Elliptic curve data - 68450.s2

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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': '68450e', 'Clabel': '68450e2', 'Cnumber': 2, 'abc_quality': 0.9545292940495189, 'absD': 2030652184298078125000, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 13320, 'ainvs': [1, 1, 0, -633875, 2176503125], 'analytic_rank': 1, 'bad_primes': [2, 5, 37], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 68450, 'degree': 3545856, 'elladic_images': ['3.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7682709754127830077795513330', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 18, 'isogeny_degrees': [1, 3], 'jinv': [-702595369, 50653000], 'lmfdb_iso': '68450.s', 'lmfdb_label': '68450.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -19, 342], 'min_quad_twist_disc': 185, 'modell_images': ['3Cs'], 'modm_images': ['3.12.0.a.1', '24.24.0-3.a.1.4', '333.36.0.?', '555.24.0.?', '1480.2.0.?', '1665.72.0.?', '2664.72.0.?', '4440.48.1.?', '13320.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.4241449037656436291247728070', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 34225], [3, 2, 34225], [5, 18, 2738], [37, 722, 50]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.15809306287362059829512383087', 'prec': 103}, 'szpiro_ratio': 5.0768884165142625, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -1, 2, 1, 0, -2, 1, -1, 1, 0, 3, 2, -4, -1, 0, 1, 3, -1, -2, 0], 'aplist': [-1, 2, 0, 1, 3, -4, 3, -2, 6, -3, -5, 0, 3, -1, -12, -3, 0, 1, 4, 6, 16, -8, 12, 6, 17], 'class_deg': 9, 'class_size': 3, 'conductor': 68450, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '68450.s', 'trace_hash': 2158856931200546666}
• 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': '0.0039401284651903931787108080398', 'prec': 110}, 'conductor': 68450, 'gens': [[395575, 495675925, 22]], 'heights': [{'__RealLiteral__': 0, 'data': '7.4241449037656436291247728070', 'prec': 100}], 'lmfdb_label': '68450.s2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12144732910368198818380962660', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.2131405555283965192815214825335529868', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [12, 0], '3': [1, 1], '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': 'a', '41': [1, 0], '43': [1, 0], '47': [3, 0]}, 'iwp0': 0, 'lmfdb_label': '68450.s2'}
• ec_torsion_growth •

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

  
  
  • id: 3257446
    {'degree': 2, 'field': [-46, -1, 1], 'lmfdb_label': '68450.s2', 'torsion': [3]}
  • id: 3257447
    {'degree': 2, 'field': [139, -1, 1], 'lmfdb_label': '68450.s2', 'torsion': [3]}
  • id: 3257448
    {'degree': 3, 'field': [-2, 7, 0, 1], 'lmfdb_label': '68450.s2', 'torsion': [2]}
  • id: 3257449
    {'degree': 4, 'field': [2116, 46, 47, -1, 1], 'lmfdb_label': '68450.s2', 'torsion': [3, 3]}
  • id: 3257451
    {'degree': 6, 'field': [-64, 20, 10, -22, 15, 0, 1], 'lmfdb_label': '68450.s2', 'torsion': [6]}
  • id: 3257450
    {'degree': 6, 'field': [1480, 0, 441, 0, 42, 0, 1], 'lmfdb_label': '68450.s2', 'torsion': [2, 2]}
  • id: 3257452
    {'degree': 6, 'field': [3244, -118, 379, -64, -31, 0, 1], 'lmfdb_label': '68450.s2', 'torsion': [6]}
  • id: 3257455
    {'degree': 12, 'field': [64, 0, 480, 0, 660, 0, 564, 0, 165, 0, 30, 0, 1], 'lmfdb_label': '68450.s2', 'torsion': [2, 6]}
  • id: 3257454
    {'degree': 12, 'field': [4096, 1280, 1040, 2616, 1500, 820, 206, 310, 215, -44, -15, 0, 1], 'lmfdb_label': '68450.s2', 'torsion': [3, 6]}
  • id: 3257453
    {'degree': 12, 'field': [16475, -25200, 35080, 31900, 5035, -4000, -3264, 616, 377, -48, -8, -4, 1], 'lmfdb_label': '68450.s2', 'torsion': [4]}
  • id: 3257456
    {'degree': 12, 'field': [16900, 0, -31140, 0, 12261, 0, 4634, 0, 351, 0, -6, 0, 1], 'lmfdb_label': '68450.s2', 'torsion': [2, 6]}
  • id: 3257457
    {'degree': 18, 'field': [-3256, 24568, -20054, -143079, 155474, 177563, -19324, 49274, 69407, -22450, -13900, -1787, -922, -50, -108, 59, 2, -2, 1], 'lmfdb_label': '68450.s2', 'torsion': [9]}
  • id: 3257458
    {'degree': 18, 'field': [842723544295, -1342869438465, 1426658414205, -1089083772580, 641619230970, -299764194810, 102661928274, -23807352312, 2286822153, 403633105, -94073985, 8734728, 26526, 49086, 23490, -1480, 303, -9, 1], 'lmfdb_label': '68450.s2', 'torsion': [9]}
• 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: 1656667
    {'conductor': 68450, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '68450.s2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1656668
    {'conductor': 68450, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '68450.s2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1656669
    {'conductor': 68450, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '68450.s2', 'prime': 37, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 2117041
    {'adelic_gens': [[10796, 13311, 9009, 20], [1, 6, 6, 37], [1, 12, 0, 1], [13303, 18, 13302, 19], [1, 9, 9, 82], [1, 18, 0, 1], [10001, 6678, 6498, 8245], [1, 0, 18, 1], [13310, 13311, 2673, 8], [6670, 9, 3321, 13312], [10, 9, 6651, 13312]], 'adelic_image': '13320.144.3.?', 'conductor': 68450, 'lmfdb_label': '68450.s2', 'prime': 0}
  • id: 285899
    {'conductor': 68450, 'elladic_image': '3.12.0.1', 'lmfdb_label': '68450.s2', 'modell_image': '3Cs', 'prime': 3}
• ec_padic •

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

  
  
  • id: 3501421
    {'lmfdb_iso': '68450.s', 'p': 7, 'prec': 20, 'unit': 4525766863090738, 'val': -1}
  • id: 3501423
    {'lmfdb_iso': '68450.s', 'p': 11, 'prec': 20, 'unit': 4666155351523134473, 'val': 1}
  • id: 3501425
    {'lmfdb_iso': '68450.s', 'p': 13, 'prec': 20, 'unit': 893188982499070495396, 'val': 1}
  • id: 3501427
    {'lmfdb_iso': '68450.s', 'p': 17, 'prec': 20, 'unit': 15302747486180038328270, 'val': 1}
  • id: 3501428
    {'lmfdb_iso': '68450.s', 'p': 19, 'prec': 20, 'unit': 348849221275118206428787, 'val': 1}
  • id: 3501431
    {'lmfdb_iso': '68450.s', 'p': 23, 'prec': 20, 'unit': 18332043932839944510575175, 'val': 1}
  • id: 3501424
    {'lmfdb_iso': '68450.s', 'p': 29, 'prec': 20, 'unit': 1679858024762806178925176870, 'val': 1}
  • id: 3501437
    {'lmfdb_iso': '68450.s', 'p': 31, 'prec': 20, 'unit': 3319446681635019945216290798, 'val': 1}
  • id: 3501422
    {'lmfdb_iso': '68450.s', 'p': 41, 'prec': 20, 'unit': 3499748878016965428333774435990, 'val': 1}
  • id: 3501420
    {'lmfdb_iso': '68450.s', 'p': 43, 'prec': 20, 'unit': 7995892322336045069917766273130, 'val': 1}
  • id: 3501426
    {'lmfdb_iso': '68450.s', 'p': 47, 'prec': 20, 'unit': 820639299485858451700776623109, 'val': 2}
  • id: 3501429
    {'lmfdb_iso': '68450.s', 'p': 53, 'prec': 20, 'unit': 220994851228342896215541585874925, 'val': 1}
  • id: 3501435
    {'lmfdb_iso': '68450.s', 'p': 61, 'prec': 20, 'unit': 113281697471795176635101016221021531, 'val': -1}
  • id: 3501419
    {'lmfdb_iso': '68450.s', 'p': 67, 'prec': 20, 'unit': 13178704742560015578898281143807304, 'val': 1}
  • id: 3501433
    {'lmfdb_iso': '68450.s', 'p': 71, 'prec': 20, 'unit': 84242706920285922956071866211556582, 'val': 1}
  • id: 3501430
    {'lmfdb_iso': '68450.s', 'p': 73, 'prec': 20, 'unit': 192775525290916787083234261362979524, 'val': 1}
  • id: 3501434
    {'lmfdb_iso': '68450.s', 'p': 79, 'prec': 20, 'unit': 887168324949371763290505003973775954, 'val': 1}
  • id: 3501436
    {'lmfdb_iso': '68450.s', 'p': 83, 'prec': 20, 'unit': 1085392067386254938571047116016702114, 'val': 1}
  • id: 3501432
    {'lmfdb_iso': '68450.s', 'p': 89, 'prec': 20, 'unit': 300416189979814146577782315675213846, 'val': 1}
  • id: 3501418
    {'lmfdb_iso': '68450.s', 'p': 97, 'prec': 20, 'unit': 27596384034408998297658176820431463638, 'val': 1}