curve #3092

y² + xy + y = x³ − 11303247961627273626159263x + 14522016996201389320585192293938087138

a-invariants: [1, 0, 1, -11303247961627273626159263, 14522016996201389320585192293938087138]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1193624120238989081597757186113730
discriminant (Δ): 1321021136520345016858053133819365485120133439119067101066260363597162250000
Faltings height: 13.2405
naive height: 184.6750
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 29, 53, 107, 127, 401, 743, 1291, 55501, 227989
regulator: 323188815.3406379418194566418951504842722419729377967011091
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:36:55 UTC
last updated: 2026-09-26 20:36:55 UTC

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

(1455915619779, 1073093834384542660)
(682222211619, 2669871361846133380)
(32349447761979, 183035874577813973860)
(27046101035599719/11881, -992766016436500162882280/1295029)
(1472388782542291/3249, 570582527806390991276900/185193)
(-1313849330901, -5206227821359807280)
(9443484246324306/4489, 69501674655672127607155/300763)
(8326153144791/4, -903905644603571095/8)
(34874428006414797219/1038361, 204954652917717149364486117440/1058089859)
(-108149668526163189/27889, -930511084858193804143840/4657463)

Commentary

Dujella - Kulesz (2005). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 78). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:36:55 UTC · history