Elliptic curve isogeny class 32400.3-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-32400.3-a
• Conductor: 32400.3
• Rank: \( 2 \)

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

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

Elliptic curves in class 32400.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 32400.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
32400.3-a1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -276\) , \( -1880\bigr] \)
32400.3-a2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 24\) , \( 0\bigr] \)
32400.3-a3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -96\) , \( 144\bigr] \)
32400.3-a4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -4596\) , \( -117656\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph