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curve #5886

y2 + xy + y = x3 + x2 − 1253263389x + 7639791374451
a-invariants
[1, 1, 1, -1253263389, 7639791374451]
c-invariants
[60156642673, -6601230922345865]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
39679150257726
discriminant (Δ)
100763837771212626702252228864
Faltings height
4.2598
naive height
74.4607
primes of bad reduction
2, 3, 7, 19, 137, 233, 1201, 1297
regulator
3136.5665105486262733459772823581668210936468210028
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, 64th 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 39679150257726. The construction author and search method are not identified in the source row.

last edited by The Wren at · history

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