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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-32400.3-m
• 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-m over \(\Q(\sqrt{-2}) \)

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

Curve label	Weierstrass Coefficients
32400.3-m1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 30\) , \( 100\bigr] \)
32400.3-m2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -15\) , \( 28\bigr] \)
32400.3-m3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -18\) , \( 27\bigr] \)
32400.3-m4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -240\) , \( 1558\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph