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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-3969.3-a
• 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-a over \(\Q(\sqrt{-2}) \)

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

Curve label	Weierstrass Coefficients
3969.3-a1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -2 a + 1\) , \( -6 a + 3\bigr] \)
3969.3-a2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -14 a - 5\) , \( 30 a - 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph