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

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

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

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

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

Isogeny class 41616.5-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
41616.5-b1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 72\) , \( 36\bigr] \)
41616.5-b2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -18\) , \( 0\bigr] \)
41616.5-b3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -188\) , \( -1020\bigr] \)
41616.5-b4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -30 a + 792\) , \( 6036 a + 828\bigr] \)
41616.5-b5	\( \bigl[a\) , \( 1\) , \( 0\) , \( 30 a + 792\) , \( -6036 a + 828\bigr] \)
41616.5-b6	\( \bigl[a\) , \( 1\) , \( 0\) , \( -13\) , \( 16\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph