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curve #4581

y2 + xy = x3 − 224125525271290582143806664985x + 41051116287478191657688706332867805265767225
a-invariants
[1, 0, 0, -224125525271290582143806664985, 41051116287478191657688706332867805265767225]
c-invariants
[10758025213021947942902719919281, -35468164472381173729280861804519698103702761321]
rank (lower bound)
≥ 12
torsion subgroup
ℤ/3ℤ
conductor (N)
558341382311826958196586943618604792370 ☆ record for ℤ/3ℤ torsion, rank ≥ 12
discriminant (Δ)
-7470773989038667208039204073219966949534207294785627321767176636964985159878832192000000 ☆ record for ℤ/3ℤ torsion, rank ≥ 12
Faltings height
15.7011 ☆ record for ℤ/3ℤ torsion, rank ≥ 12
naive height
214.3699 ☆ record for ℤ/3ℤ torsion, rank ≥ 12
primes of bad reduction
2, 3, 5, 7, 13, 17, 29, 31, 41, 89, 127, 131, 151, 3680055649, 396687343189
regulator
2969106036.2403860837557744132828092496778257113810701615672556
submitted by
jesper-petersen
submitted at
last updated

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Commentary

Curve and independent-point witnesses from the Layr Labs Elliptic Rank Challenge public repository, submission/board/3-r12-z3k3.ec. The original submission describes a K3 family with Z/3Z torsion and generic rank at least 5, specialized at t = 2417/727. The submitter reports Mestre–Nagao sieving, PARI/GP rank calculations and saturation checks. Submitted to ICARM to document these improvements and make the curve available to other researchers.

last edited by jesper-petersen at · history

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