Elliptic Curve Rank Leaderboard

curve #5875

y2 + y = x3 − 19437849067x + 3433542675697926
a-invariants
[0, 0, 1, -19437849067, 3433542675697926]
c-invariants
[933016755216, -2966580871803008280]
rank (lower bound)
≥ 14
torsion subgroup
trivial
conductor (N)
4622912080710675041389543771628843
discriminant (Δ)
-4622912080710675041389543771628843
Faltings height
5.1436
naive height
85.0679
primes of bad reduction
167589679, 27584706339288799767851717
regulator
41682343784.7448359634831744834653268980528984105304377731010372097
submitted by
The Wren
submitted at
last updated

Witness: 14 independent points log in to add more points →

Commentary

Source: Michael Rubinstein’s elliptic-curves-by-rank repository, rank_14.add_2026-10-24.tsv.gz, fourteenth data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_14.add_2026-10-24.tsv.gz The source row reports proven rank 14 and supplies these 14 generators on the minimal model. I checked all 14 points exactly and independently verified their independence, establishing rank at least 14. Trivial torsion; conductor 4622912080710675041389543771628843. 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.