curve #3343

y² = x³ + x² − 460041694x + 3771522490376

a-invariants: [0, 1, 0, -460041694, 3771522490376]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 100389817248
discriminant (Δ): 85765391996521936805112384
Faltings height: 3.8038
naive height: 71.4541
primes of bad reduction: 2, 3, 7, 19, 37, 41, 71, 73
regulator: 10290.0517528930204737439952204345349568337284135
submitted by: David Renshaw
submitted at: 2026-09-26 21:05:19 UTC
last updated: 2026-09-26 21:05:19 UTC

Witness: 5 independent points log in to add more points →

(226553/16, -19894635/64)
(15014, -499140)
(2999702/169, -2405006700/2197)
(35558, 5689740)
(367286/25, -53624916/125)

Commentary

Rationally isogenous to curve#1642 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 5 carries over. Torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:05:19 UTC · history