curve #2915

y² + xy + y = x³ − 41061306153084043265108x + 3185903340945571830683716617085118

a-invariants: [1, 0, 1, -41061306153084043265108, 3185903340945571830683716617085118]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 320501413516974788372430
discriminant (Δ): 45968882461331579842597510690020998864488751106165755191215428062500
Faltings height: 11.8226
naive height: 167.8217
primes of bad reduction: 2, 3, 5, 13, 17, 19, 23, 29, 41, 101, 179, 359, 2129, 6733
regulator: 152835.0494692347155288265081305908348001599613547251
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:10 UTC
last updated: 2026-09-26 20:28:10 UTC

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

(58085745864, 31572195682253005)
(67056207819, 27092556752728645)
(-49402075188, -71371174655444750)
(102305844864, 7474867295631130)
(46255763829, 37222952221019245)
(-114023465736, -79908620275049795)
(108694207794, 2633839132323070)

Commentary

Dujella - Eroshkin (2008). Source: https://dujella.github.io/tors/z6old678.html (curve entry 136). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:11 UTC · history