Elliptic curve data - 5610.q1

Formats: - HTML - YAML - JSON - 2024-04-25T11:50:38.850645

• 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': '5610t', 'Clabel': '5610t7', 'Cnumber': 7, 'abc_quality': 1.0433108113473337, 'absD': 552431869440, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 22440, 'ainvs': [1, 0, 1, -201236483, -1098790303234], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 5610, 'degree': 663552, 'elladic_images': ['4.6.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9607874489120620788144189750', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [901247067798311192691198986281, 552431869440], 'lmfdb_iso': '5610.q', 'lmfdb_label': '5610.q1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -201236483, -1098790303234], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.2'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '12.48.0-12.g.1.10', '24.96.0-24.bu.3.12', '88.12.0.?', '264.192.1.?', '340.12.0.?', '1020.96.0.?', '2040.192.1.?', '7480.24.0.?', '22440.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 36, 'sha_primes': [2, 3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.9607874489120620788144189750', 'prec': 100}, 'szpiro_ratio': 7.990168207406159, '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, 1, 1, 1, -1, -4, -1, 1, -1, 1, 1, 2, 4, 1, 1, -1, -1, -4, 1], 'aplist': [-1, 1, 1, -4, 1, 2, -1, -4, 0, -6, 8, -10, 6, -4, 12, 6, 12, 2, 8, -12, 2, 8, -12, -6, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 5610, 'isogeny_matrix': [[1, 4, 2, 3, 12, 4, 6, 12], [4, 1, 2, 12, 3, 4, 6, 12], [2, 2, 1, 6, 6, 2, 3, 6], [3, 12, 6, 1, 4, 12, 2, 4], [12, 3, 6, 4, 1, 12, 2, 4], [4, 4, 2, 12, 12, 1, 6, 3], [6, 6, 3, 2, 2, 6, 1, 2], [12, 12, 6, 4, 4, 3, 2, 1]], 'lmfdb_iso': '5610.q', 'trace_hash': 862212701844303008}
• 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': '0.0026809745893455576352721874716', 'prec': 110}, 'conductor': 5610, 'gens': [], 'heights': [], 'lmfdb_label': '5610.q1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.040084168149773805544910545427', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '36.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4430300533918569996167796353867365261', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-32761, 32757, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 1], '3': [3, 1], '5': [1, 0], '11': [3, 0], '17': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '5610.q1'}
• ec_torsion_growth •

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

  
  
  • id: 292297
    {'degree': 2, 'field': [-510, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 2]}
  • id: 292300
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '5610.q1', 'torsion': [6]}
  • id: 292299
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [4]}
  • id: 292298
    {'degree': 2, 'field': [85, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [4]}
  • id: 292301
    {'degree': 3, 'field': [-165, 0, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [6]}
  • id: 292305
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [12]}
  • id: 292302
    {'degree': 4, 'field': [6241, 0, 182, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 4]}
  • id: 292304
    {'degree': 4, 'field': [7225, 0, -85, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [12]}
  • id: 292303
    {'degree': 4, 'field': [28900, 0, -170, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 6]}
  • id: 292307
    {'degree': 6, 'field': [-132623775, -504900, 780300, -330, -1530, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 6]}
  • id: 292309
    {'degree': 6, 'field': [27441, 5940, 108, -330, 18, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [12]}
  • id: 292306
    {'degree': 6, 'field': [27556, -498, -489, 323, 6, -3, 1], 'lmfdb_label': '5610.q1', 'torsion': [3, 6]}
  • id: 292308
    {'degree': 6, 'field': [641350, 84150, 21675, -330, 255, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [12]}
  • id: 292311
    {'degree': 8, 'field': [1503076, 0, -221224, 0, 13901, 0, -214, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [8]}
  • id: 292313
    {'degree': 8, 'field': [3418801, 0, -155316, 0, 5207, 0, -84, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 12]}
  • id: 292312
    {'degree': 8, 'field': [58522500, 0, -2607120, 0, 32604, 0, -24, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [8]}
  • id: 292310
    {'degree': 8, 'field': [161645796, 0, -918864, 0, -25284, 0, -24, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 4]}
  • id: 292316
    {'degree': 12, 'field': [740765089, 53889660, 3593796, -17939460, -489954, 27720, 163406, 0, 24, -660, 6, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [3, 12]}
  • id: 292317
    {'degree': 12, 'field': [315184891096, 132443855280, 29069483676, 2490617580, 692436345, 16635960, 13007090, 0, 118095, -660, 546, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 12]}
  • id: 292315
    {'degree': 12, 'field': [411329822500, -53969602500, -6820038750, -2247242250, 334030875, 50069250, -4135525, 0, 43350, -660, -255, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [3, 12]}
  • id: 292314
    {'degree': 12, 'field': [24405823050625, -831439867500, -399992617500, -17852158500, 5052914250, 200277000, -34227650, 0, 173400, -660, -510, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [6, 6]}
  • id: 292320
    {'degree': 16, 'field': [279056651665, 44175752720, -39483558780, -9097592120, 3847432506, 798351528, -195362600, -57924320, 11191731, 2017640, -231224, -90240, 11946, 1400, -180, -8, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 8]}
  • id: 292319
    {'degree': 16, 'field': [45832846373721, -4369077143640, 4527675917568, -317764519416, 160293778212, -1677787656, 534087936, 18460272, -675515, -2691848, 603868, -35768, 6022, -56, 28, -8, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 8]}
  • id: 292322
    {'degree': 16, 'field': [46569173353921, 0, -4998057147596, 0, 274643551250, 0, -9387036924, 0, 229102259, 0, -3872724, 0, 43370, 0, -296, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [24]}
  • id: 292323
    {'degree': 16, 'field': [277102632960000, 0, -17930170368000, 0, 734605632000, 0, -18748350720, 0, 352614276, 0, -4595184, 0, 44130, 0, -264, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [24]}
  • id: 292321
    {'degree': 16, 'field': [26443155585882256, 0, -49702495944512, 0, -8203568279360, 0, 6494339488, 0, 980985304, 0, -102128, 0, -50960, 0, -8, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [2, 12]}
  • id: 292318
    {'degree': 16, 'field': [26501261636310561, 0, 0, 0, -8109395808084, 0, 0, 0, 989604486, 0, 0, 0, -50964, 0, 0, 0, 1], 'lmfdb_label': '5610.q1', 'torsion': [4, 4]}
  • id: 292324
    {'degree': 18, 'field': [747377296875, 0, 0, -103438665000, 0, 0, 4402836075, 0, 0, -19675920, 0, 0, 165289, 0, 0, -712, 0, 0, 1], 'lmfdb_label': '5610.q1', '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: 110128
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '5610.q1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 110129
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5610.q1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 110130
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5610.q1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 110131
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '5610.q1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 110132
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5610.q1', '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: 1700601
    {'adelic_gens': [[7936, 21, 12915, 22066], [1, 12, 12, 145], [18361, 24, 18372, 289], [5614, 3, 5655, 34], [8992, 21, 22155, 22066], [14976, 18719, 10265, 21306], [15, 106, 21134, 13211], [22417, 24, 22416, 25], [1, 24, 0, 1], [17766, 21529, 12155, 15896], [1, 0, 24, 1]], 'adelic_image': '22440.384.5.?', 'conductor': 5610, 'lmfdb_label': '5610.q1', 'prime': 0}
  • id: 27664
    {'conductor': 5610, 'elladic_image': '4.6.0.1', 'lmfdb_label': '5610.q1', 'modell_image': '2B', 'prime': 2}
  • id: 27665
    {'conductor': 5610, 'elladic_image': '3.8.0.2', 'lmfdb_label': '5610.q1', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 5610.q does not appear in ec_padic