curve #3073

y² = x³ − x² − 63101137631999143241257265x + 191341468112384598938400129107933347137

a-invariants: [0, -1, 0, -63101137631999143241257265, 191341468112384598938400129107933347137]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/4ℤ
conductor (N): 25329868104284268623200965514080
discriminant (Δ): 264010719034448686848336190538563616324955649278495244881276251650449600000000
Faltings height: 13.6763
naive height: 189.8339
primes of bad reduction: 2, 3, 5, 11, 13, 23, 29, 31, 41, 43, 53, 59, 67, 83, 582150181451
regulator: 397881275.61053330737815647226735091379561742342369116155
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:35:58 UTC
last updated: 2026-09-26 20:35:58 UTC

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

(4046893030649, 1501755661273561980)
(-207449533823, 14297651626859442556)
(-325725187176, 14555429899070970195)
(3981277360529, 1795508458242684900)
(5946541104089, 5136700039591756740)
(809049061709929, 23011314698170406393500)
(37491752675879, 224778020445313965300)
(43609403464053929, 9106892534905172551945500)
(-2910887979271, 18717827725126791300)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 43). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:35:58 UTC · history