Elliptic curve isogeny class 31212.4-g over number field Q(−2)\Q(\sqrt{-2})

• Base field: $\Q(\sqrt{-2})$
• Label: 2.0.8.1-31212.4-g
• Conductor: 31212.4
• Rank: $0$

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

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

Rank

Rank: $0$

Isogeny matrix

$\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)$

Isogeny graph

Elliptic curves in class 31212.4-g over $\Q(\sqrt{-2})$

Isogeny class 31212.4-g contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
31212.4-g1	$\bigl[a$ , $-a + 1$ , $a$ , $1060 a + 1052$ , $2631 a - 29033\bigr]$
31212.4-g2	$\bigl[a$ , $-a + 1$ , $0$ , $57 a + 99$ , $-1483 a - 3644\bigr]$
31212.4-g3	$\bigl[0$ , $-a - 1$ , $0$ , $282 a + 201$ , $-1305 a + 4014\bigr]$
31212.4-g4	$\bigl[0$ , $-a - 1$ , $0$ , $770 a + 353$ , $2817 a + 14508\bigr]$