Elliptic curve isogeny class 3969.3-g over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-3969.3-g
• Conductor: 3969.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 3969.3-g over \(\Q(\sqrt{2}) \)

Isogeny class 3969.3-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
3969.3-g1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -18 a - 50\) , \( 144 a + 6\bigr] \)
3969.3-g2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -153 a - 905\) , \( 7596 a + 3984\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph