Elliptic curve isogeny class 9216.2-o over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-9216.2-o
• Conductor: 9216.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-2}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).

Elliptic curves in class 9216.2-o over \(\Q(\sqrt{-2}) \)

Isogeny class 9216.2-o contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
9216.2-o1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -32\) , \( 360 a\bigr] \)
9216.2-o2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -2\) , \( 0\bigr] \)
9216.2-o3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 8\) , \( -8 a\bigr] \)
9216.2-o4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 48\) , \( 72 a\bigr] \)
9216.2-o5	\( \bigl[0\) , \( -a\) , \( 0\) , \( -560 a - 672\) , \( 8936 a + 3136\bigr] \)
9216.2-o6	\( \bigl[0\) , \( -a\) , \( 0\) , \( 560 a - 672\) , \( 8936 a - 3136\bigr] \)
9216.2-o7	\( \bigl[0\) , \( -a\) , \( 0\) , \( 128\) , \( -440 a\bigr] \)
9216.2-o8	\( \bigl[0\) , \( -a\) , \( 0\) , \( 768\) , \( 5544 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph