curve #5571

y² + xy = x³ − 38926999412251356300944x + 2896741268337769706721498362682864

a-invariants: [1, 0, 0, -38926999412251356300944, 2896741268337769706721498362682864]
c-invariants: [1868495971788065102445313, -2502784455846635770565056683011662465]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 42251843091178784598738
discriminant (Δ): 150177862148777673133007722448497332252475108204021368305794185022224
Faltings height: 11.8681
naive height: 167.6615
primes of bad reduction: 2, 3, 7, 31, 47, 61, 223, 263, 271, 823, 865321
regulator: 3800545.321638114221270356940671742495347982028247999
submitted by: Daniel Błażewicz
submitted at: 2026-10-23 13:27:31 UTC
last updated: 2026-10-23 13:27:31 UTC

(-90213689810, 75327891998346382)
(-6902806938, 56259384179226294)
(129115667010, 4808718847216602)
(896592416014, 829906758300427972)
(2369859756906, 3635976696938916882)
(7165911644854/81, 8788856879370250756/729)
(113002941141737704/635209, 20261900168466236935861196/506261573)

(u,v) = (324911,1190232) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.

last edited by Daniel Błażewicz at 2026-10-23 13:27:31 UTC · history