Elliptic curve isogeny class 9216.3-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-9216.3-e
• Conductor: 9216.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 9216.3-e over \(\Q(\sqrt{-2}) \)

Isogeny class 9216.3-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9216.3-e1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 5\) , \( 3 a + 4\bigr] \)
9216.3-e2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 28 a - 70\) , \( -172 a + 200\bigr] \)
9216.3-e3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a + 10\) , \( -4 a + 32\bigr] \)
9216.3-e4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 148 a + 170\) , \( -284 a + 1656\bigr] \)

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