Elliptic curve isogeny class 45000.3-o over number field Q(−1)\Q(\sqrt{-1})

• Base field: $\Q(\sqrt{-1})$
• Label: 2.0.4.1-45000.3-o
• Conductor: 45000.3
• Rank: $0$

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

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

Rank

Rank: $0$

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

Elliptic curves in class 45000.3-o over $\Q(\sqrt{-1})$

Isogeny class 45000.3-o contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
45000.3-o1	$\bigl[i + 1$ , $-i$ , $i + 1$ , $-i - 23$ , $23 i\bigr]$
45000.3-o2	$\bigl[i + 1$ , $-i$ , $i + 1$ , $-i + 102$ , $148 i\bigr]$
45000.3-o3	$\bigl[i + 1$ , $-i$ , $i + 1$ , $-i + 852$ , $-9602 i\bigr]$
45000.3-o4	$\bigl[i + 1$ , $-i$ , $i + 1$ , $-i + 1352$ , $18898 i\bigr]$