Elliptic curve isogeny class 16384.1-a over number field Q(−2)\Q(\sqrt{-2})

• Base field: $\Q(\sqrt{-2})$
• Label: 2.0.8.1-16384.1-a
• Conductor: 16384.1
• Rank: $2$

Base field $\Q(\sqrt{-2})$

Generator $a$, with minimal polynomial $x^{2} + 2$; class number $1$.

Rank

Rank: $2$

Isogeny matrix

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

Elliptic curves in class 16384.1-a over $\Q(\sqrt{-2})$

Isogeny class 16384.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16384.1-a1	$\bigl[0$ , $0$ , $0$ , $2 a$ , $0\bigr]$
16384.1-a2	$\bigl[0$ , $0$ , $0$ , $-2 a$ , $0\bigr]$