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

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

Isogeny class 9216.2-u contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
9216.2-u1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -640 a + 257\) , \( -3060 a + 10437\bigr] \)
9216.2-u2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 640 a + 257\) , \( 3060 a + 10437\bigr] \)
9216.2-u3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 9\bigr] \)
9216.2-u4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 80 a + 97\) , \( 260 a - 443\bigr] \)
9216.2-u5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -80 a + 97\) , \( -260 a - 443\bigr] \)
9216.2-u6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -40 a + 17\) , \( -60 a + 165\bigr] \)
9216.2-u7	\( \bigl[0\) , \( 1\) , \( 0\) , \( 40 a + 17\) , \( 60 a + 165\bigr] \)
9216.2-u8	\( \bigl[0\) , \( 1\) , \( 0\) , \( -23\) , \( -51\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 4 & 16 & 4 & 2 & 8 & 8 \\ 16 & 1 & 4 & 4 & 16 & 8 & 2 & 8 \\ 4 & 4 & 1 & 4 & 4 & 2 & 2 & 2 \\ 16 & 4 & 4 & 1 & 16 & 8 & 2 & 8 \\ 4 & 16 & 4 & 16 & 1 & 2 & 8 & 8 \\ 2 & 8 & 2 & 8 & 2 & 1 & 4 & 4 \\ 8 & 2 & 2 & 2 & 8 & 4 & 1 & 4 \\ 8 & 8 & 2 & 8 & 8 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph