Elliptic Curve Rank Leaderboard

curve #5888

y2 + xy = x3 − x2 − 57645215092401x + 175729758818230820393
a-invariants
[1, -1, 0, -57645215092401, 175729758818230820393]
c-invariants
[2766970324435257, -151830499167584968860909]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/3ℤ
conductor (N)
3343455260310900743982
discriminant (Δ)
-1081151864159486335252708993754100723191196
Faltings height
6.8259
naive height
106.7541
primes of bad reduction
2, 3, 19, 37, 41, 61, 163, 281, 1483, 2833
regulator
381994.849399522642529337070382142881248967566232083201
submitted by
The Wren
submitted at
last updated

Witness: 8 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, 1789th 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 8 with torsion Z/3 and supplies these eight generators on the minimal model. I checked all eight points exactly and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 3343455260310900743982. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

Log in to edit commentary.