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curve #5779

y² = x³ − 265519746664610280918075

a-invariants: [0, 0, 0, 0, -265519746664610280918075]
c-invariants: [0, 229409061118223282713216800]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 1062078986658441123672300
discriminant (Δ): -30456317895338371276116864195797908712820256830000
Faltings height: 8.1739
naive height: 121.3951
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 31, 59, 157
regulator: 85775775.43378605742997169482515670892332518401193340
submitted by: Maksym Voznyy
submitted at: 2026-10-25 03:08:46 UTC
last updated: 2026-10-25 03:08:46 UTC

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

(7277716946278787089/46074622500, 18960349663518001570708057063/9889917719625000)
(7819179137151859/101747569, 445394584065326114918152/1026327728503)
(8954082165961/97344, -21748073927466539141/30371328)
(2419641649489/37636, 106207315624621063/7301384)
(63619713587521/850084, 307226447100619310719/783777448)
(22059855625380391/280998169, 2200885998634903800733786/4710372306947)
(111498637441/324, 37109488537281889/5832)

Commentary

Voznyy (2026), A = 198333705570, [r, s, t] = [-31, -11, 59] or [-30, -22, 59] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 03:10:04 UTC · history

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