curve #5756

y² = x³ − 3335489912086480173967373799675

a-invariants: [0, 0, 0, 0, -3335489912086480173967373799675]
c-invariants: [0, 2881863284042718870307810962919200]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 13341959648345920695869495198700
discriminant (Δ): -4806212955968451703558970652071430237511219814526183517005630000
Faltings height: 10.8983
naive height: 154.0875
primes of bad reduction: 2, 3, 5, 7, 11, 17, 29, 41, 151, 179, 557
regulator: 7697333321991.11895090312817058104591260671234145592121
submitted by: Maksym Voznyy
submitted at: 2026-10-24 19:32:35 UTC
last updated: 2026-10-24 19:32:35 UTC

(14547778828492261314574259865520939581241707376874126485051/791075489621092183917193780405000375643803855689, 1194825793067186832592760799615107046635724132132525713541041290060709037992099437605976/703601720995797758165965695818124360137008050289389952082752929335372613)
(7156954345553829972030362378605723273512160201/449750846130157749844862078562291600, -251299718669922152232048369278357129250564292257612651647962750349051/301618505422715407263047682103800873188933139622536000)
(165332926932721/10404, -873537819029776523881/1061208)
(419371476511282213081/108784900, -8588124276003525342252987751229/1134626507000)
(19222663532543553594749479982353659374005224139/886568324562032667699875950938978169, -2186014594546533021465609459609168127246882641425387583167122983127112/834772850673846538974431946539000535192950206214426803)
(10042272959253111397186761872982356442739/917862622335739083491170225, -1006347639154142850218801753580356542803031545465991555594888/27807793325044693625590613557056726171625)
(528344252386008978302392577169648321370622907624294869281/7738562884635036197625733784269383370475461696, 12080575367806663894852342821196755759360541328199464391511208207896175570824496976079/680754426761954222392212020927519308684031112096607013695491889631744)
(421052597581449338601034931669704129/26249642284493709869453604, -119653339159197007836066986923178001557763162792778817/134488479692699609657444612496835040808)

Voznyy (2023), A = 702955655530590, [r, s, t] = [170, 179, 232] or [135, 174, 451] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 19:32:35 UTC · history