Elliptic curve data - 5610.q6

Formats: - HTML - YAML - JSON - 2024-04-25T13:33:36.804634

• 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': '5610t3', 'Cnumber': 3, 'abc_quality': 1.0021324187035838, 'absD': 1504091705903677440, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 22440, 'ainvs': [1, 0, 1, -780803, -272099842], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 5610, 'degree': 165888, 'elladic_images': ['4.6.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2676402683521167693971868535', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 16, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [-52643812360427830814761, 1504091705903677440], 'lmfdb_iso': '5610.q', 'lmfdb_label': '5610.q6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -780803, -272099842], '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.bs.1.20', '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': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 9, 'sha_primes': [3], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2676402683521167693971868535', 'prec': 100}, 'szpiro_ratio': 6.066284776789004, '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': '0.010723898357382230541088749887', 'prec': 107}, 'conductor': 5610, 'gens': [], 'heights': [], 'lmfdb_label': '5610.q6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.080168336299547611089821090855', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4430300533918569996167796353867365261', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[1023, -512, 1]], 'xcoord_integral_points': [1023]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 0], '3': [3, 1], '5': [1, 0], '11': [3, 0], '17': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '5610.q6'}
• ec_torsion_growth •

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

  
  
  • id: 292217
    {'degree': 2, 'field': [-21, -1, 1], 'lmfdb_label': '5610.q6', 'torsion': [4]}
  • id: 292219
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '5610.q6', 'torsion': [6]}
  • id: 292218
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '5610.q6', 'torsion': [4]}
  • id: 292216
    {'degree': 2, 'field': [234, -1, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 2]}
  • id: 292220
    {'degree': 3, 'field': [-165, 0, 0, 1], 'lmfdb_label': '5610.q6', 'torsion': [6]}
  • id: 292224
    {'degree': 4, 'field': [9, -3, -2, -1, 1], 'lmfdb_label': '5610.q6', 'torsion': [12]}
  • id: 292223
    {'degree': 4, 'field': [441, 21, 22, -1, 1], 'lmfdb_label': '5610.q6', 'torsion': [12]}
  • id: 292221
    {'degree': 4, 'field': [576, 0, -37, 0, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 4]}
  • id: 292222
    {'degree': 4, 'field': [54756, -234, -233, -1, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 6]}
  • id: 292225
    {'degree': 6, 'field': [27556, -498, -489, 323, 6, -3, 1], 'lmfdb_label': '5610.q6', 'torsion': [3, 6]}
  • id: 292227
    {'degree': 6, 'field': [28524, -22608, 1755, -205, -60, -3, 1], 'lmfdb_label': '5610.q6', 'torsion': [12]}
  • id: 292228
    {'degree': 6, 'field': [28572, -2502, -459, 311, 12, -3, 1], 'lmfdb_label': '5610.q6', 'torsion': [12]}
  • id: 292226
    {'degree': 6, 'field': [12955794, -395433, 164475, -1075, 705, -3, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 6]}
  • id: 292230
    {'degree': 8, 'field': [10816, 0, -66016, 0, 6516, 0, 164, 0, 1], 'lmfdb_label': '5610.q6', 'torsion': [8]}
  • id: 292232
    {'degree': 8, 'field': [331776, 0, 21312, 0, 793, 0, 37, 0, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 12]}
  • id: 292231
    {'degree': 8, 'field': [409425, 173460, 38908, -39964, 6077, -28, -52, -4, 1], 'lmfdb_label': '5610.q6', 'torsion': [8]}
  • id: 292229
    {'degree': 8, 'field': [27244000, 11711000, 2110025, 256180, 23426, 2192, 254, -2, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 4]}
  • id: 292235
    {'degree': 12, 'field': [425349376, 123744, 309396, -825050, 309465, 123624, -41109, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '5610.q6', 'torsion': [3, 12]}
  • id: 292234
    {'degree': 12, 'field': [813618576, -644870592, 461062044, -27982200, 156825, -3158307, 136549, 222, 1230, 590, 69, -3, 1], 'lmfdb_label': '5610.q6', 'torsion': [3, 12]}
  • id: 292236
    {'degree': 12, 'field': [1293933276, -873509670, 545433939, -85648530, 12426885, 3206610, -15175, 0, 5835, -660, -111, 0, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 12]}
  • id: 292233
    {'degree': 12, 'field': [657143694736, 4863864, 12159696, -32425850, 12159765, 4863744, -1621149, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '5610.q6', 'torsion': [6, 6]}
  • id: 292241
    {'degree': 16, 'field': [195184161, 163281528, -86866872, -153984048, 82649038, -14246912, 16297004, -8167704, -43217, 1269968, -136364, -61000, 7558, 1176, -148, -8, 1], 'lmfdb_label': '5610.q6', 'torsion': [24]}
  • id: 292242
    {'degree': 16, 'field': [324574272, -859421376, 747239856, -147807792, -25111724, 41235832, 11470316, 2282544, 3113643, 362120, 62492, 2816, -3199, -220, -30, 0, 1], 'lmfdb_label': '5610.q6', 'torsion': [24]}
  • id: 292239
    {'degree': 16, 'field': [142796317456, 0, -26743306304, 0, 4167092296, 0, -19456184, 0, 7486969, 0, -475706, 0, 9343, 0, -110, 0, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 8]}
  • id: 292237
    {'degree': 16, 'field': [391476713761, 0, 0, 0, 41865878146, 0, 0, 0, 15627651, 0, 0, 0, 13666, 0, 0, 0, 1], 'lmfdb_label': '5610.q6', 'torsion': [4, 4]}
  • id: 292238
    {'degree': 16, 'field': [12922702073856, 0, 1686687667200, 0, 94480606656, 0, 3067397040, 0, 70087321, 0, 1245590, 0, 17151, 0, 170, 0, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 8]}
  • id: 292240
    {'degree': 16, 'field': [742235536000000, 319054484000000, 79661999900000, 10751766935000, 813863576625, 51581280500, 4368186750, -328970920, -622803434, -71298698, 3587070, 906652, 45474, -4892, -250, -2, 1], 'lmfdb_label': '5610.q6', 'torsion': [2, 12]}
  • id: 292243
    {'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.q6', '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: 110108
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 36, 'j_denominator_valuation': 36, 'kodaira_symbol': 40, 'lmfdb_label': '5610.q6', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 110109
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '5610.q6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 110110
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5610.q6', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 110111
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5610.q6', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 110112
    {'conductor': 5610, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '5610.q6', '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: 1700606
    {'adelic_gens': [[1, 12, 12, 145], [17769, 21508, 980, 4709], [7936, 3, 21981, 22354], [15, 106, 21134, 13211], [2056, 21, 18075, 22066], [8992, 3, 8517, 22354], [22417, 24, 22416, 25], [1, 24, 0, 1], [5617, 24, 6102, 1687], [1, 0, 24, 1], [3741, 7484, 8, 11253]], 'adelic_image': '22440.384.5.?', 'conductor': 5610, 'lmfdb_label': '5610.q6', 'prime': 0}
  • id: 27674
    {'conductor': 5610, 'elladic_image': '4.6.0.1', 'lmfdb_label': '5610.q6', 'modell_image': '2B', 'prime': 2}
  • id: 27675
    {'conductor': 5610, 'elladic_image': '3.8.0.2', 'lmfdb_label': '5610.q6', 'modell_image': '3B.1.2', 'prime': 3}
• lmfdb_iso 5610.q does not appear in ec_padic