Elliptic curve isogeny class 36864.2-bd over number field Q(−11)\Q(\sqrt{-11})

• Base field: $\Q(\sqrt{-11})$
• Label: 2.0.11.1-36864.2-bd
• Conductor: 36864.2
• Rank: $0$

Base field $\Q(\sqrt{-11})$

Generator $a$, with minimal polynomial $x^{2} - x + 3$; class number $1$.

Elliptic curves in class 36864.2-bd over $\Q(\sqrt{-11})$

Isogeny class 36864.2-bd contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
36864.2-bd1	$\bigl[0$ , $a + 1$ , $0$ , $-43 a - 82$ , $208 a + 215\bigr]$
36864.2-bd2	$\bigl[0$ , $a + 1$ , $0$ , $-3 a + 3$ , $-3 a + 12\bigr]$
36864.2-bd3	$\bigl[0$ , $a + 1$ , $0$ , $-3 a - 2$ , $15\bigr]$
36864.2-bd4	$\bigl[0$ , $a + 1$ , $0$ , $37 a - 2$ , $64 a + 87\bigr]$

Rank

Rank: $0$

Isogeny matrix

$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$

Isogeny graph