curve #4089

y² = x³ + x² − 8926348659862790413098172786871966833962345x + 9923847233397519955807650243640217758197114155733559398977897499

a-invariants: [0, 1, 0, -8926348659862790413098172786871966833962345, 9923847233397519955807650243640217758197114155733559398977897499]
c-invariants: [428464735673413939828712293769854408030192576, -8574204009655457241820380598919188626721278904316414447165084594560]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 2147612816473088670494367390680829795178044691019176305579470386605442271215199877581241950412953706183871067576250504
discriminant (Δ): 2975376989195350591793286674044323605483111001980844700198712329118546281991654356686513015875418204396053547873960602696171611392 ★ record for rank ≥ 28
Faltings height: 23.6120 ★ record for rank ≥ 28
naive height: 308.3063 ★ record for rank ≥ 28
primes of bad reduction: 2, 3, 11, 47, 59, 25639, 2777521, 1652508644191, 2266247468510890877554719274869896886971029452559064668484218848558750686217498498522703
regulator: 187590227046331249447800170424400.9131021816157176727487889949752031560532936584555179406243687
submitted by: Matej Jurasić
submitted at: 2026-10-09 11:07:49 UTC
last updated: 2026-10-09 11:07:49 UTC

Witness: 28 independent points log in to add more points →

(1458575545770462993837, -2670046746650903189393770346334)
(2003810384379503041503, 9107627365249177251145383078750)
(2558368878270493221303, -61904134725073351066213974128430)
(2386635353150751361215, 47055823038269016526236176228382)
(1179828768980541829299, -32165215996694519980642490294238)
(1005806204723663205870, -44307903490579298594872385413557)
(875366612928439291887, 52733138851462537239728713597566)
(695784182231696641629, 63638628420819261028025651507982)
(-638326835788205299179, -123942251643492347245928321445366)
(2035857922303712100711, -13752291225321643929079610612466)
(-494562128307332485701, 119237223355500666168087540533262)
(-2939345405232599654185, -103760568325470209226569953355118)
(626786907942993008295, 67639998581182713299204458696818)
(27125768768416078563645, 4441523308942618156806281508451182)
(1362050589533733479574, 17104392849155236756269012321513)
(5602747278519705528507, -368492011249581892781849963906574)
(45962434667022402594479, 9833482449400745271347220034863618)
(280089094839255663444501, 148224395851893931101776340379859466)
(-3320334359296456876989, -54377237448633780417181873724034)
(11472674102977768092213/4, 711786476784523203293397879081807/8)
(-391160675626450609683693/121, 94082717598216148874424918748539114/1331)
(-2133903491655189569555601/1369, -7172447931264134669739670429300537002/50653)
(231536275797568306383783/361, 458197100082525668089856027063204010/6859)
(-334346817818790964021290/169, 309458914387326771243077795252944629/2197)
(-117708107469584963986059/49, 45380622107413597331624458942388586/343)
(8756351937916052568989454/1369, 23459648989009105284806395985515072377/50653)
(-13068465541516468865804731/10201, 142973764555870346024886754574986774458/1030301)
(101238375574926682815291438471/3485689, -32047678210564039176005705481771594141902586/6507781363)

Commentary

Specialization at T = -4457/649 of a rank-16 fibration of X1152 (two neighbour steps from the one in curve#3856).

last edited by Matej Jurasić at 2026-10-09 11:07:49 UTC · history