Elliptic curve isogeny class 9522.2-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-9522.2-e
• Conductor: 9522.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 9522.2-e over \(\Q(\sqrt{-2}) \)

Isogeny class 9522.2-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
9522.2-e1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( 82\bigr] \)
9522.2-e2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 189\) , \( 190\bigr] \)
9522.2-e3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -771\) , \( 1342\bigr] \)
9522.2-e4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -576\) , \( 5266\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph