Elliptic curve isogeny class 9984.2-b over number field Q(−3)\Q(\sqrt{-3})

• Base field: $\Q(\sqrt{-3})$
• Label: 2.0.3.1-9984.2-b
• Conductor: 9984.2
• Rank: $1$

Base field $\Q(\sqrt{-3})$

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

Rank

Rank: $1$

Isogeny matrix

$\left(\begin{array}{rrrrrr} 1 & 4 & 4 & 8 & 2 & 8 \\ 4 & 1 & 4 & 2 & 2 & 2 \\ 4 & 4 & 1 & 8 & 2 & 8 \\ 8 & 2 & 8 & 1 & 4 & 4 \\ 2 & 2 & 2 & 4 & 1 & 4 \\ 8 & 2 & 8 & 4 & 4 & 1 \end{array}\right)$

Isogeny graph

Elliptic curves in class 9984.2-b over $\Q(\sqrt{-3})$

Isogeny class 9984.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9984.2-b1	$\bigl[0$ , $-a + 1$ , $0$ , $42 a + 939$ , $-13529 a + 7591\bigr]$
9984.2-b2	$\bigl[0$ , $-a + 1$ , $0$ , $2 a - 1$ , $-9 a + 3\bigr]$
9984.2-b3	$\bigl[0$ , $-a + 1$ , $0$ , $-38 a + 139$ , $215 a + 167\bigr]$
9984.2-b4	$\bigl[0$ , $-a + 1$ , $0$ , $-3 a - 1$ , $-2 a - 1\bigr]$
9984.2-b5	$\bigl[0$ , $-a + 1$ , $0$ , $2 a + 59$ , $-225 a + 135\bigr]$
9984.2-b6	$\bigl[0$ , $-a + 1$ , $0$ , $82 a - 61$ , $-241 a + 47\bigr]$