curve #5943

y² + xy = x³ − 17152972308479675172682212349538x + 27959449348040127236392595741617752266611913284

a-invariants: [1, 0, 0, -17152972308479675172682212349538, 27959449348040127236392595741617752266611913284]
c-invariants: [823342670807024408288746192777825, -24156964236706671167257208931294350391471982244113]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/3ℤ
conductor (N): 5903198543007601946565130564454539165491166
discriminant (Δ): -14710973119242628176320402632511891083674776519225465481973671129517588257964483878608277864448
Faltings height: 16.8517
naive height: 227.4173
primes of bad reduction: 2, 7, 59, 79, 97, 109, 113, 139, 197, 439, 2971, 9013, 19183, 27932188183
regulator: 75972060907318.242913330863798295363358005778247889218988806194
submitted by: Maksym Voznyy
submitted at: 2026-10-26 01:53:12 UTC
last updated: 2026-10-26 01:53:12 UTC

Witness: 12 independent points log in to add more points →

(20539600825290070651837335636/12035716378009, 2525058506779981229911078024308783949119446/41754945151556857277)
(-41399680677249882213522716/26598021921, -978538156932193382597263570783605161618/4337844797073969)
(747899952835536827006436/264745441, -194915260627264543275129060470884142/4307673070511)
(-10391295008000611276192096/2342656801, -14683962072822191517449281811158816562/113386931825201)
(1057685556952249154160/36481, 34065287792356783764741488456978/6967871)
(-2627907716427300687554804229749530556/591602927506427215369, 1848682999402255086309663294250858429314322966967739002/14389492315924567628261474072347)
(-16726739681839195799195244/8642491225, 186545237951731219091775656010001957526/803449196732125)
(688395772704372794115460/390576169, 436805037025293807343072085530232986/7718956827947)
(17701791904830528222889068910246/5505348397861225, -31769830414024857411005858962406216472600270024/408486033111701097692875)
(89190353066388821544303484/30693988809, -276922997956693436479892745875938960882/5377494757370373)
(2210300375158626992184059948356/1005100308802489, 941678051094534326371433526856484045588399414/31865013706763199156013)
(5230646034459508468666/2608225, 169835796294895038225778956068316/4212283375)

Commentary

Voznyy (2026), T = 2383/632 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645

last edited by Maksym Voznyy at 2026-10-26 01:54:11 UTC · history