Elliptic curve isogeny class 19602.8-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-19602.8-f
• Conductor: 19602.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 19602.8-f over \(\Q(\sqrt{-2}) \)

Isogeny class 19602.8-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
19602.8-f1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1325\) , \( 4969\bigr] \)
19602.8-f2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -65\) , \( 209\bigr] \)
19602.8-f3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -785\) , \( -8207\bigr] \)
19602.8-f4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1025\) , \( 12881\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph