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

• Base field: $\Q(\sqrt{-1})$
• Label: 2.0.4.1-16200.2-a
• 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-a over $\Q(\sqrt{-1})$

Isogeny class 16200.2-a contains 10 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
16200.2-a1	$\bigl[i + 1$ , $i$ , $0$ , $-270 i - 390$ , $2944 i + 2592\bigr]$
16200.2-a2	$\bigl[i + 1$ , $i$ , $0$ , $270 i - 390$ , $2944 i - 2592\bigr]$
16200.2-a3	$\bigl[i + 1$ , $i$ , $0$ , $-30$ , $100 i\bigr]$
16200.2-a4	$\bigl[i + 1$ , $i$ , $0$ , $540 i - 300$ , $-980 i - 5940\bigr]$
16200.2-a5	$\bigl[i + 1$ , $i$ , $0$ , $-540 i - 300$ , $-980 i + 5940\bigr]$
16200.2-a6	$\bigl[i + 1$ , $i$ , $0$ , $15$ , $28 i\bigr]$
16200.2-a7	$\bigl[0$ , $0$ , $0$ , $-18$ , $-27\bigr]$
16200.2-a8	$\bigl[i + 1$ , $i$ , $0$ , $240$ , $1558 i\bigr]$
16200.2-a9	$\bigl[i + 1$ , $i$ , $0$ , $4320 i - 6240$ , $197524 i - 158652\bigr]$
16200.2-a10	$\bigl[i + 1$ , $i$ , $0$ , $-4320 i - 6240$ , $197524 i + 158652\bigr]$

Rank

Rank: $1$

Isogeny matrix

$\left(\begin{array}{rrrrrrrrrr} 1 & 4 & 2 & 8 & 2 & 4 & 8 & 8 & 8 & 2 \\ 4 & 1 & 2 & 2 & 8 & 4 & 8 & 8 & 2 & 8 \\ 2 & 2 & 1 & 4 & 4 & 2 & 4 & 4 & 4 & 4 \\ 8 & 2 & 4 & 1 & 16 & 8 & 16 & 16 & 4 & 16 \\ 2 & 8 & 4 & 16 & 1 & 8 & 16 & 16 & 16 & 4 \\ 4 & 4 & 2 & 8 & 8 & 1 & 2 & 2 & 8 & 8 \\ 8 & 8 & 4 & 16 & 16 & 2 & 1 & 4 & 16 & 16 \\ 8 & 8 & 4 & 16 & 16 & 2 & 4 & 1 & 16 & 16 \\ 8 & 2 & 4 & 4 & 16 & 8 & 16 & 16 & 1 & 16 \\ 2 & 8 & 4 & 16 & 4 & 8 & 16 & 16 & 16 & 1 \end{array}\right)$

Isogeny graph