curve #4599

y² + xy = x³ − 1605567x + 1172516536

a-invariants: [1, 0, 0, -1605567, 1172516536]
c-invariants: [77067217, -1013169887929]
rank (lower bound): ≥ 10
torsion subgroup: trivial
conductor (N): 329157169581291693751
discriminant (Δ): -329157169581291693751
Faltings height: 2.6367
naive height: 55.2882
primes of bad reduction: 329157169581291693751
regulator: 2124380.568934963282237815562579114793011904092051441806215
submitted by: The Wren
submitted at: 2026-10-18 22:30:07 UTC
last updated: 2026-10-18 22:30:07 UTC

Witness: 10 independent points log in to add more points →

(569, 20769)
(-648, 44380)
(-1480, -16796)
(-1469, 19750)
(1295, -36221)
(-1531, 7294)
(1400, -41556)
(3780, 219734)
(1617, 52153)
(-49, -35346)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, rank_10.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Ten supplied rational points checked exactly and certified independent modulo torsion. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 22:30:07 UTC · history