curve #3033

y² + y = x³ + x² − 572802599624085654667204322992360x + 5277993800788102208540934781543522853711433047164

a-invariants: [0, 1, 1, -572802599624085654667204322992360, 5277993800788102208540934781543522853711433047164]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/5ℤ
conductor (N): 12162741732981505634646926333085
discriminant (Δ): -6276999389525198150292437288436716172134508313702541801423357921959469631161448729511210341796875
Faltings height: 17.5514
naive height: 237.8984
primes of bad reduction: 3, 5, 7, 11, 13, 41, 53, 59, 79, 383, 208818294867814661
regulator: 27009174.4520971544696180490494615379011395167899902511
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:10 UTC
last updated: 2026-09-26 20:34:10 UTC

Witness: 8 independent points log in to add more points →

(13539127696772711, 67649036229802681341187)
(5519370865025336, 1511496915505795364744812)
(-1818541906127914, 2512696806602195467066312)
(12104774610988001, 343520619135864160480717)
(13085077793712386, 152461708305693327185287)
(25259822490750881, 2631795889070645474955277)
(14601808494860711, 165325664289917783157187)
(13455153700979036, 82361590308906363191587)

Commentary

Dujella - Lecacheux - Petricevic (2021). Source: https://dujella.github.io/tors/z5old678.html (curve entry 11). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:34:10 UTC · history