Elliptic curve data - 5610.q8

Formats: - HTML - YAML - JSON - 2024-04-24T21:58:23.429422

• 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': '5610t1', 'Cnumber': 1, 'abc_quality': 0.9924532397274934, 'absD': 6156756739584000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 22440, 'ainvs': [1, 0, 1, 43372, -1467502], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 5610, 'degree': 55296, 'elladic_images': ['4.6.0.1', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7183341240180619236995642351', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [9023321954633914439, 6156756739584000], 'lmfdb_iso': '5610.q', 'lmfdb_label': '5610.q8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 43372, -1467502], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '4.6.0.c.1', '6.24.0-6.a.1.4', '12.48.0-12.g.1.12', '24.96.0-24.bs.2.8', '44.12.0-4.c.1.2', '132.96.0.?', '264.192.1.?', '340.12.0.?', '1020.96.0.?', '1870.6.0.?', '2040.192.1.?', '3740.24.0.?', '5610.48.0.?', '11220.192.1.?', '22440.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.7183341240180619236995642351', 'prec': 100}, 'szpiro_ratio': 5.056162772186148, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
• 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': '0.032171695072146691623266249659', 'prec': 107}, 'conductor': 5610, 'gens': [], 'heights': [], 'lmfdb_label': '5610.q8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.24050500889864283326946327256', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4430300533918569996167796353867365261', 'prec': 130}, 'tamagawa_product': 216, 'torsion_generators': [[609, 15535, 1]], 'xcoord_integral_points': [33, 114, 609]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [3, 0], '5': [1, 0], '11': [3, 0], '17': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '5610.q8'}
• ec_torsion_growth •

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

  
  
  • id: 292190
    {'degree': 2, 'field': [-21, -1, 1], 'lmfdb_label': '5610.q8', 'torsion': [12]}
  • id: 292191
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '5610.q8', 'torsion': [12]}
  • id: 292189
    {'degree': 2, 'field': [234, -1, 1], 'lmfdb_label': '5610.q8', 'torsion': [2, 6]}
  • id: 292192
    {'degree': 4, 'field': [576, 0, -37, 0, 1], 'lmfdb_label': '5610.q8', 'torsion': [2, 12]}
  • id: 292193
    {'degree': 6, 'field': [12, 0, -11, 0, 1, 0, 1], 'lmfdb_label': '5610.q8', 'torsion': [3, 6]}
  • id: 292195
    {'degree': 8, 'field': [10816, 0, -66016, 0, 6516, 0, 164, 0, 1], 'lmfdb_label': '5610.q8', 'torsion': [24]}
  • id: 292196
    {'degree': 8, 'field': [409425, 173460, 38908, -39964, 6077, -28, -52, -4, 1], 'lmfdb_label': '5610.q8', 'torsion': [24]}
  • id: 292194
    {'degree': 8, 'field': [27244000, 11711000, 2110025, 256180, 23426, 2192, 254, -2, 1], 'lmfdb_label': '5610.q8', 'torsion': [2, 12]}
  • id: 292197
    {'degree': 9, 'field': [57930120, 558900, 479790, -444153, -65952, 10881, 761, -168, -3, 1], 'lmfdb_label': '5610.q8', 'torsion': [18]}
  • id: 292199
    {'degree': 12, 'field': [81, -540, 3222, -1944, -192, -846, 958, -236, 122, -56, 8, -2, 1], 'lmfdb_label': '5610.q8', 'torsion': [3, 12]}
  • id: 292200
    {'degree': 12, 'field': [576, -1800, 1563, 975, 676, 279, 275, -264, 9, 21, -4, -3, 1], 'lmfdb_label': '5610.q8', 'torsion': [3, 12]}
  • id: 292198
    {'degree': 12, 'field': [2176782336, 288334080, 16357392, 23700816, 1783788, -148236, 157273, 8944, -898, 454, 8, -2, 1], 'lmfdb_label': '5610.q8', 'torsion': [6, 6]}
  • id: 292202
    {'degree': 16, 'field': [142796317456, 0, -26743306304, 0, 4167092296, 0, -19456184, 0, 7486969, 0, -475706, 0, 9343, 0, -110, 0, 1], 'lmfdb_label': '5610.q8', 'torsion': [2, 24]}
  • id: 292201
    {'degree': 16, 'field': [391476713761, 0, 0, 0, 41865878146, 0, 0, 0, 15627651, 0, 0, 0, 13666, 0, 0, 0, 1], 'lmfdb_label': '5610.q8', 'torsion': [4, 12]}
  • id: 292203
    {'degree': 16, 'field': [12922702073856, 0, 1686687667200, 0, 94480606656, 0, 3067397040, 0, 70087321, 0, 1245590, 0, 17151, 0, 170, 0, 1], 'lmfdb_label': '5610.q8', 'torsion': [2, 24]}
  • id: 292205
    {'degree': 18, 'field': [433473221080629, 2126074485097107, -293777633534949, -71035257028842, 1409996532465, 4583844052677, 290626953006, -182826483777, -9849314736, 1225619845, 534993126, -3595257, -12193756, -1473, 113745, 698, -531, -3, 1], 'lmfdb_label': '5610.q8', 'torsion': [36]}
  • id: 292206
    {'degree': 18, 'field': [3464130517904925, -665682049234125, 48402025573275, 105944287882950, -3281859555975, -3237557521275, 284247442902, 9788271903, -11795885208, 708559045, 318410286, -14743161, -4905988, 98607, 48945, 122, -315, -3, 1], 'lmfdb_label': '5610.q8', 'torsion': [36]}
  • id: 292204
    {'degree': 18, 'field': [2137957722225462465, -819395290141939845, 180839480430149595, -26531994492988560, 2935406751109470, -371719776501225, 44713306671759, -4698003980583, 386116698933, -24449819010, 3711632535, -221487228, 18557896, -308976, 83895, -8135, -102, -6, 1], 'lmfdb_label': '5610.q8', 'torsion': [2, 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: 110098
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '5610.q8', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 110099
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '5610.q8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 110100
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5610.q8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 110101
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5610.q8', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 110102
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5610.q8', '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: 1700608
    {'adelic_gens': [[7936, 21, 12915, 22066], [1, 12, 12, 145], [11221, 24, 14972, 18989], [17769, 21508, 980, 4709], [8992, 21, 22155, 22066], [15, 106, 21134, 13211], [2056, 3, 9741, 22354], [1, 24, 0, 1], [22417, 24, 22416, 25], [5617, 24, 5514, 22111], [1, 0, 24, 1]], 'adelic_image': '22440.384.5.?', 'conductor': 5610, 'lmfdb_label': '5610.q8', 'prime': 0}
  • id: 27678
    {'conductor': 5610, 'elladic_image': '4.6.0.1', 'lmfdb_label': '5610.q8', 'modell_image': '2B', 'prime': 2}
  • id: 27679
    {'conductor': 5610, 'elladic_image': '3.8.0.1', 'lmfdb_label': '5610.q8', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 5610.q does not appear in ec_padic