Elliptic curve isogeny class 169.1-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-169.1-a
• Conductor: 169.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 169.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 169.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
169.1-a1	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -2 a - 2\) , \( 3 a + 4\bigr] \)
169.1-a2	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -2 a - 2\) , \( -144 a - 206\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph