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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-9216.2-w
• 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-w over \(\Q(\sqrt{-2}) \)

Isogeny class 9216.2-w contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9216.2-w1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -32 a + 1\) , \( -68 a + 85\bigr] \)
9216.2-w2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -12 a + 21\) , \( -24 a - 39\bigr] \)
9216.2-w3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 a + 1\) , \( -2 a + 1\bigr] \)
9216.2-w4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a - 2\) , \( 2 a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph