curve #2703

y² + xy = x³ + 39748989942083054080383x + 320437571818422693478288732687881

a-invariants: [1, 0, 0, 39748989942083054080383, 320437571818422693478288732687881]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/9ℤ
conductor (N): 21241245030798
discriminant (Δ): -4063730447065940471422153068323015658845419870708735864115382039085056
Faltings height: 12.0461
naive height: 167.7242
primes of bad reduction: 2, 3, 13, 47, 73, 97, 109, 7507
regulator: 11406.590966621937172088341457608904894634765
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:28 UTC
last updated: 2026-09-26 20:18:28 UTC

(1934039706052506/25, 85054931000790833765631/125)
(295682381436406614/30217009, 4426976963653605185075371887/166102898473)
(1413044368546244359146/4155478369, 61760011207419415193467963302309/267874602100847)

Voznyy (2021). Source: https://dujella.github.io/tors/z9old3.html (curve entry 17). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:18:29 UTC · history