curve #4616

y² + xy + y = x³ + x² − 214630437817857327585449164664810765x + 38257849046784951543981704712507790648091888800914947

a-invariants: [1, 1, 1, -214630437817857327585449164664810765, 38257849046784951543981704712507790648091888800914947]
c-invariants: [10302261015257151724101559903910916721, -33054781576422198211267150486035369050713091203322389769]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 13178037168409810631180244256476178872980088517494507510
discriminant (Δ): 479274443948392168342347831607270193387177692656290591459639231351434557159263981747516388153753600000000
Faltings height: 19.0455
naive height: 255.6763
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 37, 43, 47, 89, 101, 103, 127, 149, 191, 223, 227, 307, 571, 577, 647, 701, 1019, 1193, 171179
regulator: 818148262110058.0058859058636348340811163237678844042819975750342571953
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:25:19 UTC
last updated: 2026-10-19 03:25:19 UTC

(-534486907400021193, 16875733572310914522008596)
(-38423761587386793, 215518049231288358851283796)
(31350122852572907, 177651260325750189687296396)
(241870784678364887, 22244429680786876844116436)
(251823489496333137, 13351682266079728115172436)
(256534760134358487, 8958518767243714284113236)
(260435809401835307, 4992757239962605182929096)
(262280139979496567, 2650898646275058740319476)
(279193109043473007, 9862831100401926068409796)
(295564376669346167, 25312826417094210418892276)
(690588188824958807, 468387051332524119200192596)
(3194079629102220675/4, 4905733120161783481847098289/8)
(3611548935160590807, 6809520843353985318638864596)
(16620818124879953367, 67734765392579118077781484756)
(-259063744164820449073/841, 6685564390540445468476855170724/24389)
(71352407558228972167/81, 532091135801885542925029900084/729)

X400, T=-2357/2646.

last edited by Andrii Prokhorenkov at 2026-10-19 03:25:19 UTC · history