Elliptic curve isogeny class 67600.6-a over number field Q(−1)\Q(\sqrt{-1})

• Base field: $\Q(\sqrt{-1})$
• Label: 2.0.4.1-67600.6-a
• Conductor: 67600.6
• Rank: $1$

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

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

Elliptic curves in class 67600.6-a over $\Q(\sqrt{-1})$

Isogeny class 67600.6-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
67600.6-a1	$\bigl[i + 1$ , $i + 1$ , $i + 1$ , $7355 i + 12162$ , $455466 i - 474647\bigr]$
67600.6-a2	$\bigl[i + 1$ , $i + 1$ , $i + 1$ , $-5 i + 82$ , $1082 i - 1719\bigr]$
67600.6-a3	$\bigl[i + 1$ , $i + 1$ , $i + 1$ , $2535 i - 25618$ , $2731422 i - 1988155\bigr]$
67600.6-a4	$\bigl[i + 1$ , $i - 1$ , $0$ , $1714 i - 5398$ , $43016 i - 113108\bigr]$
67600.6-a5	$\bigl[i + 1$ , $i - 1$ , $0$ , $7154 i + 12642$ , $-393176 i + 473532\bigr]$
67600.6-a6	$\bigl[i + 1$ , $i - 1$ , $0$ , $8574 i + 58582$ , $5164160 i - 636316\bigr]$
67600.6-a7	$\bigl[i + 1$ , $i - 1$ , $0$ , $794 i - 1838$ , $-20520 i + 26940\bigr]$
67600.6-a8	$\bigl[i + 1$ , $i + 1$ , $i + 1$ , $12675 i - 28998$ , $1245458 i - 1781967\bigr]$

Rank

Rank: $1$

Isogeny matrix

$\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 2 & 4 & 6 & 12 \\ 3 & 1 & 12 & 4 & 6 & 12 & 2 & 4 \\ 4 & 12 & 1 & 12 & 2 & 4 & 6 & 3 \\ 12 & 4 & 12 & 1 & 6 & 3 & 2 & 4 \\ 2 & 6 & 2 & 6 & 1 & 2 & 3 & 6 \\ 4 & 12 & 4 & 3 & 2 & 1 & 6 & 12 \\ 6 & 2 & 6 & 2 & 3 & 6 & 1 & 2 \\ 12 & 4 & 3 & 4 & 6 & 12 & 2 & 1 \end{array}\right)$

Isogeny graph