Elliptic curve isogeny class 29241.9-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-29241.9-a
• Conductor: 29241.9
• Rank: \( 1 \)

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

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

Elliptic curves in class 29241.9-a over \(\Q(\sqrt{-2}) \)

Isogeny class 29241.9-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
29241.9-a1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 2146 a + 2785\) , \( -23041 a + 96228\bigr] \)
29241.9-a2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 121 a + 400\) , \( 1736 a + 576\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph