Elliptic curve isogeny class 322.3-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-322.3-a
• Conductor: 322.3
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 322.3-a over \(\Q(\sqrt{2}) \)

Isogeny class 322.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
322.3-a1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -19 a - 15\) , \( 49 a - 208\bigr] \)
322.3-a2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a\) , \( -3 a + 6\bigr] \)