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curve #5773

y² = x³ − 1643774670734194985319675

a-invariants: [0, 0, 0, 0, -1643774670734194985319675]
c-invariants: [0, 1420221315514344467316199200]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 6575098682936779941278700
discriminant (Δ): -1167261912639638412461877389068680964745158989630000
Faltings height: 8.4778
naive height: 125.0412
primes of bad reduction: 2, 3, 5, 19, 23, 37, 43, 59, 401
regulator: 1254236019.539553238631525292726897941055094414789832
submitted by: Maksym Voznyy
submitted at: 2026-10-25 01:42:56 UTC
last updated: 2026-10-25 01:42:56 UTC

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

(54887034667434481/384160000, -8494699912917035982994871/7529536000000)
(43380700801/196, -8322297659300449/2744)
(10775049647525299/46991025, -1039441031417030506077968/322123476375)
(55964016867881673169/55558261264, -418324984455612755998051247897/13095526646014912)
(212057913670851331/998623201, 88876004507570683544931496/31557491774801)
(2129390548034862769/17930816836, 422993437800272967511379447/2401043959241416)
(199811839, -2516677819138)

Commentary

Voznyy (2026), A = -493479658590, [r, s, t] = [37, 59, 86] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 01:42:57 UTC · history

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