curve #396

y² = x³ + x² − 61892122170276517714464524289071240329708x + 1412172132176588711941495717130133429244688284956311756421488

a-invariants: [0, 1, 0, -61892122170276517714464524289071240329708, 1412172132176588711941495717130133429244688284956311756421488]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 61378488483201168932457367234130323088140228715494483707650726959711359698105950752523718937915036383400
naive height: 293.3922 ★ record for rank ≥ 25
Faltings height: 22.5141 ★ record for rank ≥ 25
discriminant (Δ): 14312004020934458392907655489561458208436855070393963101216354206888771266515503042561943861970578893642636876946544328480000 ★ record for rank ≥ 25
primes of bad reduction: 2, 3, 5, 7, 13, 19, 67, 89, 223, 1787, 24898645430221021869269549825335198329409825157617556901356259048740151839661764611388857
regulator: 4296576243480457017833248884.400704750550944228197096332430678421658219796586556614152099
submitted by: Rayan Hatout
submitted at: 2026-08-28 02:44:21 UTC
last updated: 2026-08-28 02:44:21 UTC

Witness: 25 independent points

(312043241950671962822, 3533144698787581662418438706538)
(-157144747038377243656, 2693991004766040735804448566684)
(28026161134648407600142/9, 4676977173816192885685615749587590/27)
(-20843049399238615612, 1641078239937536988612471047580)
(396651772824013046158, 6266483728501069138170776528130)
(-234591131665541591122, 1738177662311872023228340151070)
(-87519227111728242922, 2481644461652948950843732772070)
(1291938339670784093197/4, 31102836658516306461624455960715/8)
(60952564443948938759768, 15048193163427450776699510587012980)
(1863878367181860229421/4, 68700957803904118134454330715163/8)
(-92873735930676487402, 2521753253321603828715618098970)
(1994974386122594895278, 88418227877565003934709573625570)
(45892895553952793457293/4, 9829156964648952943386185793868341/8)
(2232072047915488832963, 104803494641695909448625464193420)
(276582877268051562314, 2334937298098678856699205244446)
(-56148756462016493366, 2170326842934246091420032226974)
(696916830899595123818, 17226902944586423751044029423230)
(115189251298244867140992253041738628/866133619569, -39094635964227753853797445245489990914165774115289724/806078512788944247)
(3164806931995195687308144144333334018/13191362985688281, 924879226493074999187639720755159316905910617623740030/1515076306103463706270179)
(8275138842154799650495155254693498/16494978082801, 658520979166201070387128947522781351154193404665470/66992720480466064201)
(819147613500795440104255900751405004593/282801693206968576, -23358672183624154316993868332616937086464680129872380471895/150391402019467662966861824)
(107137119284421406266672996905306/743271169, -1108943195698849337870827736041720314353565060942/20263801880447)
(2841153203786876671617090636041329570262485828/977967557547240315052921, 150888562438014138471580179611897429713003167738266370797961413932380/967134046048985937930093462981412531)
(84742689138193008307502201694175016078525726738/12035627803015318158216121, -24653749362444153190966522000751174535064921707176464618107265108189170/41754484218811067129381142679906721581)
(493325788230938714732402449726029912370873900426/1304346572046094160345676489, -266923695511944890691555563166404165214831725942777355819150756614711462/47107439793279805115710159793275001243013)

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