Elliptic Curve Rank Leaderboard

curve #5882

y2 + xy + y = x3 + x2 − 651868319x + 5572369395461
a-invariants
[1, 1, 1, -651868319, 5572369395461]
c-invariants
[31289679313, -4814761830273305]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
16417453512642
discriminant (Δ)
4312524477436178311261122624
Faltings height
4.0287
naive height
72.4997
primes of bad reduction
2, 3, 7, 13, 233, 337, 569, 673
regulator
2746.4771621275880943660429687975217067619917334362
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_Z2xZ2.add_2026-10-24.tsv.gz, 47th data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2xZ2.add_2026-10-24.tsv.gz The source row reports proven rank 6 with torsion Z/2 × Z/2 and supplies these six generators on the minimal model. I checked all six points exactly and independently verified their independence. The full torsion group and supplied torsion generators were checked separately. Conductor 16417453512642. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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