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curve #5883

y2 = x3 − x2 − 3498139024x + 79567826043904
a-invariants
[0, -1, 0, -3498139024, 79567826043904]
c-invariants
[167910673168, -68745594237894080]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
17133028377072
discriminant (Δ)
4696650581912870563444690944
Faltings height
4.2295
naive height
77.5401
primes of bad reduction
2, 3, 23, 29, 71, 73, 223, 463
regulator
1823.5993845615217196730783595840518814132253060892
submitted by
The Wren
submitted at
last updated

Witness: 6 independent points log in to add more points →

Commentary

Source: Michael Rubinstein’s elliptic-curves-by-rank repository, torsion/torsion_Z2xZ2.add_2026-10-24.tsv.gz, 50th data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2xZ2.add_2026-10-24.tsv.gz The source row reports proven rank 6 with torsion Z/2 × Z/2 and supplies these six generators on the minimal model. I checked all six points exactly and independently verified their independence. The full torsion group and both supplied torsion generators were checked separately. Conductor 17133028377072. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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