curve #3154

y² + xy = x³ + x² − 38571071591410009853076102166713x + 92080247327630793222539238086556781671613495893

a-invariants: [1, 1, 0, -38571071591410009853076102166713, 92080247327630793222539238086556781671613495893]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6079407764174347190838952870883489846790
discriminant (Δ): 9698286074605509032414188770020665372548407130681321736313578084564998993312227778981960051600
Faltings height: 16.9340
naive height: 229.8038
primes of bad reduction: 2, 3, 5, 17, 29, 31, 47, 83, 109, 157, 163, 173, 239, 661, 1451, 6451, 9521, 500287
regulator: 127919889148.677772355198488538557524170790221187905031662382
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:39:53 UTC
last updated: 2026-09-26 20:39:53 UTC

Witness: 11 independent points log in to add more points →

(2805623144749566, 77128970464110215021391)
(3323630218922198, 24470566189147100521855)
(481068969899454, 271359971324787336123123)
(3761147067952439, 14656590861460502403363)
(6461205431245551/4, 1474931527803400182716799/8)
(3305642756265693, 26452373852286949182705)
(681748693262835946/25, 549425082947725528720834391/125)
(12874806296226731/4, 285920811786033964445309/8)
(39872343899331846, 7870410730613798345082303)
(26762119889759109, 4269328140533857610422338)
(12935850320720133466/3481, 1636391970361286513248038257/205379)

Commentary

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 39). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:39:53 UTC · history