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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.5-m
• 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-m over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.5-m contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41616.5-m1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 361 a - 544\) , \( -3708 a + 2421\bigr] \)
41616.5-m2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 121 a - 224\) , \( 1028 a - 811\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph