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curve #6454

y2 = x3 − x2 − 6099257287511604327177425x + 4757878866571085040818203272713556177
a-invariants
[0, -1, 0, -6099257287511604327177425, 4757878866571085040818203272713556177]
c-invariants
[292764349800557007704516416, -4110807340715660889168124285578285438464]
rank (lower bound)
≥ 10
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
2031996162762000342302590303680
discriminant (Δ)
4742116784884200346899309928315753577707877021661379793338624445124864000000
Faltings height
13.2386
naive height
182.8242
primes of bad reduction
2, 3, 5, 11, 13, 19, 23, 47, 59, 67, 107, 137, 727, 1009, 3527
regulator
64169287.91882239654000836872981984840827655217920977013650
submitted by
The Wren
submitted at
last updated

Witness: 10 independent points log in to add more points →

Commentary

Z/2xZ/2 X400a family y^2=x(x+A)(x+B), with A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=1507/2908. Family equations as posted by wgxli with curve #4252: https://elliptic-rank.icarm.cloud/curve/4252 Section formulas from the Layr-Labs elliptic-rank-challenge-public repository, submission/research/x400a-family.gp, commit 7482bf9: https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/7482bf9/submission/research/x400a-family.gp Rank bounds [10,10]. The ten displayed points were checked exactly on the global minimal model, and the torsion subgroup was computed as Z/2xZ/2. The minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. The conductor is 2031996162762000342302590303680.

last edited by The Wren at · history

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