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curve #5861

y² = x³ − 17529404162458308126075

a-invariants: [0, 0, 0, 0, -17529404162458308126075]
c-invariants: [0, 15145405196363978220928800]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 70117616649833232504300
discriminant (Δ): -132744964445630204683509402243865795336999230000
Faltings height: 7.7209
naive height: 115.9595
primes of bad reduction: 2, 3, 5, 29, 41, 47, 113, 269
regulator: 434944587.1878313318611347837238959026027567001487326
submitted by: Maksym Voznyy
submitted at: 2026-10-25 15:34:31 UTC
last updated: 2026-10-25 15:34:31 UTC

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

(135145849/4, -1160377544557/8)
(96274077932491/1863225, 882580542646565246336/2543302125)
(1678435061429761/61528336, -25402141579218837743359/482628267584)
(23680493611/25, 3644027513373016/125)
(4861354395855571/65173329, 331714677202523905068856/526144285017)
(122712593281/4624, 10712836525908671/314432)
(1772351204479/30625, 2250303380305021558/5359375)

Commentary

Voznyy (2026), A = -50960266530, [r, s, t] = [-48, 15, 113] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 15:34:31 UTC · history

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