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

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

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

Curve label	Weierstrass Coefficients
9216.2-t1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 8 a - 9\) , \( 17 a + 2\bigr] \)
9216.2-t2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 44\) , \( 60 a - 96\bigr] \)
9216.2-t3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 4\) , \( 0\bigr] \)
9216.2-t4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -8 a + 16\) , \( -16 a - 16\bigr] \)

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