Elliptic curve isogeny class 92.2-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-92.2-a
• Conductor: 92.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 92.2-a over \(\Q(\sqrt{2}) \)

Isogeny class 92.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
92.2-a1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1\) , \( -a - 2\bigr] \)
92.2-a2	\( \bigl[a\) , \( a\) , \( a\) , \( -7 a - 9\) , \( 4 a + 5\bigr] \)
92.2-a3	\( \bigl[a\) , \( a\) , \( a\) , \( -2 a - 4\) , \( -4 a - 6\bigr] \)
92.2-a4	\( \bigl[a\) , \( a\) , \( a\) , \( -37 a - 59\) , \( -188 a - 259\bigr] \)