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curve #5464

y² = x³ − 1215942493949131

a-invariants: [0, 0, 0, 0, -1215942493949131]
c-invariants: [0, 1050574314772049184]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 944850556496172234811749649452
discriminant (Δ): -638718976191412430732742763029552
Faltings height: 4.9736
naive height: 82.9917
primes of bad reduction: 2, 3, 13, 137, 52517708027
regulator: 19771643556.17392377579735112340133801796544672226012083375
submitted by: jesper-petersen
submitted at: 2026-10-22 07:10:13 UTC
last updated: 2026-10-22 07:10:13 UTC

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

(131183, 32273566)
(172943, 62901974)
(819923, 741617656)
(953411, 930283580)
(1471769/4, 1763571485/8)
(15400177/144, 4648128823/1728)
(471637465/36, 10242649868867/216)
(1214235971/3025, 41911499602856/166375)
(8776758497/1024, 822244170719023/32768)
(15478806425/484, 1925777886914851/10648)

Commentary

Rank-10 Mordell curve found through Mestre's polynomial cube-completion construction using the integer sextuple (-55,-53,-11,17,47,55).

last edited by jesper-petersen at 2026-10-22 07:10:13 UTC · history

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