Elliptic curve isogeny class 1764.1-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1764.1-a
• Conductor: 1764.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1764.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 1764.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1764.1-a1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -113\) , \( -516\bigr] \)
1764.1-a2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 7\) , \( 0\bigr] \)
1764.1-a3	\( \bigl[a\) , \( 0\) , \( a\) , \( -8\) , \( -4\bigr] \)
1764.1-a4	\( \bigl[a\) , \( 0\) , \( a\) , \( -458\) , \( -3838\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph