Elliptic curve isogeny class 41616.5-g over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.5-g
• Conductor: 41616.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 41616.5-g over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.5-g contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
41616.5-g1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -6576\) , \( -247536\bigr] \)
41616.5-g2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 17220 a - 3696\) , \( -1101912 a - 1018512\bigr] \)
41616.5-g3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -17220 a - 3696\) , \( 1101912 a - 1018512\bigr] \)
41616.5-g4	\( \bigl[a\) , \( 1\) , \( 0\) , \( 904\) , \( -17856\bigr] \)
41616.5-g5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -456\) , \( -3168\bigr] \)
41616.5-g6	\( \bigl[a\) , \( 1\) , \( 0\) , \( -136\) , \( 544\bigr] \)
41616.5-g7	\( \bigl[a\) , \( 1\) , \( 0\) , \( -6936\) , \( -223488\bigr] \)
41616.5-g8	\( \bigl[a\) , \( 1\) , \( 0\) , \( -110976\) , \( -14248080\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 2 & 8 & 4 & 8 & 2 & 4 \\ 2 & 1 & 4 & 16 & 8 & 16 & 4 & 8 \\ 2 & 4 & 1 & 16 & 8 & 16 & 4 & 8 \\ 8 & 16 & 16 & 1 & 2 & 4 & 4 & 8 \\ 4 & 8 & 8 & 2 & 1 & 2 & 2 & 4 \\ 8 & 16 & 16 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 4 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 8 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph