curve #5792

y² + y = x³ − 2481571

a-invariants: [0, 0, 1, 0, -2481571]
c-invariants: [0, 2144077128]
rank (lower bound): ≥ 3
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 804028923
discriminant (Δ): -2660339543294403
Faltings height: 1.6387
naive height: 42.9720
primes of bad reduction: 3, 17, 107
regulator: 202.22074621862611219429359107606523254081095
submitted by: jesper-petersen
submitted at: 2026-10-25 10:16:20 UTC
last updated: 2026-10-25 10:16:20 UTC

Witness: 3 independent points log in to add more points →

(151, 980)
(217, 2781)
(1171, 40040)

Commentary

Burkhardt-quartic construction with (a,b,c,d)=(0,-2,-1,2) and t=-5/17. Cubesum parameter k=16371. PARI/GP 2.17.4 returned matching rank bounds [3,3]. Three rational-point witnesses verified by exact arithmetic.

last edited by jesper-petersen at 2026-10-25 10:16:21 UTC · history