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

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

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

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

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

Isogeny class 9216.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9216.2-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 64 a - 63\) , \( 292 a - 37\bigr] \)
9216.2-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -64 a - 63\) , \( -292 a - 37\bigr] \)
9216.2-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 24 a + 17\) , \( -12 a - 101\bigr] \)
9216.2-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -24 a + 17\) , \( 12 a - 101\bigr] \)
9216.2-a5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a - 3\) , \( -4 a - 1\bigr] \)
9216.2-a6	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a - 3\) , \( 4 a - 1\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph