Elliptic curve isogeny class 1024.1-f over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1024.1-f
• Conductor: 1024.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1024.1-f over \(\Q(\sqrt{2}) \)

Isogeny class 1024.1-f contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
1024.1-f1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 66\) , \( 308 a + 616\bigr] \)
1024.1-f2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 66\) , \( -308 a - 616\bigr] \)
1024.1-f3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 6\) , \( 0\bigr] \)
1024.1-f4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 6\) , \( 0\bigr] \)
1024.1-f5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -44 a - 66\) , \( -196 a - 280\bigr] \)
1024.1-f6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -44 a - 66\) , \( 196 a + 280\bigr] \)
1024.1-f7	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 66\) , \( -308 a + 616\bigr] \)
1024.1-f8	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 66\) , \( 308 a - 616\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 4 & 16 \\ 16 & 1 & 8 & 4 & 2 & 8 & 16 & 4 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 8 & 2 \\ 2 & 8 & 4 & 2 & 4 & 1 & 2 & 8 \\ 4 & 16 & 8 & 4 & 8 & 2 & 1 & 16 \\ 16 & 4 & 8 & 4 & 2 & 8 & 16 & 1 \end{array}\right)\)

Isogeny graph