Elliptic curve isogeny class 16200.2-d over number field Q(−1)\Q(\sqrt{-1})

• Base field: $\Q(\sqrt{-1})$
• Label: 2.0.4.1-16200.2-d
• Conductor: 16200.2
• Rank: $1$

Base field $\Q(\sqrt{-1})$

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

Elliptic curves in class 16200.2-d over $\Q(\sqrt{-1})$

Isogeny class 16200.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
16200.2-d1	$\bigl[i + 1$ , $i$ , $i + 1$ , $-i - 9$ , $-9 i\bigr]$
16200.2-d2	$\bigl[i + 1$ , $i$ , $i + 1$ , $-i + 36$ , $-18 i\bigr]$
16200.2-d3	$\bigl[i + 1$ , $i$ , $i + 1$ , $-i + 306$ , $2196 i\bigr]$
16200.2-d4	$\bigl[i + 1$ , $i$ , $i + 1$ , $-i + 486$ , $-3888 i\bigr]$

Rank

Rank: $1$

Isogeny matrix

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

Isogeny graph