Elliptic curve isogeny class 29241.8-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-29241.8-a
• Conductor: 29241.8
• Rank: \( 1 \)

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

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

Elliptic curves in class 29241.8-a over \(\Q(\sqrt{-2}) \)

Isogeny class 29241.8-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
29241.8-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 76\) , \( -790\bigr] \)
29241.8-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 20\bigr] \)
29241.8-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -59\) , \( -142\bigr] \)
29241.8-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -914\) , \( -10402\bigr] \)

Rank

Rank: \( 1 \)

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