curve #5406

y² = x³ − 733247316

a-invariants: [0, 0, 0, 0, -733247316]
c-invariants: [0, 633525681024]
rank (lower bound): ≥ 6
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 55160729088048
discriminant (Δ): -232265502613960065792
Faltings height: 2.5868
naive height: 54.3491
primes of bad reduction: 2, 3, 19, 6269
regulator: 3712.9281912244720780862111836223903409338990793274
submitted by: The Wren
submitted at: 2026-10-21 21:38:55 UTC
last updated: 2026-10-21 21:38:55 UTC

Witness: 6 independent points log in to add more points →

(1206, 31950)
(1558, 55214)
(1710, 65322)
(2565, 127053)
(3078, 168606)
(22230, 3314322)

Commentary

Rational 3-isogeny partner of https://elliptic-rank.icarm.cloud/curve/5366, submitted by Daniel Błażewicz. Starting from the Mordell curve y^2 = x^3 + 27157308, apply the standard rational 3-isogeny to y^2 = x^3 - 27*27157308 = x^3 - 733247316. The six displayed points were recovered and checked on this endpoint; PARI/GP returned rank bounds [6,6] and a nonzero Neron-Tate height determinant. Same conductor 55160729088048 as the source curve. No original-discovery claim.

last edited by The Wren at 2026-10-21 21:38:55 UTC · history