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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-9216.2-s
• Conductor: 9216.2
• Rank: \( 0 \)

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

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

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

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

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

Curve label	Weierstrass Coefficients
9216.2-s1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 40 a - 176\) , \( 368 a - 832\bigr] \)
9216.2-s2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -40 a - 176\) , \( 368 a + 832\bigr] \)
9216.2-s3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -16\) , \( 16 a\bigr] \)
9216.2-s4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 4\) , \( 0\bigr] \)
9216.2-s5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 8\) , \( 4 a\bigr] \)
9216.2-s6	\( \bigl[0\) , \( -a\) , \( 0\) , \( 64\) , \( 120 a\bigr] \)