curve #5524

y² + xy = x³ − 1641229088708526250x + 762380484302045179492302500

a-invariants: [1, 0, 0, -1641229088708526250, 762380484302045179492302500]
c-invariants: [78778996258009260001, -658696738555135529468363250001]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 852132368352046470
discriminant (Δ): 31846827818354933709094631265287454678763859660021760000
Faltings height: 9.4000
naive height: 137.4395
primes of bad reduction: 2, 3, 5, 13, 37, 71, 101, 107, 587, 131111
regulator: 47034.498281984064643505618883156482918896390782366
submitted by: Daniel Błażewicz
submitted at: 2026-10-22 21:27:28 UTC
last updated: 2026-10-22 21:27:28 UTC

(13966257140, 1643783615865350)
(-88685740031560/218089, 3759479194914841112470/101847563)
(109349230292/121, 5525854184408626/1331)
(6726331674410/11449, 1184424839814105550/1225043)
(22704701159780/7921, 98716961409563516230/704969)
(286818482903540/508369, 1449791780673454843030/362467097)

(u,v) = (34151,96960) 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 21:27:28 UTC · history