curve #5840

y² = x³ − 2960500878075

a-invariants: [0, 0, 0, 0, -2960500878075]
c-invariants: [0, 2557872758656800]
rank (lower bound): ≥ 5
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 959202284496300
discriminant (Δ): -3786292274003789478784830000
Faltings height: 3.9706
naive height: 70.9559
primes of bad reduction: 2, 3, 5, 13, 17, 29, 31
regulator: 207295.657873044590096131099166490866527770610417
submitted by: jesper-petersen
submitted at: 2026-10-25 11:05:20 UTC
last updated: 2026-10-25 11:05:20 UTC

Witness: 5 independent points log in to add more points →

(14911, 595634)
(3450889/4, 6410552837/8)
(65740531/225, 532996106804/3375)
(71938321/1024, 607544875769/32768)
(9783390409/595984, 556507976885627/460099648)

Commentary

Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(23,-14,-9,-1) and specialization t=-14/9. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=17881110. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].

last edited by jesper-petersen at 2026-10-25 11:05:20 UTC · history