curve #2926

y² = x³ + x² − 4123297792196061474931925360x + 83669201239698270468036960902365235322900

a-invariants: [0, 1, 0, -4123297792196061474931925360, 83669201239698270468036960902365235322900]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 359205984868965105754362480
discriminant (Δ): 1462334959627307100638822367377826970284472869262436134127789989986463654401600000000
Faltings height: 14.8675
naive height: 202.3730
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 43, 47, 79, 83, 163, 167, 293, 419, 1777
regulator: 449342.1581512648361958399956174255556002247759302334
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:39 UTC
last updated: 2026-09-26 20:28:39 UTC

Witness: 7 independent points log in to add more points →

(7863233370580, 227448753821255216250)
(-53445032541830, 389075979691181365440)
(-19322069176277, 395127953404498572804)
(11983227764095, 189682759293189672510)
(21829310745364, 63737975851715924730)
(-10451426017445, 354431812482973625400)
(-69898364293205, 174278079763945040940)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 65). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:40 UTC · history