Elliptic curve isogeny class 29241.5-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-29241.5-a
• Conductor: 29241.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 29241.5-a over \(\Q(\sqrt{-2}) \)

Isogeny class 29241.5-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
29241.5-a1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -a + 7\) , \( -7 a - 1\bigr] \)
29241.5-a2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -46 a - 83\) , \( -212 a - 270\bigr] \)
29241.5-a3	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -691 a - 773\) , \( 11758 a + 2979\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph