Elliptic curve isogeny class 1922.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1922.1-c
• Conductor: 1922.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1922.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 1922.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1922.1-c1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 1\bigr] \)
1922.1-c2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 165 a - 111\) , \( 818 a - 1207\bigr] \)
1922.1-c3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)
1922.1-c4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -21\) , \( 41\bigr] \)
1922.1-c5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -165 a - 111\) , \( -818 a - 1207\bigr] \)
1922.1-c6	\( \bigl[1\) , \( -1\) , \( 1\) , \( -331\) , \( 2397\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph