curve #3149

y² + xy + y = x³ − 25608438138583363750453644220110015973x + 48850271826555999667034974046685502042020878022915152756

a-invariants: [1, 0, 1, -25608438138583363750453644220110015973, 48850271826555999667034974046685502042020878022915152756]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/4ℤ
conductor (N): 233675553798276919489685212875169920733360530
discriminant (Δ): 43901144711529974212502442412124160345561657331462507912713532669894266250553022326471074064930727642982967227500
Faltings height: 20.3994
naive height: 270.0216
primes of bad reduction: 2, 3, 5, 7, 17, 23, 29, 31, 41, 43, 59, 79, 173, 223, 257, 347, 599, 1801, 5347, 129581, 149803
regulator: 67368427010950.0241967447432735718944818702401684787386527138
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:39:38 UTC
last updated: 2026-09-26 20:39:38 UTC

Witness: 11 independent points log in to add more points →

(3714957595181452035, 2232891675453869424154155112)
(52942253926750485753565/9409, 8310030562840609480525630480819646/912673)
(-1345845383538959330, -8993194126322818500991676173)
(136594593573114679885/169, 11765792953857756289686076177004/2197)
(33525830666154009430/9, 61255029266872647391477837154/27)
(-3412633787657997006074/961, -290378335563937316532841984514086/29791)
(5734295604847363066128340/2313441, 2734109536714773679614687066086811472/3518743761)
(26073998596261383583015/15876, 6701149472546673454267582436523907/2000376)
(4835510255543659655290/841, 233536810144194765033662425506703/24389)
(488738899328903792325838/205209, 108772538266988726031103049829145046/92959677)
(4361448006818835011738153245/2690185689, 475106929099042848174688263019971056373626/139531861131363)

Commentary

Voznyy (2022). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 10). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:39:38 UTC · history