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curve #5783

y² = x³ − 23449377908806800972363

a-invariants: [0, 0, 0, 0, -23449377908806800972363]
c-invariants: [0, 20260262513209076040121632]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 93797511635227203889452
discriminant (Δ): -237545276101935732688153519867196397149195228208
Faltings height: 7.7694
naive height: 116.5414
primes of bad reduction: 2, 3, 17, 113, 307, 16657
regulator: 184701075.4760051491608131625626678534628283682283976
submitted by: Maksym Voznyy
submitted at: 2026-10-25 04:06:08 UTC
last updated: 2026-10-25 04:06:08 UTC

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

(2030138503/9, 91378579499630/27)
(2895361032703/28561, 4870915763676312518/4826809)
(8172732903706503841/70023424, -23364202340768630997549206897/585956012032)
(57307163872303/1329409, -364840685234089774930/1532808577)
(501325729/16, 5472502489871/64)
(8836529576641/128164, 25310623315054444993/45882712)
(5153748883716494803/166365278641, 5377297571570634772767914852/67856903486812439)

Commentary

Voznyy (2026), A = 58940494674, [r, s, t] = [-72, 54, 113] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 04:06:08 UTC · history

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