curve #1145

y² = x³ + x² − 28399271396545109800x − 58236076752015354870599489152

a-invariants: [0, 1, 0, -28399271396545109800, -58236076752015354870599489152]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 892331075985258840
discriminant (Δ): 788273668101383807494994476803260459372334827613258777600
Faltings height: 9.8936
naive height: 145.9923
primes of bad reduction: 2, 3, 5, 7, 17, 19, 29, 53, 71, 73, 313, 1319
regulator: 573339.52012222038967873733037658666980912652469748
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:31 UTC
last updated: 2026-09-23 21:37:31 UTC

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

(-3102201584, -3109857582720)
(-3108901384, -2468383847280)
(-3115030309, -1444383161970)
(-3070442437, -3911106857658)
(-573587682492712/187489, 291147725115812117280/81182737)
(361022171513/16, 210217284133151403/64)

Commentary

Obtained by computing a rational isogeny from curve#1111 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 21:37:31 UTC · history