curve #1162

y² + xy = x³ + 46524263872954400x + 13490405295879813538469375

a-invariants: [1, 0, 0, 46524263872954400, 13490405295879813538469375]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 965575150587952905
discriminant (Δ): -85065061547688494796290171100936035530110547655859375
Faltings height: 8.8378
naive height: 129.2512
primes of bad reduction: 3, 5, 7, 11, 13, 19, 23, 29, 137, 173, 347, 617
regulator: 276991.02745939693646544486082098299243157800924115
submitted by: David Renshaw
submitted at: 2026-09-23 21:38:00 UTC
last updated: 2026-09-23 21:38:00 UTC

Witness: 6 independent points log in to add more points →

(532637450, 13761333456275)
(233764106, 6094167446387)
(10876343075, 1134514175511275)
(881912531, 27210688978667)
(421169675, 10382165439050)
(-108836989621/625, 5137022971960067/15625)

Commentary

Obtained by computing a rational isogeny from curve#1112 and mapping all 6 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.

last edited by David Renshaw at 2026-09-23 21:38:00 UTC · history