curve #721

y² = x³ + x² − 11712365221079813568905560558013055583385x + 483221095808553401511844197015832928474710876829023872739275

a-invariants: [0, 1, 0, -11712365221079813568905560558013055583385, 483221095808553401511844197015832928474710876829023872739275]
c-invariants: [562193530611831051307466906784626668002496, -417503026778590138909606547405350636509994999020984386054748544]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 226231950703081720025074686186875147270240368051924923100481452322141455102539095243936195677320
discriminant (Δ): 1955434162767713080267659121454020873333901774117793087706921082220154461899988364291832701212799633550021023109748000000
Faltings height: 21.8964
naive height: 288.3980
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 73, 109, 17615983211, 384462236833, 3082378345805842342494593, 30662811114709101360572400566528284523
regulator: 209992225096295304688242551.5627993293182316885877456622897175078526859110141085531282113
submitted by: FNacc
submitted at: 2026-09-12 11:41:00 UTC
last updated: 2026-09-12 11:41:00 UTC

Witness: 25 independent points log in to add more points →

(56054278831334869455, 53104239915546911014401451050)
(-41676061813687736945, 948134719168099041696260135850)
(-716722043511932813434415/7744, -599709467527487784941414243175621945/681472)
(1796356194058450920176777461/65723449, -228253746775420690308947559752247249172890/532820001043)
(-39063076295044117925, -938687823054794921990059833270)
(3527063536513071847705/16, 187832753674578490150024706612475/64)
(77774139184496355685, -206744980266680667671959192170)
(1128889820945277850075, 37761219062842233536025204733770)
(-62959444240336195755/4, 6517288531231942952910243446625/8)
(875140989967771986445/9, 13866012401192784829501965810350/27)
(49362716067340277035, -159210452638748404309716065430)
(49489553275802483183862739/26265625, 91412828175303316348055365531037437648638/134611328125)
(31520170500751656797455/361, -2436835122181495586722425103649250/6859)
(172666769065613420815, 1899668292966336193191091786410)
(251191942155941599765, -3659334054295334220453175495110)
(5703180445919590736995/49, -286308041285212395027201666379050/343)
(3390526722649087192525/49, -21921209849482686127544441339310/343)
(705379628994442030405, 18525402625288653677018547861750)
(849793832077262057839, 24580650210661485317930414753430)
(56906512658878313845, 31535831664502625934791884710)
(86711796818730083755, 345834191276965040967718943850)
(426108823108213692895, 8535837183238864351481338086090)
(1473570229151536294143925/5041, -1680191871447975149752707348138939930/357911)
(1297315143907056647668270/11449, -957546114575833247546854395624996225/1225043)
(472079741004779503351/9, 3100440833011575277674354057230/27)

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