curve #401

y² = x³ − 94624210289371976970836667748793555136557175x + 356735513818524391040758052970937761657716127823131580058975168250

a-invariants: [0, 0, 0, -94624210289371976970836667748793555136557175, 356735513818524391040758052970937761657716127823131580058975168250]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 23832433994917006690442043397523785208509789967293679948888524812389512387119806381441975621763494871158237352600
naive height: 315.4029 ★ record for rank ≥ 27
Faltings height: 24.1326 ★ record for rank ≥ 27
discriminant (Δ): -753013978293095771757766913020681392316355197840905853317049914994261912464501856102076217818550299734616265600928194683955180000000 ★ record for rank ≥ 27
primes of bad reduction: 2, 3, 5, 7, 13, 29, 223, 431, 3331, 27529, 7699337, 10562286239439132134180618208961215130924135879373607219102965797276072491381856960361
regulator: 3971539583109684022794626776334.9071738702159665641213959620882043080199825109890771999307827
submitted by: NDElkies
submitted at: 2026-08-28 16:50:56 UTC
last updated: 2026-08-28 16:50:56 UTC

Witness: 27 independent points

(4742052291173541678285, 121067645094309470975516570594850)
(4672581244944957732885, 128890427125914309184281694164150)
(5094033525046336479105, 83081855614765767365112651266850)
(17803375292248074326385, 2077273712704959510690822975860850)
(7400497292662334332605, 248545775422691027491886927146350)
(2225480400065436267705, 396451088351607732745916930793750)
(5931711615229052159185, 64501643555476812516881082474350)
(7843803694114400974185, 311630898605142215047175315238150)
(5760636075784521271785, 52973274189981602728616710710150)
(7270966955409355254189, 230477613248607206113061639201538)
(10667288722763781708135, 749128635810845409803051215142100)
(5659571354725947126510, 49833193710395427577700606342100)
(1055979908642570761710, 507928897863932218158360841793100)
(5561272757878372459785, 50021500442673654062521981050150)
(7412797892361708496185, 250270739645408861671886647008150)
(40288666410427169452305, 7870201680441971311950002136101550)
(5007035147612437973985, 92071417406396361896796823612350)
(5723163682064517090535, 51435607085481962243825749178900)
(-6082250357260696603215, 840986494217309413112603347897650)
(5667360898331597089485, 49958114415942478693539854685150)
(-3964348927887365651865, 818263371548520966356934592482900)
(8959414861238392829385, 477640215532715482835293965485850)
(8352625053574689520935, 386143869315144023613928187513100)
(7346387889174072782085, 240976385153319213044293227521850)
(6064780925990827691329, 77023101819459713596213751967842)
(6219587641276712875305, 93839946783651806659501163588550)
(53255292977901815306065/9, 1708941046523090336750544075511550/27)

Commentary

Noam D. Elkies and Zev Klagsbrun, January 2026

last edited by NDElkies at 2026-08-28 20:42:33 UTC · history