curve #5521

y² = x³ − x² − 18927071065520828080x + 31620557720848313232843942400

a-invariants: [0, -1, 0, -18927071065520828080, 31620557720848313232843942400]
c-invariants: [908499411144999747856, -27320161865361946166307167746496]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 140285463605723280
discriminant (Δ): 2001149712175050916552953979254975806440075855253629440000
Faltings height: 9.8695
naive height: 144.7750
primes of bad reduction: 2, 3, 5, 13, 61, 101, 139, 199, 439, 601
regulator: 62648.250233125627849034918561854345450992043304650
submitted by: Daniel Błażewicz
submitted at: 2026-10-22 21:24:20 UTC
last updated: 2026-10-22 21:24:20 UTC

(643732360, 140368610159400)
(2205709480, 24577522692840)
(2363607025, 9434871680520)
(10441510885/4, 8214788813205/8)
(994014612218290/380689, 343855631395088726550/234885113)
(27151495700314570/13300609, 1872512715028414603515930/48507321023)

(u,v) = (14039,87361) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 6.

last edited by Daniel Błażewicz at 2026-10-22 21:24:20 UTC · history