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curve #5884

y2 = x3 − x2 − 731136329x + 6170904154569
a-invariants
[0, -1, 0, -731136329, 6170904154569]
c-invariants
[35094543808, -5331450622284800]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
92543227347648
discriminant (Δ)
8564248927918464681051131904
Faltings height
4.0762
naive height
72.8439
primes of bad reduction
2, 3, 7, 11, 17, 19, 41, 47, 89, 113
regulator
902.70565577515455743086899084482646533310640394665
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, 85th 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 both supplied torsion generators were checked separately. Conductor 92543227347648. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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