curve #716

y² + xy = x³ − 106666469731938409505302816930992721437286640x + 420602440396919252439538669229713706997549597053772759857593671936

a-invariants: [1, 0, 0, -106666469731938409505302816930992721437286640, 420602440396919252439538669229713706997549597053772759857593671936]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 1510533766562522587207107094561590004046682188335028910565632652367888999995529500495658558554783663782
naive height: 315.7484
Faltings height: 24.1683
discriminant (Δ): 1248295727703595515223046105300071572176734805072549681866646332300380851334822313538631702875954525838372825335149653436447725453312
primes of bad reduction: 2, 3, 7, 11, 13, 23, 41, 43, 53, 71, 139907, 11781248030100448859460308953109691192279071597920147765590505923988336601349059597533
regulator: 4710726955923861033721427757.62104694330760957556342828204218025027488376121718955165906658
submitted by: FNacc
submitted at: 2026-09-11 21:02:27 UTC
last updated: 2026-09-11 21:02:27 UTC

Witness: 26 independent points log in to add more points →

(10469559793851555436600, -671891002507418194261888183246256)
(6403931606337260782048, -12044757210499233439284338310896)
(11239964850141663580384, 801059530688988009105595683809296)
(4938315400629762638476, 119500064323171210418679076940308)
(6678449957659181873608, 78140517328965691275437878627408)
(7611981974165900618848, 222967950825130913164442080399504)
(5492047613545477008520, 20963629312711406561003030626384)
(16799728604783966743254, -1835766026936897366873247226305714)
(13358787140247996803488, 1174580539014516912967681678639888)
(16180259979405399357040, -1711933540256382247932752850823664)
(15389160875910968885728, 1556808460987987540488222850605328)
(22014235119553082066650, 2956535889669767370213586317980506)
(68878981524870794840464/9, -6187842949963588541652190733223008/27)
(43451360863975928011126/9, -3638294340845048369931361056163990/27)
(10669741933237554290164, 705108756647387435422171234843180)
(2162454949125320676576, 447272960862392927979595096601616)
(39948728018193395200960/9, -5021654710738934476595178717013328/27)
(433479881775005570796280, 285319359225179775580617475664232016)
(11114439264849593488387/4, -3053346250564892302372214982618301/8)
(-6161390303124281434484/25, -83560982660400167827358297658277276/125)
(39640100029829849135872/9, -5139778594883389739132934783208784/27)
(19005177566830420343475991564/1651225, -1797478085192740295091285068706997931155232/2121824125)
(21062148743769791958016, -2741795716756231081898982950162192)
(-10890246158710666359584, -539139132541498563735481638398192)
(9775388537360745050104, 558583023030681290327969004831160)
(673579424086074442573608184/3025, -17463201146694618815997985900626777013712/166375)

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