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curve #5879

y2 = x3 − 354477825x + 2563556726025
a-invariants
[0, 0, 0, -354477825, 2563556726025]
c-invariants
[17014935600, -2214913011285600]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/3ℤ
conductor (N)
27241252179300
discriminant (Δ)
11644037991312089783130000
Faltings height
3.6896
naive height
70.6721
primes of bad reduction
2, 3, 5, 19, 31, 37, 154321
regulator
737.39720662420622065167924950328536689913025114114
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_Z3.add_2026-10-24.tsv.gz, 106th data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z3.add_2026-10-24.tsv.gz The source row reports proven rank 6 with torsion Z/3 and supplies these six generators on the minimal model. I checked all six points exactly and independently verified their independence. The torsion subgroup is Z/3; conductor 27241252179300. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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