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curve #5889

y2 + xy = x3 − 358603413x + 2613749632417
a-invariants
[1, 0, 0, -358603413, 2613749632417]
c-invariants
[17212963825, -2258305501854025]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/3ℤ
conductor (N)
1436973356350
discriminant (Δ)
10757160703641083480000
Faltings height
3.4760
naive height
70.7068
primes of bad reduction
2, 5, 7, 19, 23, 9395053
regulator
290.343182126088856571513016487280305014516604163
submitted by
The Wren
submitted at
last updated

Witness: 5 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, 28th 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 5 with torsion Z/3 and supplies these five generators on the minimal model. I checked all five points exactly and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 1436973356350. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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