Elliptic curve isogeny class 316.2-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-316.2-a
• Conductor: 316.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 316.2-a over \(\Q(\sqrt{2}) \)

Isogeny class 316.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
316.2-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 3 a - 6\) , \( -2 a + 2\bigr] \)
316.2-a2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2 a - 11\) , \( -11 a - 3\bigr] \)