curve #4614

y² + xy = x³ − x² + 488225455860425405389707941901x + 109501822963723455114968886412042369981576138405

a-invariants: [1, -1, 0, 488225455860425405389707941901, 109501822963723455114968886412042369981576138405]
c-invariants: [-23434821881300419458705981211239, -94609575040657065324789816325856495228258699032509]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 21357673831470329498862245870108862655389387058826297009910
discriminant (Δ): -5179967916414405378536526676755075757484431093818227170550417445419962568031162879152094385110000
Faltings height: 17.2366
naive height: 230.1477
primes of bad reduction: 2, 3, 5, 17, 31, 37, 59, 71, 79, 89, 103, 113, 181, 199, 491, 613, 797, 881, 967, 2311, 3187, 4483, 2057370727
regulator: 247577706279840650.2426704842172850349624270996238382815573730176660579
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:24:50 UTC
last updated: 2026-10-19 03:24:50 UTC

(-699118876277934, 329876930361058766880557)
(1849888710364031, 341665724785189133518547)
(14096541075978066, 1708081552229443134165377)
(30901649347082226, 5443614820873134409114657)
(218765883467514744572066/73599241, -233889093282983675224541830530473537/631407888539)
(-151393135909504270/49, 96100987762034329767144395/343)
(2952510409721006, 369704319591464341984697)
(-6074784410826903094192624036553000626897591/1406884371705302430043904089, -8653280858212845601398326213552460386156938036318913417525121539/52770062432395353485086300541430022046813)
(1043737465292166416458626/770007001, 7171591810902272783344393364823818393/21366924270749)
(17406472803285070946/3481, 99978634188033532720461549283/205379)
(20605619635090631, 2978008419484529210293547)
(122280466212893870, 42761774828284583932458905)
(161920716631895186, 65157328531613664220063937)
(185969074101420461361548365607926262782591614/95276498162172412815249134521, 10097628994098038368739515204383765034162763189017579087588307021429/29408893169941704427171360479535491919035181)
(133510799299281430678484281432333501/58077953478986032656, -155084157730742631511936311980512182192517562588823557/442605653304655175453784458304)
(-638839665251529930459255990781844114/1649832623692143787521, -22150316179209245053479855452910475395402442772417609513/67013118810232195477478376178431)

X720, T=4706/177.

last edited by Andrii Prokhorenkov at 2026-10-19 03:24:50 UTC · history