curve #4389

y² + xy = x³ − x² − 2901306793424294000920200731460x + 1902122995488681439009074759037940669119809516

a-invariants: [1, -1, 0, -2901306793424294000920200731460, 1902122995488681439009074759037940669119809516]
c-invariants: [139262726084366112044169635110089, -1643434268102220136621573212161276539356157426437]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 488442904773890620855613130
discriminant (Δ): 7629740629241212680441937013457494621781929923761202777263910285354089918948352500
Faltings height: 15.8288
naive height: 222.0417
primes of bad reduction: 2, 3, 5, 7, 13, 19, 31, 41, 67, 73, 109, 271, 1621, 2857, 3691
regulator: 149025059.895452984635971514516842452809090605877942123
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:18 UTC
last updated: 2026-10-17 10:21:18 UTC

(983411569364385, 84684471625326216)
(550624418147902, 21714854859716740689198)
(981441736076172, 107066463932136963198)
(973973256740428, 511940054815506639686)
(962655470361228, 1123525739194632701886)
(3546527149229650852/9, 6678837582989221355109685022/27)
(-1948575585918945, -12526000684111456916394)
(522407813131326210/529, 2727845788925787308480478/12167)

BASE dujella/z6old678.html#pre124 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:18 UTC · history