Elliptic Curve Rank Leaderboard

curve #5876

y2 + xy = x3 − x2 − 4598899594x + 121393996760584
a-invariants
[1, -1, 0, -4598899594, 121393996760584]
c-invariants
[220747180521, -104883419838832245]
rank (lower bound)
≥ 13
torsion subgroup
trivial
conductor (N)
70507020932326816464044574994
discriminant (Δ)
-141014041864653632928089149988
Faltings height
4.4016
naive height
78.3833
primes of bad reduction
2, 57649, 611519895681857590452953
regulator
1032569482.719564619392165809214612873343715946924089069980287004
submitted by
The Wren
submitted at
last updated

Witness: 13 independent points log in to add more points →

Commentary

Source: Michael Rubinstein’s elliptic-curves-by-rank repository, rank_13.add_2026-10-24.tsv.gz, seventh data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_13.add_2026-10-24.tsv.gz The source row reports proven rank 13 and supplies these 13 generators on the minimal model. I checked all 13 points exactly and independently verified their independence, establishing rank at least 13. Trivial torsion; conductor 70507020932326816464044574994. 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.