Elliptic curve isogeny class 3528.2-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-3528.2-a
• Conductor: 3528.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 3528.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 3528.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3528.2-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \)
3528.2-a2	\( \bigl[a\) , \( 1\) , \( a\) , \( -97\) , \( 29\bigr] \)
3528.2-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( -62\) , \( -202\bigr] \)
3528.2-a4	\( \bigl[a\) , \( 1\) , \( a\) , \( -1007\) , \( -12487\bigr] \)

Rank

Rank: \( 0 \)

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