curve #3147

y² + xy = x³ − 383374717580497363154900202498080x + 2879389675529515659996623813736834069739008230400

a-invariants: [1, 0, 0, -383374717580497363154900202498080, 2879389675529515659996623813736834069739008230400]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 18162299398040319190762625468282356831590
discriminant (Δ): 24542472321177320793608928536383882128172154882795763337528915081758988183148817299025921024000000
Faltings height: 17.5447
naive height: 236.6933
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 31, 41, 43, 47, 59, 79, 97, 227, 251, 313, 401, 479, 809, 1237, 5051
regulator: 555853851.825898935427041172190811701825207476127383096972249
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:39:31 UTC
last updated: 2026-09-26 20:39:31 UTC

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

(10222582257296860, 169062350496870992799220)
(1372813218934720, 1534820842725334778184160)
(10219419373199620, 169715584061380857068620)
(12096824883468160, 109268524171575891121120)
(-3348848459627990, -2031181154480665510223780)
(10733752821040392, 31826227508330885362392)
(9253378175289580, 352418791701523131041200)
(16540018728322540, 1031142223146984238763440)
(9045526143720352, 389464439425823252056192)
(-22525101328090064, -293519745534554811980048)
(107172210905879890, 34536353639961300559387090)

Commentary

Dujella - Peral (2019). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 30). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:39:31 UTC · history