Elliptic curve isogeny class 9984.1-b over number field Q(−3)\Q(\sqrt{-3})

• Base field: $\Q(\sqrt{-3})$
• Label: 2.0.3.1-9984.1-b
• Conductor: 9984.1
• 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 9984.1-b over $\Q(\sqrt{-3})$

Isogeny class 9984.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9984.1-b1	$\bigl[0$ , $a$ , $0$ , $-42 a + 981$ , $13529 a - 5938\bigr]$
9984.1-b2	$\bigl[0$ , $a$ , $0$ , $-2 a + 1$ , $9 a - 6\bigr]$
9984.1-b3	$\bigl[0$ , $a$ , $0$ , $38 a + 101$ , $-215 a + 382\bigr]$
9984.1-b4	$\bigl[0$ , $a$ , $0$ , $3 a - 4$ , $2 a - 3\bigr]$
9984.1-b5	$\bigl[0$ , $a$ , $0$ , $-2 a + 61$ , $225 a - 90\bigr]$
9984.1-b6	$\bigl[0$ , $a$ , $0$ , $-82 a + 21$ , $241 a - 194\bigr]$