curve #291

y² + xy = x³ − 32356893962437167577665120678966x + 70815900914955776688514954298475586029129608100

a-invariants: [1, 0, 0, -32356893962437167577665120678966, 70815900914955776688514954298475586029129608100]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 967103940121593907456018158744343407877042377493071668867434050863060490
naive height: 229.2767
Faltings height: 16.8462
discriminant (Δ): 1672431809981109761845400476081515346404222021387897188257148315954011227463592027472504422400
primes of bad reduction: 2, 3, 5, 7, 19, 67, 1913, 452987475501263063687, 596384365544879622910136838689861872111709
regulator: 11911494704568385671.59492978385144012914912926971982570345455926078673169367
submitted by: 7fff-zip
submitted at: 2026-08-23 15:35:48 UTC
last updated: 2026-08-23 15:35:48 UTC

(3109664958487548, 16349676628881294447306)
(14725772430442518439500/9878449, -4996135166191932841160997233361930/31047965207)
(132174851803103925852/24649, -878188239031207706935274498142/3869893)
(-1974904281748042720788/316969, 31188689181722461208626071572862/178453547)
(39120905606379832281/4096, -208570651194025239401720836029/262144)
(1895439006073341096750204/590733025, -76570361656546112045396394266775318/14357766172625)
(4152665650831548, 89775995766739293145146)
(8888612437732306773762636/2303328049, -6463529987567855587078381043855901558/110543623055657)
(420347285115840834/121, 24340131856209856045352826/1331)
(1520805118323343068204/124609, 53761781344859572852795004879898/43986977)
(135501270086484548, 49835431591309166721185306)
(44919777983838705642892/3560769, -8683724869146400848303579491718202/6719171103)
(17672568504604186397942796/5277877201, -1416110589620410746346316484412447254/383432500775449)
(29792148219347613/16, -8350172277934878657640551/64)
(49746647778795766288452300/2433152929, -338526330738361524559819367131073416410/120020134528783)
(1986328898981088, -119923030402767279571494)
(67028834566826758764/19321, -47776679934822831718334592690/2685619)
(858700679747567357108/249001, -1938943046522967227412784007266/124251499)
(-35647861724683347/16, -23238888461172488479987551/64)

No commentary yet.