Elliptic curve isogeny class 1296.3-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-1296.3-a
• Conductor: 1296.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 1296.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 1296.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1296.3-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \)
1296.3-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 27\bigr] \)
1296.3-a3	\( \bigl[a\) , \( -1\) , \( a\) , \( -2\) , \( 5\bigr] \)
1296.3-a4	\( \bigl[a\) , \( -1\) , \( a\) , \( -32\) , \( -57\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph