Elliptic curve isogeny class 5400.3-a over number field Q(−2)\Q(\sqrt{-2})

• Base field: $\Q(\sqrt{-2})$
• Label: 2.0.8.1-5400.3-a
• Conductor: 5400.3
• Rank: $1$

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

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

Rank

Rank: $1$

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 5400.3-a over $\Q(\sqrt{-2})$

Isogeny class 5400.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
5400.3-a1	$\bigl[a$ , $-a$ , $0$ , $-12 a - 9$ , $29 a - 10\bigr]$
5400.3-a2	$\bigl[0$ , $-a + 1$ , $0$ , $-9$ , $-3 a + 12\bigr]$