curve #2081

y² + xy = x³ − 40433972577094231020x + 98266127788802232618276416400

a-invariants: [1, 0, 0, -40433972577094231020, 98266127788802232618276416400]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/4ℤ
conductor (N): 3397916818895170749870
discriminant (Δ): 59275829358511193519678529705531832109289309962649600000000
Faltings height: 10.1044
naive height: 147.0522
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 31, 401, 449, 641, 1272881
regulator: 1423234.18739605823669318716674039928493446385584448045
submitted by: Seojun Jang
submitted at: 2026-09-26 05:35:15 UTC
last updated: 2026-09-26 05:35:15 UTC

(-362579400, 335974863716820)
(3306984840, 26780271807780)
(8132750190, 554378516542530)
(37028359395/4, 5753512729540395/8)
(-306164821800/49, 112184200634108940/343)
(68175087165/16, 3698267202717795/64)
(564805090008/169, 47228177252075364/2197)
(607102583800/81, 339007592956732820/729)

Specialization of a known (\mathbb{Z}/4\mathbb{Z})-torsion family. Exact rank 8 verified by PARI/GP, with matching 2-descent upper bound.

last edited by Seojun Jang at 2026-09-26 05:35:15 UTC · history