Elliptic curve isogeny class 41616.9-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.9-c
• Conductor: 41616.9
• Rank: \( 1 \)

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

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

Elliptic curves in class 41616.9-c over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.9-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41616.9-c1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -22 a - 50\) , \( 128 a + 107\bigr] \)
41616.9-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -23 a + 47\) , \( -50 a - 209\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph