curve #4019

y² + xy + y = x³ + x² − 5595393575697345282005154117580831574480x − 155575264826699624670982943133663576392041878775640633168719

a-invariants: [1, 1, 1, -5595393575697345282005154117580831574480, -155575264826699624670982943133663576392041878775640633168719]
c-invariants: [268578891633472573536247397643879915575041, 134417028810268475713714921180234285701202327779824407690960255]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 199500119263603519815431870142834901369753749343131572760786463422
discriminant (Δ): 755728547883892635943672209275166861463045058530861411150682843908683617224785189292255508270661903285874141897894751232
Faltings height: 21.7698
naive height: 286.1819
primes of bad reduction: 2, 3, 7, 17, 19, 29, 31, 37, 43, 47, 59, 61, 83, 163, 193, 263, 653, 701, 947, 1693, 2311, 4637, 10457, 56599, 57329, 7057319
regulator: 591399625560959953580669486.540606602694630287462101833071314527965420448
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:47:06 UTC
last updated: 2026-10-05 04:47:06 UTC

Witness: 17 independent points log in to add more points →

(-397120289686607819252477535659/8015441841, 4002220565116303446226241075993945381044189/717614492582889)
(-95178059711366656572513553830999/2236810386409, 247466280794418917560725677646144232326373593817/3345366903482141173)
(-4555964533352491648726626171133959/105366940225600, 80385402140113749470594249439961748573744202662119/1081574782705347904000)
(133372353561603835232770138574419/1486119474225, -462223167098079121066239442966203565483501398983/1811676236846099625)
(11509457247428618222555054221/131767441, 224823911822689808441910936807205844684843/1512558455239)
(-1245750142958115454748871838941834219/25681199967095401, -169942300414667638145164194064063009655348114810840887/4115503437305721231828149)
(72402795866076380175086026027581/641205367009, 414692339578658540444704638763223679185483670893/513447121248557777)
(-4551183752610281082310101186996131/107046730702921, -81884020395779748064697142064366739511048859469561/1107541764694128956219)
(7283953096127815283420950001581/53160219225, 15745046179407870864853355794741305081132209201/12256885945612125)
(601902580777803065717822777611899/566861421604, 14729248584996985894864951505473650393453043873423/426791098048494808)
(1832038050407961406793023534278847954501/7830389869187657641, 73795339359578764007869656645438805799020590918979987078079/21911649822037806608752648939)
(1211812840339376994076684226974676399876161/552343044131733017241, 1333206894152538729677153264155990173982092055908690491720907523/12981154943786685157078036921539)
(-1618375281168173851599557034594675669/41755820524608100, -472725136797358005608551808130371442784061364861054751/8532484997525883459521000)
(-3030271550347372806453590783703540107120711/61152791712040224731089, -62055995304688409170930093394824702726239221591352420063519911/15122529207764968696651707861670937)
(205637088171306361594036578304161722491/1789527786727228900, -2029622328896132006420457465332188854729262817177263380179/2393909175738358990840337000)
(9925267153564510158810034195307509541832114789/51531907874307708644948281, 899433297734042989953606486113995584964025230849923634037224742842721/369925553739878968721619845255114936429)
(16544405814662945651335577432508543672008941/1466286284766650248521, -67292582234490815895378250576530028990103111793014495403796152551/56147207128679767695332255040069)

Commentary

Unlisted rational-isogeny neighbor of curve#3472 (source contributor: Steps Unbounded). Source equation and witness provenance are credited to that entry. Exact rank 17: 17 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:47:06 UTC · history