Elliptic curve isogeny class 41616.2-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.2-f
• Conductor: 41616.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 41616.2-f over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.2-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41616.2-f1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 14 a - 7\) , \( -10 a - 4\bigr] \)
41616.2-f2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 46 a - 23\) , \( 150 a + 60\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph