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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-32400.3-n
• Conductor: 32400.3
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

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

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

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

Curve label	Weierstrass Coefficients
32400.3-n1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -30\) , \( 90\bigr] \)
32400.3-n2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 210\) , \( -422\bigr] \)
32400.3-n3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -870\) , \( -2150\bigr] \)
32400.3-n4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -510\) , \( 4698\bigr] \)