Elliptic curve isogeny class 41616.7-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.7-e
• Conductor: 41616.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 41616.7-e over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.7-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41616.7-e1	\( \bigl[a\) , \( -a\) , \( 0\) , \( 107 a + 127\) , \( 155 a - 1000\bigr] \)
41616.7-e2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -14 a + 65\) , \( 137 a + 388\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph