curve #5894

y² = x³ − 8436069078217487964075

a-invariants: [0, 0, 0, 0, -8436069078217487964075]
c-invariants: [0, 7288763683579909600960800]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 2733286381342466100360300
discriminant (Δ): -30744256964741535050433158008413955027941630000
Faltings height: 7.5991
naive height: 114.4968
primes of bad reduction: 2, 3, 5, 7, 13, 73, 97, 109, 151
regulator: 942156506.8710100564617454296257095351737203152523878
submitted by: jesper-petersen
submitted at: 2026-10-25 20:19:14 UTC
last updated: 2026-10-25 20:19:14 UTC

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

(84451277131/1225, 24223961494350904/42875)
(81205167349579/3200521, 508843190477879119408/5725732069)
(1619329811491441/14273284, 64974786237974392439639/53924466952)
(9663230637808801/81252196, 947527374423977104197649/732407294744)
(16143409265627371/290736601, 1999952342689455848519644/4957349783651)
(22903293713362699/554555401, 3251992610387544529382968/13059225138149)
(29520739105318279/1342709449, 2303285130428510077689658/49200902339707)

Commentary

Burkhardt quartic specialization b=-1, c=-a-d, t=d, with a=1/4, d=23/19, followed by rational cube scaling. The resulting cubesum curve is u^3+v^3=954513206010. PARI/GP 2.17.4 ellrank bounds [7,7].

last edited by jesper-petersen at 2026-10-25 20:19:14 UTC · history