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

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

Isogeny class 9216.2-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
9216.2-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -44 a + 213\) , \( 832 a + 455\bigr] \)
9216.2-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 44 a + 213\) , \( -832 a + 455\bigr] \)
9216.2-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a + 3\) , \( 2 a - 7\bigr] \)
9216.2-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a + 3\) , \( -2 a - 7\bigr] \)
9216.2-c5	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 a + 13\) , \( -16 a - 1\bigr] \)
9216.2-c6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a + 13\) , \( 16 a - 1\bigr] \)
9216.2-c7	\( \bigl[0\) , \( -1\) , \( 0\) , \( 36 a - 27\) , \( 96 a + 87\bigr] \)
9216.2-c8	\( \bigl[0\) , \( -1\) , \( 0\) , \( -36 a - 27\) , \( -96 a + 87\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 12 & 4 & 12 & 6 & 2 & 4 & 3 \\ 12 & 1 & 12 & 4 & 2 & 6 & 3 & 4 \\ 4 & 12 & 1 & 3 & 6 & 2 & 4 & 12 \\ 12 & 4 & 3 & 1 & 2 & 6 & 12 & 4 \\ 6 & 2 & 6 & 2 & 1 & 3 & 6 & 2 \\ 2 & 6 & 2 & 6 & 3 & 1 & 2 & 6 \\ 4 & 3 & 4 & 12 & 6 & 2 & 1 & 12 \\ 3 & 4 & 12 & 4 & 2 & 6 & 12 & 1 \end{array}\right)\)

Isogeny graph