Elliptic curve data - 61710.da4

Formats: - HTML - YAML - JSON - 2024-04-19T02:54:12.102132

• 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': '61710cz', 'Clabel': '61710cz5', 'Cnumber': 5, 'abc_quality': 1.0120982194921988, 'absD': 2552002046892934249779000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 22440, 'ainvs': [1, 0, 0, -300673810, 2005244394572], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 17], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 61710, 'degree': 26542080, 'elladic_images': ['8.12.0.6', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6104289409771925051477681455', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 78, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [1696892787277117093383481, 1440538624914939000], 'lmfdb_iso': '61710.da', 'lmfdb_label': '61710.da4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -2484908, -1506795694], 'min_quad_twist_disc': -11, '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', '8.12.0-4.c.1.5', '12.24.0.g.1', '24.96.0-24.bu.4.28', '33.8.0-3.a.1.2', '66.24.0-6.a.1.2', '132.48.0.?', '264.192.1.?', '1020.48.0.?', '2040.192.1.?', '3740.12.0.?', '7480.24.0.?', '11220.96.0.?', '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': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.4114813045780072331167963565', 'prec': 100}, 'szpiro_ratio': 6.362369185194257, '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, 0, 1, -2, 4, 1, 1, 1, 1, 4, 1], 'aplist': [1, 1, 1, 4, 0, -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': 61710, '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': '61710.da', 'trace_hash': 16648581758393307}
• 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': '0.00073117488800333390052877840135', 'prec': 113}, 'conductor': 61710, 'gens': [], 'heights': [], 'lmfdb_label': '61710.da4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.080664690377710455785118165313', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.7117865607927292247927618538119005103', 'prec': 130}, 'tamagawa_product': 108, 'torsion_generators': [[40927, -40927, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 0], '3': [7, 0], '5': [1, 0], '11': 'a', '17': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '61710.da4'}
• ec_torsion_growth •

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

  
  
  • id: 2956206
    {'degree': 2, 'field': [-935, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [4]}
  • id: 2956204
    {'degree': 2, 'field': [-510, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 2]}
  • id: 2956205
    {'degree': 2, 'field': [-66, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [4]}
  • id: 2956207
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '61710.da4', 'torsion': [6]}
  • id: 2956211
    {'degree': 4, 'field': [15, -18, 19, -2, 1], 'lmfdb_label': '61710.da4', 'torsion': [12]}
  • id: 2956212
    {'degree': 4, 'field': [6809, -176, 177, -2, 1], 'lmfdb_label': '61710.da4', 'torsion': [12]}
  • id: 2956208
    {'degree': 4, 'field': [12321, 0, -288, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 4]}
  • id: 2956209
    {'degree': 4, 'field': [12750, 0, -288, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [8]}
  • id: 2956210
    {'degree': 4, 'field': [262659, 1014, -1013, -2, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 6]}
  • id: 2956213
    {'degree': 6, 'field': [-96, -24, -80, -48, 1, -3, 1], 'lmfdb_label': '61710.da4', 'torsion': [6]}
  • id: 2956216
    {'degree': 8, 'field': [1461681, 0, -382212, 0, 24024, 0, -468, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 8]}
  • id: 2956217
    {'degree': 8, 'field': [33604465, -2268680, 2315614, -94244, 48063, -1132, 382, -4, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 12]}
  • id: 2956218
    {'degree': 8, 'field': [58522500, 0, -2607120, 0, 32604, 0, -24, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [24]}
  • id: 2956214
    {'degree': 8, 'field': [70459236, 0, 11247984, 0, 636, 0, 264, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 4]}
  • id: 2956215
    {'degree': 8, 'field': [337089600, 0, 0, 0, 28305, 0, 0, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [8]}
  • id: 2956219
    {'degree': 12, 'field': [576, -1800, 1563, 975, 676, 279, 275, -264, 9, 21, -4, -3, 1], 'lmfdb_label': '61710.da4', 'torsion': [3, 6]}
  • id: 2956221
    {'degree': 12, 'field': [24688, 113952, 1808, -22560, -3336, 11520, -128, 144, 87, -42, -1, -6, 1], 'lmfdb_label': '61710.da4', 'torsion': [12]}
  • id: 2956222
    {'degree': 12, 'field': [174293524, -2297632, 7351377, -9579260, 3485485, 1519188, -430739, -63546, 14265, 1070, -203, -6, 1], 'lmfdb_label': '61710.da4', 'torsion': [12]}
  • id: 2956220
    {'degree': 12, 'field': [20631307104, 1412137728, -1300046628, -220489080, 101066590, 10860348, -3365959, -215526, 50985, 1920, -373, -6, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 6]}
  • id: 2956227
    {'degree': 16, 'field': [86769225, 0, -45943200, 0, 13452030, 0, -493260, 0, 726271, 0, 110044, 0, 5646, 0, 124, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [24]}
  • id: 2956224
    {'degree': 16, 'field': [11019960576, 0, 0, 0, 1180035216, 0, 0, 0, 102252456, 0, 0, 0, 11241, 0, 0, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 8]}
  • id: 2956228
    {'degree': 16, 'field': [45832846373721, -4369077143640, 4527675917568, -317764519416, 160293778212, -1677787656, 534087936, 18460272, -675515, -2691848, 603868, -35768, 6022, -56, 28, -8, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 24]}
  • id: 2956226
    {'degree': 16, 'field': [26849955613991625, 162255333555000, -168925150840500, 13317943618800, -6603655944954, -69426378120, 28219734072, -4349490216, 1083583879, 3081496, -1172336, 303688, -50918, 112, 4, -8, 1], 'lmfdb_label': '61710.da4', 'torsion': [2, 12]}
  • id: 2956223
    {'degree': 16, 'field': [36679114064162241, 0, 0, 0, 11791327020876, 0, 0, 0, 2704199526, 0, 0, 0, -46644, 0, 0, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [4, 4]}
  • id: 2956225
    {'degree': 16, 'field': [1279164393002250000, 0, -12991909687200000, 0, -271540165572000, 0, 2212204600800, 0, -4209590490, 0, -125733360, 0, 1399368, 0, -3792, 0, 1], 'lmfdb_label': '61710.da4', 'torsion': [16]}
  • id: 2956229
    {'degree': 18, 'field': [3464130517904925, -665682049234125, 48402025573275, 105944287882950, -3281859555975, -3237557521275, 284247442902, 9788271903, -11795885208, 708559045, 318410286, -14743161, -4905988, 98607, 48945, 122, -315, -3, 1], 'lmfdb_label': '61710.da4', '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: 1487562
    {'conductor': 61710, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '61710.da4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1487563
    {'conductor': 61710, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '61710.da4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1487564
    {'conductor': 61710, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '61710.da4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1487565
    {'conductor': 61710, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '61710.da4', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1487566
    {'conductor': 61710, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '61710.da4', '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: 2072985
    {'adelic_gens': [[7936, 21, 12915, 22066], [1, 12, 12, 145], [4079, 22416, 4068, 22151], [5614, 3, 5655, 34], [8992, 21, 22155, 22066], [16, 11223, 3281, 7394], [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': 61710, 'lmfdb_label': '61710.da4', 'prime': 0}
  • id: 259918
    {'conductor': 61710, 'elladic_image': '8.12.0.6', 'lmfdb_label': '61710.da4', 'modell_image': '2B', 'prime': 2}
  • id: 259919
    {'conductor': 61710, 'elladic_image': '3.4.0.1', 'lmfdb_label': '61710.da4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 61710.da does not appear in ec_padic