Elliptic curve isogeny class 41616.8-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.8-d
• Conductor: 41616.8
• Rank: \( 2 \)

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

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

Elliptic curves in class 41616.8-d over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.8-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
41616.8-d1	\( \bigl[a\) , \( -a\) , \( 0\) , \( -12 a - 6\) , \( 20 a - 18\bigr] \)
41616.8-d2	\( \bigl[a\) , \( -a\) , \( 0\) , \( -272 a - 226\) , \( -2444 a - 178\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph