curve #3091

y² + xy = x³ − 9035181921539049674277655x + 10331090455438547826922930169998866152

a-invariants: [1, 0, 0, -9035181921539049674277655, 10331090455438547826922930169998866152]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 12619320802739804855437753113854835
discriminant (Δ): 1097313133865711912941521070855065466307654513728837769895080511232128515625
Faltings height: 13.2056
naive height: 184.0031
primes of bad reduction: 3, 5, 7, 11, 23, 47, 59, 61, 199, 2293, 7793, 12697, 14149, 4396001
regulator: 2729169860.541515073714011677527520629114220998646795720695
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:36:51 UTC
last updated: 2026-09-26 20:36:51 UTC

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

(-1192655789981, -4405732679347000322)
(-1535894425831, -4537073679302325922)
(1573951946219, 96634425169578503)
(-3046688303548, -3094860249041875702)
(659123427857, 2159199149931114113)
(-2519972651731, -4134852402819764947)
(1046346772519, 1422230454617674678)
(1504053209435011/25, 58258911526403305422326/125)
(7863439448351/4, 3263960924390316949/8)
(40714222883260469/26896, 1545195960311326667536447/4410944)

Commentary

Dujella - Kulesz (2001). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 64). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:36:51 UTC · history