curve #4133

y² + xy + y = x³ − x² − 553458616702819570651893653129977495662x + 5005092197204584484230581680486517807900742265792354312061

a-invariants: [1, -1, 1, -553458616702819570651893653129977495662, 5005092197204584484230581680486517807900742265792354312061]
c-invariants: [26566013601735339391290895350238919791761, -4324399658384760994255675510732542358765432288568518986558009]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 599703577527291904964877914134409193416380772606047160245323861803629109504900979580327648384070
discriminant (Δ): 28132802339578420242837891811651148501009053540151262266228846281132644483086032965139622457815508086240353177600000
Faltings height: 21.0531
naive height: 279.2414
primes of bad reduction: 2, 5, 7, 11, 13, 17, 37, 41, 73, 2893027185580912804336390508337001709638089508475716816859294452948448806276130004521
regulator: 266749079756360698879690696.5475588401834100270765940894801786610008349112955165278598135
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:05:10 UTC
last updated: 2026-10-11 01:05:10 UTC

(14708203432529139481, -6823069608210615702444168141)
(5035668134608444281, 48432969305179195210473933459)
(13172192550373733401, 540202389899697453593820979)
(20300785210109867842041, 2892470663386765841409260487807219)
(1776752062631074841, 63461345670319583646109609139)
(-27008941931278746629, -15838603336108339802167732071)
(10161276076320318681, 20746414454655243393464695859)
(3745490067104744380409/289, 14773574454745892719931980993667/4913)
(236715064920520759521, 3624650361766235985309424872099)
(807153866570185054089/49, -6489449318225413858063342363243/343)
(14398787857614009369, 4603151225186278866141957299)
(-11682235505383345955, 99380065279812265726493637447)
(139178857833699882289, 1619868771246379596707753714251)
(-23618639923594102439, -70011472594311863499385527501)
(13102899562215673081, 1662420745788289209300234259)
(26322588823536578521, 93139622380267462788841626099)
(258202932799807095081, 4132332076779729266310276048659)
(14436839794257013081, 4884546449435368668793574259)
(13133845096380421361, 1270033729249791883632468739)
(14328077485054351681, -4069372098076240987427605541)
(12484090263215904281, 6429748680684108169759102259)
(14077222934866824681, 1894695983781461071401123459)
(18486091702320844121, -33032723845242776317859399821)
(10200123654211329241, -20518100910578624534132421581)
(-16595196210288562919, -98079154675293403182706401741)

X1092; T=-17/265

last edited by Andrii Prokhorenkov at 2026-10-11 01:05:10 UTC · history