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curve #5778

y² = x³ − 10178534735684846916363

a-invariants: [0, 0, 0, 0, -10178534735684846916363]
c-invariants: [0, 8794254011631707735737632]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 13571379647579795888484
discriminant (Δ): -44756309965914574478576302767751545084207836208
Faltings height: 7.6303
naive height: 114.8723
primes of bad reduction: 2, 3, 11, 43, 47, 59, 113, 131
regulator: 48407419.88483480230572146590751632834520963680303500
submitted by: Maksym Voznyy
submitted at: 2026-10-25 02:07:45 UTC
last updated: 2026-10-25 02:07:45 UTC

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

(24430063, -66347647822)
(20378192614709161/594969664, -2513710158140635203717397/14512500044288)
(114957634055922777/2570287204, 36692783142581417513624451/130308420668392)
(1113546963, -37158759397728)
(1099535333856579921/343435024, -1152958612445359598294216793/6364537864768)
(996913798819/39601, -598868802176995864/7880599)
(818935265507671/20403289, -21512063194978137343642/92161656413)

Commentary

Voznyy (2026), A = 38832088174, [r, s, t] = [-43, 47, 59] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 02:07:45 UTC · history

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