Elliptic curve data - 4400.t2

Formats: - HTML - YAML - JSON - 2026-04-20T07:00:40.834560

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '4400r', 'Clabel': '4400r2', 'Cnumber': 2, 'abc_quality': 0.922044169862911, 'absD': 21296000000000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 1320, 'ainvs': [0, 1, 0, 3592, 207188], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 4400, 'degree': 6912, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2400668105150659075679546843', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 19, 'isogeny_degrees': [1, 3], 'jinv': [80062991, 332750], 'lmfdb_iso': '4400.t', 'lmfdb_label': '4400.t2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 9, -25], 'min_quad_twist_disc': -20, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '60.8.0-3.a.1.1', '264.8.0.?', '440.2.0.?', '1320.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.35587172810188514004348279168', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 275], [3, 2, 400], [5, 18, 176], [11, 12, 400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.25779932626192958914965710377', 'prec': 107}, 'szpiro_ratio': 4.528869824519498, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 1, 0, 0, 0, -1, 0, -2, 0, 1, 0, -2, 0, 0, 0, 3, 0, 1, 0], 'aplist': [0, 1, 0, -1, 1, -2, 3, 1, 6, -9, -5, -5, -6, 8, 6, -9, -6, 5, 8, 9, 10, -14, -6, -15, -8], 'class_deg': 3, 'class_size': 2, 'conductor': 4400, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '4400.t', 'trace_hash': 1120270579722552823}
• 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': '0.083732036483692517600313471047', 'prec': 107}, 'conductor': 4400, 'gens': [[188, 2750, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.35587172810188514004348279168', 'prec': 103}], 'lmfdb_label': '4400.t2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.48607716552816537453890757949', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1515469012969828301289089312574636520', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': [23, 188]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': 'a', '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4400.t2'}
• ec_torsion_growth •

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

  
  
  • id: 228881
    {'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '4400.t2', 'torsion': [3]}
  • id: 228882
    {'degree': 3, 'field': [-8, 2, 0, 1], 'lmfdb_label': '4400.t2', 'torsion': [2]}
  • id: 228885
    {'degree': 6, 'field': [-11, 88, 49, -16, -11, 0, 1], 'lmfdb_label': '4400.t2', 'torsion': [6]}
  • id: 228883
    {'degree': 6, 'field': [16, -32, 118, 16, -7, -2, 1], 'lmfdb_label': '4400.t2', 'torsion': [2, 2]}
  • id: 228884
    {'degree': 6, 'field': [54, 0, 0, -14, 0, 0, 1], 'lmfdb_label': '4400.t2', 'torsion': [3]}
  • id: 228886
    {'degree': 12, 'field': [-146, -630, -775, 7, 393, 48, -252, -228, -174, -46, -7, -1, 1], 'lmfdb_label': '4400.t2', 'torsion': [4]}
  • id: 228887
    {'degree': 12, 'field': [2809, -6360, 6549, -3960, 1968, -912, 355, -66, 6, -18, 15, -6, 1], 'lmfdb_label': '4400.t2', 'torsion': [3, 3]}
  • id: 228888
    {'degree': 12, 'field': [15625, 0, -11250, 0, 4275, 0, 700, 0, 171, 0, -18, 0, 1], 'lmfdb_label': '4400.t2', 'torsion': [2, 6]}
  • id: 228890
    {'degree': 18, 'field': [64, 0, 0, -768, 0, 0, 2384, 0, 0, 896, 0, 0, 374, 0, 0, -30, 0, 0, 1], 'lmfdb_label': '4400.t2', 'torsion': [6]}
  • id: 228889
    {'degree': 18, 'field': [134094240, 332739360, -375047280, 553808880, 212040000, -149344560, 25577556, 37417680, -4342464, -2752260, 1111800, 211140, -73910, -2760, 4050, -50, -114, 0, 1], 'lmfdb_label': '4400.t2', 'torsion': [9]}
• 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: 83226
    {'conductor': 4400, 'conductor_valuation': 4, 'discriminant_valuation': 13, 'j_denominator_valuation': 1, 'kodaira_symbol': -9, 'lmfdb_label': '4400.t2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 83227
    {'conductor': 4400, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '4400.t2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 83228
    {'conductor': 4400, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '4400.t2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1692570
    {'adelic_gens': [[4, 3, 9, 7], [329, 1314, 0, 1319], [1315, 6, 1314, 7], [661, 6, 663, 19], [1201, 6, 963, 19], [263, 1314, 789, 1301], [1, 6, 0, 1], [3, 4, 8, 11], [938, 387, 175, 667], [1, 0, 6, 1]], 'adelic_image': '1320.16.0.?', 'conductor': 4400, 'lmfdb_label': '4400.t2', 'prime': 0}
  • id: 21816
    {'conductor': 4400, 'elladic_image': '3.4.0.1', 'lmfdb_label': '4400.t2', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 156588
    {'lmfdb_iso': '4400.t', 'p': 7, 'prec': 20, 'unit': 7132387163686668, 'val': 1}
  • id: 156592
    {'lmfdb_iso': '4400.t', 'p': 13, 'prec': 20, 'unit': 736216123792016647447, 'val': 1}
  • id: 156594
    {'lmfdb_iso': '4400.t', 'p': 17, 'prec': 20, 'unit': 113246817860100728658706, 'val': 1}
  • id: 156595
    {'lmfdb_iso': '4400.t', 'p': 19, 'prec': 20, 'unit': 4659252997871618406731112, 'val': -1}
  • id: 156599
    {'lmfdb_iso': '4400.t', 'p': 23, 'prec': 20, 'unit': 56678800107451040112624425, 'val': 1}
  • id: 156591
    {'lmfdb_iso': '4400.t', 'p': 29, 'prec': 20, 'unit': 1977298914707462777682383127, 'val': 1}
  • id: 156604
    {'lmfdb_iso': '4400.t', 'p': 31, 'prec': 20, 'unit': 503210537363996667803718062, 'val': 1}
  • id: 156587
    {'lmfdb_iso': '4400.t', 'p': 37, 'prec': 20, 'unit': 259596196766969597073596842267, 'val': 1}
  • id: 156589
    {'lmfdb_iso': '4400.t', 'p': 41, 'prec': 20, 'unit': 3792355310840067235588888742767, 'val': 1}
  • id: 156590
    {'lmfdb_iso': '4400.t', 'p': 43, 'prec': 20, 'unit': 5297477744387151971604698168773, 'val': 1}
  • id: 156602
    {'lmfdb_iso': '4400.t', 'p': 47, 'prec': 20, 'unit': 1659293900447255783324256476514, 'val': 1}
  • id: 156596
    {'lmfdb_iso': '4400.t', 'p': 53, 'prec': 20, 'unit': 278246869194124431418577083514275, 'val': 1}
  • id: 156597
    {'lmfdb_iso': '4400.t', 'p': 59, 'prec': 20, 'unit': 2928329315140566426322176053854395, 'val': 1}
  • id: 156603
    {'lmfdb_iso': '4400.t', 'p': 61, 'prec': 20, 'unit': 6754709561916257157011027220491953, 'val': 1}
  • id: 156586
    {'lmfdb_iso': '4400.t', 'p': 67, 'prec': 20, 'unit': 20382245607686688657679924413630154, 'val': 1}
  • id: 156601
    {'lmfdb_iso': '4400.t', 'p': 71, 'prec': 20, 'unit': 126351936580110174211725977754215968, 'val': 1}
  • id: 156598
    {'lmfdb_iso': '4400.t', 'p': 73, 'prec': 20, 'unit': 214001516561318590077463501098405592, 'val': 1}
  • id: 156593
    {'lmfdb_iso': '4400.t', 'p': 79, 'prec': 20, 'unit': 777476946550085127318863855399770743, 'val': 1}
  • id: 156585
    {'lmfdb_iso': '4400.t', 'p': 83, 'prec': 20, 'unit': 1244719486374950081890754147929431783, 'val': 1}
  • id: 156600
    {'lmfdb_iso': '4400.t', 'p': 89, 'prec': 20, 'unit': 2651377908916918900789615956585921701, 'val': 1}
  • id: 156584
    {'lmfdb_iso': '4400.t', 'p': 97, 'prec': 20, 'unit': 14220957280979894224529068126734053800, 'val': 1}