Elliptic curve isogeny class 55552.2-e over number field Q(−3)\Q(\sqrt{-3})

• Base field: $\Q(\sqrt{-3})$
• Label: 2.0.3.1-55552.2-e
• Conductor: 55552.2
• Rank: $1$

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

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

Rank

Rank: $1$

Isogeny matrix

$\left(\begin{array}{rrrrr} 1 & 3 & 3 & 3 & 3 \\ 3 & 1 & 9 & 9 & 9 \\ 3 & 9 & 1 & 9 & 9 \\ 3 & 9 & 9 & 1 & 9 \\ 3 & 9 & 9 & 9 & 1 \end{array}\right)$

Isogeny graph

Elliptic curves in class 55552.2-e over $\Q(\sqrt{-3})$

Isogeny class 55552.2-e contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
55552.2-e1	$\bigl[0$ , $-1$ , $0$ , $-139 a + 422$ , $3273 a + 190\bigr]$
55552.2-e2	$\bigl[0$ , $-1$ , $0$ , $1301 a - 3258$ , $-19159 a - 21954\bigr]$
55552.2-e3	$\bigl[0$ , $-1$ , $0$ , $101 a + 22$ , $-167 a + 510\bigr]$
55552.2-e4	$\bigl[0$ , $-1$ , $0$ , $-7979 a + 422$ , $305673 a - 171170\bigr]$
55552.2-e5	$\bigl[0$ , $-1$ , $0$ , $-13179 a + 36502$ , $2179225 a + 46814\bigr]$