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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-9216.2-p
• Conductor: 9216.2
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
9216.2-p1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 100 a - 28\) , \( -396 a - 288\bigr] \)
9216.2-p2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -100 a - 28\) , \( -396 a + 288\bigr] \)
9216.2-p3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 12\) , \( -36 a\bigr] \)
9216.2-p4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 17\) , \( -26 a\bigr] \)

Rank

Rank: \( 1 \)

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