Elliptic curve data - 286650.mt5

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '286650mt', 'Clabel': '286650mt3', 'Cnumber': 3, 'abc_quality': 1.001183037889812, 'absD': 29340994362639164485166250000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 10920, 'ainvs': [1, -1, 1, -1752148355, -26999381475853], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 286650, 'degree': 254803968, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '4.2216147452456350715198928616', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 331, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [443915739051786565201, 21894701746029840], 'lmfdb_iso': '286650.mt', 'lmfdb_label': '286650.mt5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -158925, -23336703], 'min_quad_twist_disc': 105, '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', '12.48.0.c.2', '56.12.0.bb.1', '105.8.0.?', '120.96.0.?', '130.6.0.?', '168.96.1.?', '210.24.0.?', '260.12.0.?', '312.96.0.?', '390.24.0.?', '420.96.0.?', '546.24.0.?', '780.96.1.?', '840.192.1.?', '1092.96.0.?', '1560.192.1.?', '2184.192.1.?', '2730.48.0.?', '3640.24.0.?', '5460.192.1.?', '10920.384.5.?'], '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': '11.225828839686173863474885740', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.8946345701668733859692142048', 'prec': 100}, 'szpiro_ratio': 6.00555666214731, '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, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, -6, 0, 4, 0], 'aplist': [1, 0, 0, 0, 0, 1, -6, 4, 0, -6, 4, 10, 6, -8, 0, -6, -12, -14, 4, 0, 2, 8, 12, 6, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 286650, 'isogeny_matrix': [[1, 2, 4, 3, 4, 6, 12, 12], [2, 1, 2, 6, 2, 3, 6, 6], [4, 2, 1, 12, 4, 6, 12, 3], [3, 6, 12, 1, 12, 2, 4, 4], [4, 2, 4, 12, 1, 6, 3, 12], [6, 3, 6, 2, 6, 1, 2, 2], [12, 6, 12, 4, 3, 2, 1, 4], [12, 6, 3, 4, 12, 2, 4, 1]], 'lmfdb_iso': '286650.mt', 'trace_hash': 2121124656377701610}
• 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': '0.00021535354382291909707200779568', 'prec': 113}, 'conductor': 286650, 'gens': [[-14777979, 4825588700, 23]], 'heights': [{'__RealLiteral__': 0, 'data': '11.225828839686173863474885740', 'prec': 100}], 'lmfdb_label': '286650.mt5', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.023406375376431875456331842104', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.612286259196925029049726621045203893', 'prec': 130}, 'tamagawa_product': 192, 'torsion_generators': [[48099, -24050, 1]], 'xcoord_integral_points': [48099]}
• lmfdb_label 286650.mt5 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12183515
    {'degree': 2, 'field': [-68, -1, 1], 'lmfdb_label': '286650.mt5', 'torsion': [4]}
  • id: 12183516
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '286650.mt5', 'torsion': [4]}
  • id: 12183514
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '286650.mt5', 'torsion': [2, 2]}
  • id: 12183517
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '286650.mt5', 'torsion': [6]}
  • id: 12183518
    {'degree': 4, 'field': [-26, -143, -55, -1, 1], 'lmfdb_label': '286650.mt5', 'torsion': [2, 4]}
  • id: 12183519
    {'degree': 4, 'field': [79, 53, 8, -1, 1], 'lmfdb_label': '286650.mt5', 'torsion': [2, 6]}
  • id: 12183521
    {'degree': 4, 'field': [81, -9, -8, -1, 1], 'lmfdb_label': '286650.mt5', 'torsion': [12]}
  • id: 12183520
    {'degree': 4, 'field': [924, -168, -5, -1, 1], 'lmfdb_label': '286650.mt5', 'torsion': [12]}
  • id: 12183522
    {'degree': 6, 'field': [-2366, -16338, 2220, -25, -75, -3, 1], 'lmfdb_label': '286650.mt5', 'torsion': [12]}
  • id: 12183525
    {'degree': 8, 'field': [5520, -1680, 2026, -720, 431, -88, 34, -4, 1], 'lmfdb_label': '286650.mt5', 'torsion': [8]}
  • id: 12183526
    {'degree': 8, 'field': [6241, 4187, 2177, 582, 38, -114, -7, -1, 1], 'lmfdb_label': '286650.mt5', 'torsion': [2, 12]}
  • id: 12183524
    {'degree': 8, 'field': [81225, 0, -63600, 0, 5830, 0, -160, 0, 1], 'lmfdb_label': '286650.mt5', 'torsion': [8]}
  • id: 12183523
    {'degree': 8, 'field': [1218816, -642528, 214290, -31398, 5569, -232, 80, -2, 1], 'lmfdb_label': '286650.mt5', 'torsion': [2, 4]}
  • id: 12183528
    {'degree': 12, 'field': [-1271299526, -271513914, -79970922, -4480325, 840345, 104826, 180824, 38652, 8880, 260, -162, -3, 1], 'lmfdb_label': '286650.mt5', 'torsion': [2, 12]}
  • id: 12183527
    {'degree': 12, 'field': [386841, -1004094, 1024209, -55410, 66870, -50454, 22741, -5406, 1770, -290, 69, -6, 1], 'lmfdb_label': '286650.mt5', 'torsion': [3, 12]}
  • id: 12183534
    {'degree': 16, 'field': [3600, -4800, -1160, -480, 8816, -6400, 6854, -8704, 4017, -1192, 1022, -184, 153, -40, 22, -4, 1], 'lmfdb_label': '286650.mt5', 'torsion': [24]}
  • id: 12183530
    {'degree': 16, 'field': [13094656, -14383744, 23883952, -21969520, 18944348, -11112280, 6481860, -2745016, 1166681, -360464, 113664, -24464, 5594, -728, 124, -8, 1], 'lmfdb_label': '286650.mt5', 'torsion': [2, 8]}
  • id: 12183531
    {'degree': 16, 'field': [14017536, 0, -92428128, 0, 152195940, 0, -55851588, 0, 7916689, 0, -507992, 0, 15450, 0, -212, 0, 1], 'lmfdb_label': '286650.mt5', 'torsion': [2, 8]}
  • id: 12183532
    {'degree': 16, 'field': [935947476, 764622396, 162959490, -76819494, -5413355, -4975870, -564098, -609936, 906622, -321368, 81478, -13322, 1738, -240, 44, -6, 1], 'lmfdb_label': '286650.mt5', 'torsion': [2, 12]}
  • id: 12183529
    {'degree': 16, 'field': [128935573776, 4511430864, 78927048, 2956262844, 353844817, -65845250, 31370402, 6019362, -811185, 37172, 70532, -5080, -433, 254, 18, -6, 1], 'lmfdb_label': '286650.mt5', 'torsion': [4, 4]}
  • id: 12183533
    {'degree': 16, 'field': [274964945641, 0, -67784995852, 0, 2028449438, 0, 277115316, 0, 2470535, 0, -14244, 0, 4958, 0, 128, 0, 1], 'lmfdb_label': '286650.mt5', 'torsion': [24]}
  • id: 12183535
    {'degree': 18, 'field': [228847246401600, -16471716508800, -57637821628800, -5392553101200, 4669937722800, 350001615600, 353500725180, 314014680, 6454580580, -939852990, 90895140, 13706280, 2220499, -23457, -10521, -1364, 21, 0, 1], 'lmfdb_label': '286650.mt5', '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: 7101728
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '286650.mt5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7101729
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '286650.mt5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 7101730
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '286650.mt5', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7101731
    {'conductor': 286650, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '286650.mt5', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7101732
    {'conductor': 286650, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '286650.mt5', 'prime': 13, '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: 3471183
    {'adelic_gens': [[9099, 7276, 10900, 5379], [2168, 10917, 2643, 86], [1, 12, 12, 145], [15, 106, 9614, 1691], [3119, 10896, 4668, 10631], [1696, 3, 4581, 10834], [10897, 24, 10896, 25], [1, 24, 0, 1], [8649, 10468, 500, 2309], [2737, 24, 3222, 1687], [1, 0, 24, 1]], 'adelic_image': '10920.384.5.?', 'conductor': 286650, 'lmfdb_label': '286650.mt5', 'prime': 0}
  • id: 1017047
    {'conductor': 286650, 'elladic_image': '4.6.0.1', 'lmfdb_label': '286650.mt5', 'modell_image': '2B', 'prime': 2}
  • id: 1017048
    {'conductor': 286650, 'elladic_image': '3.4.0.1', 'lmfdb_label': '286650.mt5', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 286650.mt does not appear in ec_padic