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

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

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

Curve label	Weierstrass Coefficients
9216.2-k1	\( \bigl[0\) , \( a\) , \( 0\) , \( 40 a - 176\) , \( -368 a + 832\bigr] \)
9216.2-k2	\( \bigl[0\) , \( a\) , \( 0\) , \( -40 a - 176\) , \( -368 a - 832\bigr] \)
9216.2-k3	\( \bigl[0\) , \( a\) , \( 0\) , \( -16\) , \( -16 a\bigr] \)
9216.2-k4	\( \bigl[0\) , \( a\) , \( 0\) , \( 4\) , \( 0\bigr] \)
9216.2-k5	\( \bigl[0\) , \( a\) , \( 0\) , \( 8\) , \( -4 a\bigr] \)
9216.2-k6	\( \bigl[0\) , \( a\) , \( 0\) , \( 64\) , \( -120 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph