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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.7-b
• Conductor: 41616.7
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
41616.7-b1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -40 a + 19\) , \( 89 a - 166\bigr] \)
41616.7-b2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 3 a - 56\) , \( -2 a + 193\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph