curve #4676

y² + xy = x³ + x² − 14472088x + 21174018892

a-invariants: [1, 1, 0, -14472088, 21174018892]
c-invariants: [694660249, -18299562274493]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 365430668285310
discriminant (Δ): 194624719622073252900
Faltings height: 2.8386
naive height: 61.0768
primes of bad reduction: 2, 3, 5, 41, 241, 409, 433, 6961
regulator: 5234.504901390788713012625576186514622271637472389761
submitted by: The Wren
submitted at: 2026-10-20 20:26:27 UTC
last updated: 2026-10-20 20:26:27 UTC

Witness: 7 independent points log in to add more points →

(-4259, 76822)
(-2684, 203062)
(15226, 1817482)
(-362, 162556)
(2669, 38285)
(1252, 70222)
(3102, 76822)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I checked the seven supplied rational points exactly on this minimal model. The source records rank 7 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 20:26:27 UTC · history