curve #2847

y² + xy = x³ − 75532826995689993241153458590x − 5840213618603934546445210719307440984003900

a-invariants: [1, 0, 0, -75532826995689993241153458590, -5840213618603934546445210719307440984003900]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3774400763265296702670
discriminant (Δ): 12844853975180953519852403222801879684904561284319108254340330981753898623680425536000000
Faltings height: 15.6146
naive height: 211.0967
primes of bad reduction: 2, 3, 5, 11, 29, 113, 181, 277, 313, 14639, 15193
regulator: 955558.348417906455069102374657102513446612120141
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:07 UTC
last updated: 2026-09-26 20:25:07 UTC

(-207427058050208, -950044687422111532814)
(329688080136540, 2256702237605723222610)
(1770804080101511260/9, 2356434359469010158129722470/27)
(-105637632121324145/1156, -21492782850147037633254635/39304)
(-53362557561389300600/388129, -337288001548961885585058687730/241804367)

Voznyy (2022). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 74). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:07 UTC · history