Clabel': '98736by4', 'Cnumber': 4, 'abc_quality': 1.0382088586045655, 'absD': 12535173747885735936, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1496, 'ainvs': [0, -1, 0, -2718622232, -54558722956560], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 98736, 'degree': 30965760, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.7343625311649807176701606273', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 52, 'isogeny_degrees': [1, 2, 4], 'jinv': [306234591284035366263793, 1727485056], 'lmfdb_iso': '98736.ca', 'lmfdb_label': '98736.ca1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1404247, -640608535], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '88.24.0.?', '136.24.0.?', '748.12.0.?', '1496.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '101.11082500242425366559363840', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 2057], [3, 4, 32912], [11, 72, 816], [17, 18, 5808]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8422677142058501362219567169', 'prec': 100}, 'szpiro_ratio': 6.676731142334556, '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, 2, 0, 4, 0, 1, 0, 0, 0, 2, 0, -2, 0, -1, 0, -4, 0], 'aplist': [0, -1, 2, 4, 0, 2, -1, -4, 4, -2, 4, -6, 6, -4, 0, 6, -4, 6, 4, -4, -10, 4, 12, -6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 98736, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '98736.ca', 'trace_hash': 1700665103832486708}
• 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': '0.00057065538332903577361067186525', 'prec': 113}, 'conductor': 98736, 'gens': [[-49645130744800200840334959261434699129462077622, 9401673008453993198624353797614131835490468502499944464889310630, 1284204561392337628443]], 'heights': [{'__RealLiteral__': 0, 'data': '101.11082500242425366559363840', 'prec': 100}], 'lmfdb_label': '98736.ca1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.020907992644584328736468111612', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.4560975417541581536973469598731594656', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-30103, 0, 1]], 'xcoord_integral_points': [-30103]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [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, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '98736.ca1'}
• ec_torsion_growth •

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

  
  
  • id: 4589011
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [2, 2]}
  • id: 4589012
    {'degree': 2, 'field': [22, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [4]}
  • id: 4589013
    {'degree': 2, 'field': [47, -1, 1], 'lmfdb_label': '98736.ca1', 'torsion': [4]}
  • id: 4589014
    {'degree': 4, 'field': [196, 0, -6, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [2, 4]}
  • id: 4589018
    {'degree': 8, 'field': [-610203, 0, -6380, 0, -2706, 0, 0, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [6]}
  • id: 4589015
    {'degree': 8, 'field': [-85599, 16592, 13640, 1632, 530, -272, -56, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [2, 4]}
  • id: 4589017
    {'degree': 8, 'field': [752, 1132, 119, -202, 318, -28, 34, -2, 1], 'lmfdb_label': '98736.ca1', 'torsion': [8]}
  • id: 4589016
    {'degree': 8, 'field': [12241, 2184, -1288, 432, 230, -24, 8, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [8]}
  • id: 4589020
    {'degree': 16, 'field': [34225, 0, 4978352, 0, 3574492, 0, 1016688, 0, 239862, 0, 30096, 0, 2236, 0, 80, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [2, 8]}
  • id: 4589021
    {'degree': 16, 'field': [35344, 0, -3824, 0, 60076, 0, 34308, 0, 33417, 0, 8808, 0, 1018, 0, 52, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [2, 8]}
  • id: 4589019
    {'degree': 16, 'field': [43335889, -55507856, 35549312, -18816144, 13310050, -7645512, 2959360, -630496, 59303, -14552, 9248, 1088, -42, -136, 0, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [4, 4]}
  • id: 4589024
    {'degree': 16, 'field': [84989961, 0, -39136908, 0, 495060778, 0, -110906304, 0, 10397199, 0, -43904, 0, 7746, 0, 0, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [12]}
  • id: 4589023
    {'degree': 16, 'field': [671276281, 0, -532126612, 0, 188147452, 0, 73011012, 0, 3184782, 0, 5892, 0, -884, 0, 44, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [12]}
  • id: 4589022
    {'degree': 16, 'field': [6858757679929, 0, -2989130114792, 0, 127426362124, 0, -10416996096, 0, 200362254, 0, -2581800, 0, 26956, 0, -272, 0, 1], 'lmfdb_label': '98736.ca1', 'torsion': [2, 6]}
• 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: 2422960
    {'conductor': 98736, 'conductor_valuation': 4, 'discriminant_valuation': 19, 'j_denominator_valuation': 7, 'kodaira_symbol': -15, 'lmfdb_label': '98736.ca1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2422961
    {'conductor': 98736, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '98736.ca1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2422962
    {'conductor': 98736, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '98736.ca1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 2422963
    {'conductor': 98736, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '98736.ca1', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 2313281
    {'adelic_gens': [[7, 6, 1490, 1491], [936, 1419, 1177, 254], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [12, 1089, 1463, 958], [285, 968, 198, 1099], [1489, 8, 1488, 9], [1087, 0, 0, 1495]], 'adelic_image': '1496.48.0.?', 'conductor': 98736, 'lmfdb_label': '98736.ca1', 'prime': 0}
  • id: 397421
    {'conductor': 98736, 'elladic_image': '8.12.0.11', 'lmfdb_label': '98736.ca1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 5136693
    {'lmfdb_iso': '98736.ca', 'p': 5, 'prec': 20, 'unit': 4303433136472, 'val': 1}
  • id: 5136694
    {'lmfdb_iso': '98736.ca', 'p': 7, 'prec': 20, 'unit': 973418707136854, 'val': 1}
  • id: 5136699
    {'lmfdb_iso': '98736.ca', 'p': 13, 'prec': 20, 'unit': 753121152851608893689, 'val': 1}
  • id: 5136690
    {'lmfdb_iso': '98736.ca', 'p': 19, 'prec': 20, 'unit': 912283746466202882031953, 'val': 1}
  • id: 5136704
    {'lmfdb_iso': '98736.ca', 'p': 23, 'prec': 20, 'unit': 71970319153186965394030999, 'val': 1}
  • id: 5136698
    {'lmfdb_iso': '98736.ca', 'p': 29, 'prec': 20, 'unit': 236606345871896957501402506, 'val': 1}
  • id: 5136695
    {'lmfdb_iso': '98736.ca', 'p': 31, 'prec': 20, 'unit': 10135012456032264246244722057, 'val': 1}
  • id: 5136709
    {'lmfdb_iso': '98736.ca', 'p': 37, 'prec': 20, 'unit': 516187443222596127723300857499, 'val': 1}
  • id: 5136696
    {'lmfdb_iso': '98736.ca', 'p': 41, 'prec': 20, 'unit': 2904615699311864229020498396198, 'val': 1}
  • id: 5136697
    {'lmfdb_iso': '98736.ca', 'p': 43, 'prec': 20, 'unit': 3820203357771460041307686412523, 'val': 1}
  • id: 5136702
    {'lmfdb_iso': '98736.ca', 'p': 53, 'prec': 20, 'unit': 270843261262536204099051676578057, 'val': 1}
  • id: 5136707
    {'lmfdb_iso': '98736.ca', 'p': 59, 'prec': 20, 'unit': 2759429114228104977576134530188190, 'val': 1}
  • id: 5136708
    {'lmfdb_iso': '98736.ca', 'p': 61, 'prec': 20, 'unit': 6777504721093234216840816504555718, 'val': 1}
  • id: 5136692
    {'lmfdb_iso': '98736.ca', 'p': 67, 'prec': 20, 'unit': 23697093263495728634848172122261329, 'val': 1}
  • id: 5136706
    {'lmfdb_iso': '98736.ca', 'p': 71, 'prec': 20, 'unit': 147509309478419613086276909938687161, 'val': 1}
  • id: 5136703
    {'lmfdb_iso': '98736.ca', 'p': 73, 'prec': 20, 'unit': 195429710732643787494434065329214860, 'val': 1}
  • id: 5136700
    {'lmfdb_iso': '98736.ca', 'p': 79, 'prec': 20, 'unit': 626396078973635887328657305511543012, 'val': 1}
  • id: 5136701
    {'lmfdb_iso': '98736.ca', 'p': 83, 'prec': 20, 'unit': 4202030166322742022694920569200436, 'val': 2}
  • id: 5136705
    {'lmfdb_iso': '98736.ca', 'p': 89, 'prec': 20, 'unit': 8207976696138228886412734132570807243, 'val': 1}
  • id: 5136691
    {'lmfdb_iso': '98736.ca', 'p': 97, 'prec': 20, 'unit': 21796962878609678862837813632062000438, 'val': 1}