Elliptic curve isogeny class 1026.1-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-1026.1-a
• Conductor: 1026.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1026.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 1026.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
1026.1-a1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -235 a - 340\) , \( -2616 a - 1480\bigr] \)
1026.1-a2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)
1026.1-a3	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -5 a - 5\) , \( -a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph