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

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

Isogeny class 41616.5-v contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
41616.5-v1	\( \bigl[a\) , \( 0\) , \( a\) , \( -100 a + 351\) , \( 1692 a + 1490\bigr] \)
41616.5-v2	\( \bigl[a\) , \( 0\) , \( a\) , \( 100 a + 351\) , \( -1692 a + 1490\bigr] \)
41616.5-v3	\( \bigl[a\) , \( 0\) , \( a\) , \( 31\) , \( 50\bigr] \)
41616.5-v4	\( \bigl[a\) , \( 0\) , \( a\) , \( -9\) , \( 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph