Elliptic curve isogeny class 3600.2-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-3600.2-f
• Conductor: 3600.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 3600.2-f over \(\Q(\sqrt{-2}) \)

Isogeny class 3600.2-f contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
3600.2-f1	\( \bigl[a\) , \( 0\) , \( a\) , \( -439\) , \( -6598\bigr] \)
3600.2-f2	\( \bigl[a\) , \( 0\) , \( a\) , \( 1\) , \( 2\bigr] \)
3600.2-f3	\( \bigl[a\) , \( 0\) , \( a\) , \( 141\) , \( -362\bigr] \)
3600.2-f4	\( \bigl[a\) , \( 0\) , \( a\) , \( -39\) , \( -38\bigr] \)
3600.2-f5	\( \bigl[a\) , \( 0\) , \( a\) , \( -19\) , \( 38\bigr] \)
3600.2-f6	\( \bigl[a\) , \( 0\) , \( a\) , \( -539\) , \( -4738\bigr] \)
3600.2-f7	\( \bigl[a\) , \( 0\) , \( a\) , \( -319\) , \( 2258\bigr] \)
3600.2-f8	\( \bigl[a\) , \( 0\) , \( a\) , \( -8639\) , \( -307678\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph