Elliptic curve data - 4410.z1

Formats: - HTML - YAML - JSON - 2026-02-23T12:37:06.173907

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

  
  {'Ciso': '4410bb', 'Clabel': '4410bb7', 'Cnumber': 7, 'abc_quality': 1.0818126452233845, 'absD': 6947055801000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 840, 'ainvs': [1, -1, 1, -2352083, -1387851573], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 4410, 'degree': 55296, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0864272040780631785395413117', 'prec': 100}, 'faltings_index': 6, 'faltings_ratio': 12, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [16778985534208729, 81000], 'lmfdb_iso': '4410.z', 'lmfdb_label': '4410.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -5334, -150368], 'min_quad_twist_disc': 21, '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', '12.24.0.g.1', '21.8.0-3.a.1.1', '24.96.1.dj.3', '40.12.0.v.1', '42.24.0-6.a.1.3', '56.12.0-4.c.1.5', '60.48.0.c.3', '84.48.0.?', '120.192.5.?', '168.192.1.?', '280.24.0.?', '420.96.0.?', '840.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 2205], [3, 8, 49], [5, 6, 882], [7, 26, 90]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.56416598521635168028924232152', 'prec': 103}, 'szpiro_ratio': 6.6287525156399, '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, -1, 0, 0, 1, 0, -1, 0, 0, -2, 0, 0, 1, 6, 0, 4, -1], 'aplist': [1, 0, -1, 0, 0, -2, 6, 4, 0, 6, -8, 2, -6, -4, 0, 6, 0, 10, -4, 0, -2, 8, 12, 18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 4410, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '4410.z', 'trace_hash': 42315228074103430}
• 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': '0.015408215956501267424569445105', 'prec': 107}, 'conductor': 4410, 'gens': [], 'heights': [], 'lmfdb_label': '4410.z1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.12190917955198110120337250196', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9258203092475464288809400470542944029', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[-3541, 3537, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 1], '3': 'a', '5': [0, 0], '7': 'a'}, 'iwp0': 5, 'lmfdb_label': '4410.z1'}
• ec_torsion_growth •

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

  
  
  • id: 230280
    {'degree': 2, 'field': [-10, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [2, 2]}
  • id: 230283
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '4410.z1', 'torsion': [6]}
  • id: 230282
    {'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [4]}
  • id: 230281
    {'degree': 2, 'field': [105, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [4]}
  • id: 230287
    {'degree': 4, 'field': [58, 8, -7, -2, 1], 'lmfdb_label': '4410.z1', 'torsion': [12]}
  • id: 230285
    {'degree': 4, 'field': [134, 16, -15, -2, 1], 'lmfdb_label': '4410.z1', 'torsion': [2, 6]}
  • id: 230284
    {'degree': 4, 'field': [169, 0, 16, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [2, 4]}
  • id: 230286
    {'degree': 4, 'field': [274, 26, -25, -2, 1], 'lmfdb_label': '4410.z1', 'torsion': [12]}
  • id: 230288
    {'degree': 6, 'field': [-3, 0, 0, -18, 0, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [6]}
  • id: 230289
    {'degree': 8, 'field': [-16224, 24960, -6368, -1280, 724, -80, -52, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [2, 4]}
  • id: 230292
    {'degree': 8, 'field': [394, -284, 334, -92, 27, 20, -2, -4, 1], 'lmfdb_label': '4410.z1', 'torsion': [2, 12]}
  • id: 230291
    {'degree': 8, 'field': [718, 40, 28, -128, 45, 20, -2, -4, 1], 'lmfdb_label': '4410.z1', 'torsion': [24]}
  • id: 230290
    {'degree': 8, 'field': [2661, 2112, -785, -458, 284, 28, -25, -2, 1], 'lmfdb_label': '4410.z1', 'torsion': [8]}
  • id: 230293
    {'degree': 12, 'field': [576, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [3, 6]}
  • id: 230296
    {'degree': 12, 'field': [2713, 1080, 3720, 2412, 2364, 864, 478, 0, 60, -36, 12, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [12]}
  • id: 230295
    {'degree': 12, 'field': [56884, 65880, 40800, 36108, 14685, 5400, 2818, 0, 375, -36, 30, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [12]}
  • id: 230294
    {'degree': 12, 'field': [670009, 1083240, -511800, -287892, 139380, 21600, -19682, 0, 1500, -36, -60, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [2, 6]}
  • id: 230301
    {'degree': 16, 'field': [11236, 0, 1844, 0, 1865, 0, 1596, 0, 344, 0, -234, 0, 140, 0, -16, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [24]}
  • id: 230299
    {'degree': 16, 'field': [761434, -155992, 307252, -298072, 146330, -18592, 37752, -18328, -4213, 2776, 2208, -1112, -118, 112, 4, -8, 1], 'lmfdb_label': '4410.z1', 'torsion': [2, 24]}
  • id: 230297
    {'degree': 16, 'field': [1028196, 3163680, 4867200, 2808000, 1000684, 350560, 176000, 8640, -10659, 12440, 800, -1360, 314, -40, 0, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [4, 4]}
  • id: 230300
    {'degree': 16, 'field': [2702176, 2268736, -1396624, -1603056, 450058, 417536, -131376, -9008, 7023, -6224, 4536, -2128, 658, -168, 44, -8, 1], 'lmfdb_label': '4410.z1', 'torsion': [2, 12]}
  • id: 230298
    {'degree': 16, 'field': [14561856, 0, -12434112, 0, 5363200, 0, -1105752, 0, 163209, 0, -16328, 0, 1110, 0, -48, 0, 1], 'lmfdb_label': '4410.z1', 'torsion': [2, 8]}
  • id: 230302
    {'degree': 18, 'field': [6416, -57216, 196440, -391852, 670104, -832416, 737272, -482226, 243258, -91671, 24507, -3798, 578, -396, 336, -160, 48, -9, 1], 'lmfdb_label': '4410.z1', '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: 83710
    {'conductor': 4410, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '4410.z1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 83711
    {'conductor': 4410, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '4410.z1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 83712
    {'conductor': 4410, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '4410.z1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 83713
    {'conductor': 4410, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4410.z1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1692709
    {'adelic_gens': [[162, 679, 77, 92], [699, 196, 112, 27], [1, 12, 12, 145], [631, 504, 630, 1], [15, 106, 374, 11], [232, 483, 357, 274], [817, 24, 816, 25], [599, 0, 0, 839], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '840.384.5.?', 'conductor': 4410, 'lmfdb_label': '4410.z1', 'prime': 0}
  • id: 21963
    {'conductor': 4410, 'elladic_image': '4.6.0.1', 'lmfdb_label': '4410.z1', 'modell_image': '2B', 'prime': 2}
  • id: 21964
    {'conductor': 4410, 'elladic_image': '3.4.0.1', 'lmfdb_label': '4410.z1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 4410.z does not appear in ec_padic