curve #3028

y² = x³ + x² − 453220454411081041475408053976625x + 3713747448382841638829425541194406169971714250000

a-invariants: [0, 1, 0, -453220454411081041475408053976625, 3713747448382841638829425541194406169971714250000]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 31602563084617300276824095632860
discriminant (Δ): 67008919404042181171177088715917552997924897283354170042932893816038021962155357655250000
Faltings height: 17.1042
naive height: 237.1954
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 29, 37, 79, 109, 127, 233, 3613, 6659, 3477917
regulator: 34331805.7328147433758740668499614526968975760832394168
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:33:59 UTC
last updated: 2026-09-26 20:33:59 UTC

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

(7897185698712315, 791892431774850716925615)
(-8585429915368875, 2640456633311322595662375)
(12291329513849820, 25341040176735910770)
(1757983318732800, 1709510604433197899787300)
(12292093458085875, 172387650860123180625)
(10443296941646145, 345836990554602929727345)
(-10358652366744495, 2701295946670331624909295)
(1355808910864875, 1761181248419137157468625)

Commentary

Dujella - Peral - Tadic (2019). Source: https://dujella.github.io/tors/z6old678.html (curve entry 27). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:33:59 UTC · history