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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-32400.3-d
• Conductor: 32400.3
• Rank: \( 1 \)

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

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

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

Isogeny class 32400.3-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
32400.3-d1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -180\) , \( 8100\bigr] \)
32400.3-d2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 180\) , \( -270\bigr] \)
32400.3-d3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -45\) , \( 0\bigr] \)
32400.3-d4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -450\) , \( 3888\bigr] \)
32400.3-d5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -138\) , \( 623\bigr] \)
32400.3-d6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -7200\) , \( 238788\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph