curve #3103

y² = x³ + x² − 110907705551334904313030730340x + 14209200477703631816262785853057594833158688

a-invariants: [0, 1, 0, -110907705551334904313030730340, 14209200477703631816262785853057594833158688]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/4ℤ
conductor (N): 145656839839920898983128703362734440
discriminant (Δ): 88835400640482808517413128935824815772867139230167026631153435878271927187778220960000
Faltings height: 15.4368
naive height: 212.2491
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 47, 53, 149, 461, 7129, 100384235521
regulator: 1535175225.914308048988931790517428157111542017473658541936
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:37:25 UTC
last updated: 2026-09-26 20:37:25 UTC

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

(7487174762891, 3657763636175745336240)
(66153929096078, 2676141294657606477702)
(-13347561044449, 3960703205400133720710)
(181718532279926, 236339226851902975710)
(129109836878846, 1429021260168509457450)
(145247830530626, 1079064641655703813110)
(188267470213646, 44272970533769727750)
(-199927079309134, 5328358228788194289690)
(68197418265338, 2638704196747226745522)
(196182979265096, 40497737305751926200)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 23). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:37:25 UTC · history