Elliptic curve isogeny class 42050.5-a over number field Q(−1)\Q(\sqrt{-1})

• Base field: $\Q(\sqrt{-1})$
• Label: 2.0.4.1-42050.5-a
• Conductor: 42050.5
• Rank: $1$

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

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

Elliptic curves in class 42050.5-a over $\Q(\sqrt{-1})$

Isogeny class 42050.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
42050.5-a1	$\bigl[i$ , $1$ , $0$ , $10$ , $700\bigr]$
42050.5-a2	$\bigl[i$ , $1$ , $0$ , $-70$ , $204\bigr]$
42050.5-a3	$\bigl[i$ , $1$ , $0$ , $1020 i + 650$ , $-844 i + 16092\bigr]$
42050.5-a4	$\bigl[i$ , $1$ , $0$ , $-1020 i + 650$ , $844 i + 16092\bigr]$

Rank

Rank: $1$

Isogeny matrix

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

Isogeny graph