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curve #5361

y² = x³ + 47700681504129

a-invariants: [0, 0, 0, 0, 47700681504129]
c-invariants: [0, -41213388819567456]
rank (lower bound): ≥ 9
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 27304260191500253734128583692
discriminant (Δ): -982953366894009134428629012912
Faltings height: 4.4339
naive height: 76.5151
primes of bad reduction: 2, 3, 10513, 504144937
regulator: 38788698796.761407536646237839523596258000366699565007586
submitted by: Maksym Voznyy
submitted at: 2026-10-21 20:18:30 UTC
last updated: 2026-10-21 20:18:30 UTC

Witness: 9 independent points log in to add more points →

(1880856541033/104325796, 7798485961908848341/1065583680344)
(-2941582838797847/82855319716, -40975572169822361573269/23849572358971736)
(27214050/1849, 567175611111/79507)
(1792498918611/13402921, -2423683308034461810/49068093781)
(663846/25, 1018761231/125)
(-15853722321/786769, 4387052727563280/697864103)
(184298356/15625, 13719457565371/1953125)
(45504150/361, 310590200343/6859)
(-29869114368/1555009, -12357625407166497/1939096223)

Commentary

Reynya - Voznyy (2026)

last edited by Maksym Voznyy at 2026-10-21 20:18:30 UTC · history

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