Elliptic curve isogeny class 3600.1-g over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-3600.1-g
• Conductor: 3600.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3600.1-g over \(\Q(\sqrt{2}) \)

Isogeny class 3600.1-g contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
3600.1-g1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -54\) , \( 510\bigr] \)
3600.1-g2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 6\) , \( -18\bigr] \)
3600.1-g3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1814\) , \( 4350\bigr] \)
3600.1-g4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -274\) , \( 1550\bigr] \)
3600.1-g5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -74\) , \( -210\bigr] \)
3600.1-g6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1334\) , \( 18942\bigr] \)
3600.1-g7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1154\) , \( -14898\bigr] \)
3600.1-g8	\( \bigl[a\) , \( -1\) , \( 0\) , \( -21334\) , \( 1202942\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph