curve #3098

y² = x³ − 2901413377029475814340493444042767x + 60112620677766830193510638729425884294374453937874

a-invariants: [0, 0, 0, -2901413377029475814340493444042767, 60112620677766830193510638729425884294374453937874]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/4ℤ
conductor (N): 10643425470423138685313977205583814561080
discriminant (Δ): 2135585449091365911375153164289023147081516734556338209789986342749841864148133028672081132100000000
Faltings height: 17.9901
naive height: 242.7651
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 71, 173, 227, 593, 41003011621931
regulator: 170788516.4407746391280732545640938323262913782795197805629
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:37:13 UTC
last updated: 2026-09-26 20:37:13 UTC

Witness: 10 independent points log in to add more points →

(9646618920345158, 5746431883465628287663500)
(22516670868944423, 2489661273896584110839880)
(-11731608543750967, 9619575762996283592576250)
(31932595197275909, 155981139952020471555390)
(32234760310611533, 284153673834028171923750)
(33132846938761673, 594386933433533810843130)
(14198652836651958, 4666790390939468272881400)
(32130881903267393, 243651479979758871850830)
(32807820520613813, 486179240037017139923310)
(11055368642843465, 5421035543526884598589062)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 27). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:37:14 UTC · history